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TI
W
I. Arithi
and more
Rule, cone
winexed.
II. Vulge
III. Deci
{'ery plain
nterest, Ai
IV. Duo(
iaeMuring
V. ACol
in the forej
A new ai
readily cal<
flalarieA, *i
The who]
Remembra
This Woi
M recommc
for private ]
A C(
THE
W
TUTOR'S ASSISTANT;
BEING A
COMPENDIUM OF ARITHMETIC,
AND
COMPLETE aUESTION-BOOK j
CONTAINING,
I. Arithmetic in whole numbers: being a brief exnlanation of all its RhIab in . n.»
«inl«d * * '^"** ''"*"' of queatlons in real Businesa, wlS» thei? iSaww!
II Vulgar Fractiona, which are treated with a great deal of plainDeaa and perapicuity.
*«rini«?n^.!i"v''''M.*^® extracUoa of the Square, Cube, and Biquadrate Roota after a
&?rS?An^il^^KR^r,r for SJSJycri^SiuJn of
TV n ^"""'*f ' and Pensions m arrears, &c., either by Simple or Compound SitereS.
«^^f^^^^^ «PP«ed 10
inThe^^^eJcfnlrTuteJ?''^"''"'' promiacuoualy arranged, for the exercise of the scholar
TO WHICH ARB ADnSD,
for private persons.
BY FRANCIS WALKINGAME,
WRITINa-MASTBR AND ACCOUNTAJn*.
TO WHICH 18 ADDED,
A COMPENDIUM OF BOGK-KEEPINgT
BY ISAAC FISHER.
MONTREAL-AKMOUll «t JIAMbav
KIKOfiTOK-RAMSAT, ARlTiuR '&
HAMlLTOlf— RA 1I8AT k M^VmUJCK,
1845.
CO.
i !.
10/
\i
■3 C <? / ^'
tf%
PREFACE.
The public, no doubt, will be surprised to find there is another
attempt made to publish a book of Arithmetic, when there arc
-such numbers already extant on the same subject, and several
of them that have so lately made their appearance in the world ;
but I flatter myself, that the following reasons which induced
me to compile it, the method, and the conciseness of the rules,
which are laid down in so plam and familiar a manner, will
have some weight towards its having a favourable reception.
Having some time ago drawn up -a set of rules and proper ques-
tions, with their answers annexed, for the use of my own school,
and divided them into several books, as well for more ease to
myself, as the readier improvement of my scholars, I found them,
by experience, of infinite use ; for when a master takes upon
him thatlaborioiis, (though unnecessary,) method of writing ou^
the rules and questions in the children's books, he must either be
toiling and slaving himself after the fatigue of the sc^hool is
over, to get ready the books for the next day, or else must lose
Jhat time which would be much better spent in instructing and
opening the minds of his pupils. There was, however, still an
inconvenience which hindered them from giving me the satis-
faction I at first expected ; i. e. where there are several boys in a
class, some one or other must wait till the boy who first has the
book, finishes th€ writing out of those rules or questions he
wants, which detains the others from making that progress they
otherwise might, had they a proper book of rules and examples
for each ; to remedy which, I was prompted to compile one in
order to have it printed, that might not only be of use to my own
, ..„,. „« .,,,.,, ,,u:ci3 as Y/uiild have iheir scholars make
a quick progress. It will also be of great use to sucli gentle-
a3
IV
PREFACE.
men as hare acquired some knowledge of numbers at school to
make them the more perfect ; likewise to such as have com-
pleted themselves therein, it will prove, after an impartial perusal,
on account of its great variety and brevity, a most agreeable
and entertaining exercise-book. I shall not presume to say
any thing more in favour of this work, but beg leave to refer the
unprejudiced reader to the remark of a certain autihor,* con-
cerning compositions of this nature. His words are as follows :—
" And now, after all, it is possible that some who like beat
to tread the old beaten path, and to sweat at their business, when
they may do it with pleasure, may start an objection, against the
use of this well-intended Assistant, because the course of arith-
metic IS always the same; and therefore say, that some boys
lazily mchned, when they see another at work upon the same
question, will be apt to make his operation pass for their own
But these little forgeries are soon detected by the diligence of
the tutor : therefore, as different questions io different boys do
not m the least promote their improvement, so neither do the
questions hinder it. Neither is it in the power of any master
(in the course of his business) how full of spirats soever he be,
to frame new questions at pleasure in any rule : but the same
question will frequently occur in the same rule, notwithstanding
his greatest care and skill to the contrary.
"It may also be further objected, that to teacfh by a printed
book is*an argument of ignorance and incapacity ; which is no
less trifling than the former. He, indeed, (if any such there
be,) who is afraid his scholars will improve too fa^t, will, un-
doubtedly, decry this method : but that master's ignorance can
never be brought in question, who can begin and end it readily ;
and, most certainly, that scholar's non-improvement can be as
little questioned, who makes a much greater progress ty this,
than by the common method."
To enter into a long detail of every rule, would tire the reader,
and swell the preface to an unusual length ; I shall, therefore,
only give a general idea of the method of proceeding, and leave
the rest to speak for itself; which I hope the kind reader will
find to answer the title, and the recommendation given it. As
it school to
have com-
ial perusal,
agreeable
me to say
to refer the
thor,* con-
follows : —
like best
ness, when
against the
ie of arUh'
)me boys
1 the same
their own
ligence of
It boys do
her do the
ny master
ver he be,
t the same
thstanding
' a printed
hich is no
such there
, will, un-
•rance can
it readily ;
can be as
J€ by this,
he reader,
therefore,
and leave
eader will
Bn it. As
PREFACE. V
10 the rules, they follow in the same manner as iae table of
contents specifies, and in much the same order as they are gen-
erally taught in schools. I have gone through the four funda-
mental rules in Integers first, before those of the several de-
nominations ; in order that they being well understood, the lattei-
will be performed with much more ease and dispatch, according
to the rules shown, then by the customary method of dotting.
In multiplication I have shown both the beauty and use of that
excellent, rule, in resolving. most questions that occur i- mer-
chandising; and have prefixed before Reduction, several Bills
of Parcels, which are applicable to real business. In working
I Interest by Decimals, I have- added tables to the rules, for the
readier calculating of Annuitiesi &c. and hp ve not only shown the
use, but the method of .making them: as likewise an Interest
Table, calculated for the easier finding of the Interest of any sum
of money at aifty rate per cent, by Multiplication and Addition
only ; It is also useful in calculating Rates, Incomes, and Serv-
ants Wages, for any number of months, weeks, or days ; and
I may venture to say, I have gone through the whole with so
much plamness and perspicuity, that there is none better extant.
I ha^e nothing further to add, but a return of my sincere thanks
to all those gentlemen, schoolmasters, and others, whose kind
approbation and encouragement have now established the use of
this book in almost every school of eminence throughout the
kingdom : but I think my gratitude more especially due to those
who have favoured me with their remarks ; though I must still
beg of every candid and judicious reader, that if he should, by
chance, find a transpo.ltion of a letter, or a false figure, to excuse
It ; for, notwithstanding there has been great care taken in cor.
recting, yet errors of the press will inevitably creep in ; and
«ome niay also have slipped my observation ; in either of which
cases the admonition of a good-natured reader will be very ac
ceptable to his much oblicrpH and n^""* ^v«.i:-„. i--~ui
o — 7 **'"^* ^J'^os vLTcuicni liumbie servant,
F. WALKINGAME.
i
i
'a
ARITHMETICAL TAI
1
3LES.
10 Q/IK,
'
i
u
T
H
nits
N
UMRl
1
12
123
1.234
RATION.
ens
C. of Thousands 123,456
Millions i 9'^ ^'IT
undreds
H
Thousands
X. ef Millions . .
]
12,345,678
IB
r V
ll
If
V '
ii
>
MULTIPLICATION.
1
2
3
2
4
6
3
6
9
12
15
18
4
8
12
16
20
24
28
5
10
15
20
6
7
8
16
24
9
18
27
36
10
20
30
40
60
60
70
80
90
100
no
120
130
140
150
160
170
180
190
200
11
22
33
44
55
66
77
88
99
110
121
132
143
154
165
176
187
198
209
220
12
24
36
48
60
72
84
96
108
120
132
144
156
168
180
192
204
216
228
240
12
18
24
14
21
4
8
28
35
42
49
32
5
10
25
30
40
48
45
54
6
12
30
35
36
42
7
8
14
16
21
56
63
72
24
27
32
36
40
44
48
40
45
48
56
64
9
18
54
63
70
77
84
91
72
80
88
96
81
90
99
108
10
20
30
33
50
55
60
60
66
72
11
22
12
24
36
13
26
39
52
56
60
65
70
75
78
104
112
120
117
126
135
144
153
162
171
if
.i
r
r
t
14
15
28
30
42
45
84
90
98
105
16
32
48
51
54
64
68
80
85
96
112
128
136
144
152
17
18
34
36
102
108
119
126
72
76
90
19
38
57
60
95
114
120
133
140
201 40
80 100
160
180
Note.— This 1
in 4 are 2, and 2a
'able may be applied to Division by reversing it : as the 2b
in G are 3, &c.
.
s.
12,345
123,450
,234,567
,345,678
11
12
22
24
33
36
44
48
55
60
66
72
~77
84
88
96
99
108
110
120
121
132
132
144
143
156
154
168
165
180
176
192
187
204
198
216
209
228
220
240
as the 28
ARITHMETICAL TABLES.
Vll
FEN'CE.
20d. are Is. 8d.
24
30
36
40
48
50
60
70
72
Wa.
6
5
4
3
2
2
1
1
2
2
3
3
4
4
5
5
6
6
4
2
lU
TABLES OF MONEY. s
HII.I.INUK.
PO.l. are 6s. 8d.
i 20s. are £1 Oa.
IWa. uvc.
£6 Os.
84 •
• 7
1 30 •• 1 10
IHO • .
6 10
90 .
• 7 6
40 • • 2
140 ••
7
96 .
■ 9
'50 • • 2 10
1.50 . .
7 10
100 .
. 8 4
60 •• 3
IGO ••
8
108 .
• 9
70 • . 3 10
170 .•
8 10
110
• 9 2
60 •• 4
IHO ..
9
120
• 10
90 •• 4 10
190 • •
9 10
130 •
• 10 10
100 •• 6
200 ••
10
140 .
. U 8
110 •• 5 10
210 ■•
10 10
PRACTICE TABLES.
or A PODND.
01. is 1 half
8 1 third
1 fourth
1 fifth
4 1 sixth
6 1 eighth
1 tenth
8 1 twelfth
1 twentieth
8 1 thirtieth
6 1 fortieth
6d.
4-
or A BHILLIN'O.
19
half
third
3 1 fourth
2 1 sixth
IJ 1 eighth
1 1 twelfth
OF A TON.
10 cwt. 1 half
5 1 fourth
4 1 fifth
2J 1 eighth
2 1 tenth
OF A CWT.
qrs.
2 or
0....
0....
lb.
r>6
•28-
■ 16-
.14.
is 1 half
• 1 fourth
■ • •! seventh
• • • 1 eighth
OF A QUARTER.
141bH 1 half
7 1 fourth
4 1 seventh
3^'- 1 eighth
CUSTOMARY WEIGHT
A Firkin of Butter is 56 lbs.
A Firkin of Soap 64
A Barrel of Soap 256
A Barrel of Butter 224
A Barrel of Candles 120
A Fa,?gfot of Steel-
■120
OF GOODS.
A Stone of Glass 5
A Stone of Iron or Shot 14
A Bairel of Anchovies 30
A Barrel of Pot Ashes 200
A Seam of Glass, 24 stone,
or-. 120
lbs.
TABLES OF WEIGHTS AND MEASURES.
TROY WEIGHT.
21 <rr. make 1 dwt.
20 dwt 1 ounce
12 oz 1 pound
apothecaries'.
20 gr. make 1 scruple
3 per 1 dram
8 dr I ounce
12 07. 1 pound
AVOIRDUPOIS.
16 dr. make 1 oz.
16 oz 1 lb.
14 lb 1 stone
28 lb 1 quarter
4 qrs I cwt.
20 cwt I ton
WOOL weight.
7 lbs. make 1 clove
2 cloves 1 stone
2 stone 1 tod
6J tods 1 wey
2 weys 1 sac
12 sacks- - •- 1 last
CLOTH MEASURE.
2| inch make 1 nail
4 nails 1 quar.
3 quar 1 Fl. ell
4 quar 1 yard
5 quar 1 En. ell
quar 1 Fr. ell
I SOLID MEASURE.
J1728 in. make 1 sol. ft.
27 feet 1 y.<ird
LAND MEASURE.
9 feet make 1 yard
30 yds 1 pole
40 poles 1 rood
4 roods 1 acre,
LONG MEASURE.
3 bar. corn 1 inch
12 inches 1 foot
3 feet 1 yard
feet 1 fathom
5i yards-". 1 pole
40 poles 1 furlong
8 fur 1 mile
3 miles 1 league
69 J miles 1 degree
afir\>-;pM»tm~^ma n iin a lktm
-li
I viii
ARITHMETICAL TABLES.
1
0U> 8TANDABD.
Gals.
8
17
36
53
70
106
3
3
2
1
3
P.
1
1
1
1
1
"Gins;
3-93
3*86
3>46
17
34
69
03
38
06
ALE AND BEER.
1
12
2i
50
75
100
151
302
1
2
1
2
3
1
1
1
1
1
1*60
2-41
10
38
22
83
44
66
33
4
2
4
9
2
2
U
2
3
gills make 1
pints 1
quarts* ••• 1
Sallons* • • 1
rkins • • • 1
kilderkins* 1
barrel**" 1
barrels* *'«1
banels*«**l
pint
quart
gal.
fir.
kild.
bar.
hhd.
gun.
utt
WINE MEASURE.
2 pints* .-l quart
4 quarts* 1 gallon
10 gallons* 1 anker
18 gallons* 1 runlet
42 gallons* 1 tierce
63 gallons* 1 hogshead
B. P. G. a P. Gills.
1
2
4
1
1
1
8 1
33
82 2
1
2
1
0*25
1*01
2*02
0*07
0*14
0*28
0*66
2*24
1*63
84 eallons
2 nogs
2 pipes
1 puncheon
1 pipe
1 tun
DRY MEASURE.
3 3
37 1
0*21
2*52
2 pints make 1 quart
4 quarts 1 gallon
2 gallons • * • 1 peck
4 pecks 1 bushel
2 bushels* • * • 1 strike
4 bushels* •*•! sack
8 bushels* • • • 1 quarter
4 quarters* • • 1 chald.
10 quarters* * * 1 last
COAL MEASURE.
3 bushels* '1 sack
36 bushels* '1 chaldron
NIW STANDARD.
Gals.
1
9
18
36
64
73
109
Q.
1
1
2
3
3
P.
1
1
1
I
GUIs.
0*07
0*13
0-64
0*91
1-82
3 64
1*45
3-27
2-91
1
3
8
1
14
3
34
3
62
1
69
3
104
3
209
3
266
2*68
3*87
3*70
3*55
3*40
3 11
2*22
B. P. G. Q. P. Gills.
1 3*75
3 1 3*02
13 1 2*04
3 13 0*17
1 3 1 2 0*36
3 3 10 0*70
7 3 1*40
31 1 1*66
77 2 1 1 2*13
2 3 110 0*62
34 3 1 1 2*34
I
=1
4in>ARD.
GUliT.
0-07
013
0-64
0-91
1-82
3-64
1-45
3-27
2'9I
T5B
2-65
2-68
3.87
70
56
40
11
22
P. Gills.
1 3-75
302
204
017
035
0-70
1-40
166
213
1
1
1
1
1
0-52
2.34
CONTENTS
PART l.~ARITHMETIC IN WHOLE NUMBERS.
Introduction 13
Numeration 13
Integers, Addition '.'. 15
Subtraction 16
Mnltiplicadon 16
Diviaion 19
Tables gi
Addition of several denominations. 28
— -Subtraction 34
Multiplication 37
Division 43
Bills of Parcels 44
Reduction 47
Single Rule of Three Direct 53
— Inverse.... 56
Double Rule of Three 58
Practice 60
TareandTret 67
Simple Interest 70
Commission 71
Purchasing of Stocks 71
Brokerage 71
Compound Interest !.*.!!.* 74
Rebate or Discount i 75
Equation of Payments 76
Barter 77
Profit and Loss ."*..*.*.*'..! 79
Fellowship. gQ
^without Time ...!.!.' 80
with Time 82
Alligation Medial 83
Alternate 85
Position, or Rule of False 88
Double , 90
Exchange 91
Comparison of Weights and Mea-
sures 95
Conjoined Proportion 96
Progression, Arithmetical 97
-Geometrical 100
Permutation 104
PART II.— VULGAR FRACTIONS.
Reduction 106
Addition 112
Subtraction ,,,, = ,= 112
Multiplication 113
Division 114
The Rule of Three Direct. 114
'Inverse .... Ijd
The Double Rule of Three 116
C0NTEKT8.
PART III.— DECIMALS.
Numeration.. 117
Addition 1 18
Subtraction 119
Multiplication 119
Contracted Multiplication 120
Division 121
Contracted 122
Reduction 123
Decimal Tablesof Coin, Weights,
and Measures 126
The Rule of Three 129
Extraction of the Square Root 130
Vulgar Fractions. . . 13I
Mixed Numbers 132
Extract of the Cube Root ...134
Vulgar Fractions . . . 136
Mixed Numbers. 13G
Biquadrate Root 138
A general Rule for extrticti»g the
Roots of all powers 138
Simple Intereiit 14C
for days 14^
Annuities and Pensions, &c. in
Arrears l-j|3f
Present worth of Annuities 14*
Annuities, &c. in Reversion IS0
Rebate or Discount 153
Equation of Payments 154
Compound Interest l&S
A nnuities, &c. in Arrears 157
Present worth of Annuities IGO
Annuities, &c. in Reversion 169
Purcha«ag Freehold or Real Es-
tates 164
in Reversion 165
Rebate or Discount ..)66
PART IV.-~DUODECIMALS.
Multiplication qf Feet and Inches, 163
Measuring tiy the Foot Square. , . 171
Measuring by the Yard Square. . . 171
Measuring t^ the Square of 100
Feet 173
Measuring by the Rod. 171
Multiplying sex-cral Figures by
several, and the operation in one
line only ,, . . 171.
PART V.~aUESTIONa
A "Collection of Cluestions, set
down promiscuously for the
greater trial of the foregoing
Rules 17C
A general Table for ctdeukCinf'
Interests, Rents, Incomes and
Servante' Wages I8l^
A COMPENDIUM OP BOOK-KEEI*lNa. tat>
EXPLANATIOir OF THE CHARAOTIBt.
Pftf«
ctiHgthe
138~
\4$
141^
, &c. in
U$
iea 14*
Ion 1&9
m
154
155
157
ies IGO
on 1G9
164
n 166
16*
u
m
urea by
n in on*
ralatini
let
dnr
and
.181'
.I8ti
I
EXPLANATION OP THE CHARACTERS MADE USB OF IN
THIS COMPENDIUM.
KsEqual.
— Minus, or Less.
-+- Plus, or More.
X Multiplied by.
-t- Divided by.
2357
63
: : So is.
7_2-HS*=10.
The Sign of Equality; as* 4 qrs.«=l cwu
signifies that 4 qrs. are equal to 1 cwt.
The Sign of Subtraction ; as, 8—2-6, that
is, 8 lessened by 2 is equal to 6w
The Sign of Addition ; as 4-f 4=6>, that is.
4 added to 4 more, is equal to 8.
The Sign of Multiplication ; as, 4 X 6=24,
that is, 4 multiplied by 6 is equal to 2i.
The Sign of Division ; as, 8+2=4, that is,
8 divided by 2 is equal to 4.
Numbers placed like a fraction do likeAvise
denote Division ; the upper number being
the dividend, and the lower the divisor.
The Sign of Proportion ; as, 2 : 4 : : 8 : 16,
that is, as 2 is to 4, so is 8 to 16.
Shows that the difference between 2 and 7
added to 5. is equal to 10.
Signifies that the sum of 2 and 5 taken from
0, is equal to 2.
Prefixed to any number, signifies th*
Square Root of that nu^iber is required.
Signifies the Cube, or Thlnl Power.
Denotes the Biquadnile» or Fourth Power,
&c.
i.e.
id v^U that is.
Ar
bers,
all it
Nt
MUL
Teac
and t
THE
TUTOR'S ASSISTANT
BKf. -i
A COMPENDIUM OP ARITHMETIC.
PART I.
ARITHMETIC IN WHOLE NUMBERS.
THE INTRODUCTION.
Arithmetic is the Art or Science of computing by Num-
bers, and has five principal or fundamental Rules, upon which
all its operations depend, viz : —
Notation, or Numehation, Addition, Subtraction,
Multiplication, and Division.
NUMERATION
Teacheth the different value of Figures by their different Places,
and to read and write any Sum or Number.
THE TABLE.
m 52
= s
c o .
9 8 7
9
-i
7
en m
c c
CO CO ii
3 s S
O o <?
-a
r-
tn
tn
^ O
6 .5 4
6
5
4
tn
0)
S )S 4->
» « C
3 2 1
3
2
1
H
KUMERATION.
consisting of three PiVurerorpN. % '•'"•''. Million. ; each
of each from the lef *h»n^' '^= "''■ "««'""' the firat Piem,
•i"e„s.andthethi?dassomfnv.t' T^"^ ""'"'""''• "•« "K
•hem: ,h„,, the firs IWdoVthlleft'hr* '''"''''',''""«" °»"
^reda„dEighty.sevenMi,,t",f:„'5':„tt;:V^?r
THE APPLICATION.
WHt. aov,n in proper Figures tke following Number,.. <
( ) Twenty-three.
n\ ^r ^^'!.'''■*•' *"'' Fifty-fonr.
• rt'Z '^^""'^l'^- Two Hundred and Pour
•nd Forty.five. '>"«y-««'» Thousand, Two Hundred
fJ„7 «„":'"""• ^'"' ^»''-' ""O Fortyon. Thou.«,d.
ThUaa^S. F?:i''Sl7red'^- "'""•"'• "^^ «-Sred and T,n
I ) 800061057 (■•) aaiflooTOO
I' One.
n Two.
ni Three.
IV Four
V Five.
VI Six,
VII 8even.
Vni Eight
Notation by Roman Letters.
rX Nine.
X Ten.
Xr Eleven.
XH Twelve.
Xm Thirteen,
XIV Fourten.
XV Fifteen.
XVi Si: ..en..
f)
ADDITION OF INTEGERS.
the right hand,
» Millions; each
I the first F\gu*"9
5ds, the next as
It is written over
ead, Nine Hud-
my of the rest
g" lumbers.
d Fifty-six.
Two Hundred
ne Thousand,
d Fifty-seven
rivo Hundred
ur.
dred and Ten
Numbers.
•) 6207064
') 2071009
') 70064000*
£1900700
e.
en.
n.
XVII
XVIII
XIX
XX
XXX
XL
L
LX
LXX
LXXX
XC
C
CC
Seventeen.
Eighteen.
Nineteen.
Twenty.
Thirty.
Forty.
Fifty.
oixty.
Seventy.
Eighty.
Ninety.
Hundred.
Two Hundred.
ccc
cccc
D
DC
Dec
DCCC
DCCCC
M
MDCCCXII
MDCCCXXXVII
Three Hundred.
Four Hundred.
Five Hundred.
Six Hundred.
Seven Hundred.
Eight Hundred.
Nine Hundred.
One Thousand.
One Thousand Ei^ht
Hundred and Twelve.
One Thousand Eight
Hundred and Thirty
Seven.
INTEGERS.
ADDITION
JAmal Sum.'^^ '""' '' "*''' ®""' '°^^'^^^» '^ -^ke one wholr
&c ; then beginning with the first row of uiifs^add ^1;!;
he top; when done, set down the Units, and carry the Teis to.
Proof. Bc?in at the top of the Sura, and reckor»-thi» Fl»™-.
AeTrnte Su™ •'"'' "' ^""Z"" "«'■" "P. and. ?;*:«rn
we nrst, the bum is supposed to be ri.rht.
Qrs.
(')275
110
473
354
271
352
Months. £
r)1234 75215
^098 37502
3314 91474
«'?32 32145
2646 47258
{ ) What ,s the sum of 43, 401. 9747, 3464, 2203, 314, 974f
('•) Add 216031. 29S?fi5. 47l«»i r^^o o.^./I^aJJ^..
d 640 to<rpth,.» "' ^ ' ""'^^ ''^'^''^ »«^^ '^^^l*
1,3 Ans. 73082B.
Years.
(*)271048
325476
107584
625606
754087
279736
•nd 640 together.
16
SUBTRACTION OF INTEGERS.
^-^^y u ^'''" ^'l^ ^' ^^^» B. £104, C. £274. D £391 nnd F
£703, how much is given in all ? ^-^'^^ ^' ^lf\l^ ^
n How many days are in the twelve Calendar Monthsf>
Ans. 365.
SUBTRACTION
'rS ii ^ ^k. ?^'^ «^^'^
_ ^f^ 3^7616 152471 3150»74
Hem. 117 ~" ~
> "■
Proof 871
MULTIPLICATION
To this Rule belong three principal Members, viz.
3 The mS-"""''' "' ^r^"' '» ^ "•uUiplied.
£391, and E
Ans, 1528
Months ?
Ans. 365.
MULTIPLICATION OF INTEGERS. ^
id shows the
nust borrow
i rcmember-
•gether, and
3750215
3150974
MULTIPLICATION TABLE.
s given, as
f perfonns
VIZ.
ng.
nit's place
the Unit's
carry the
ire in the
) the pro-
down the
itipiied.
2 3 4
^ "f 8 9 10 11 12
2
4
6
8
3
6
9
12
4
8
12
16
6
10
15
20
6
12
18
24
7
14
21
27
8
16
24
32
9
18
28
36
10
20
30
40
11
22
33
44
12
24
36
48
10 12
16 18
20 24
25 30
30 36
35 42
40 48
45 54
50 60
55 66
60 72
14 16
21 24
28 32
35 40
42 48
49 56
56 64
63 72
70 80
77 88
84 96
18 20
27 30
36 40
45 50
54 60
63 70
72 80
81 90
90 100
99 110
108 120
22 24I
33 36
44 48
55 60
66 72
77 84
88 96
99 108
110 120
121 132
132 144
Multiplicand (>) 25104736
Multiplier 2
Product 50209472
(*) 52471021
(») 7925437521
4
037104107 (.) 931047 (•) ,098616 (,) 3,36104
(") 4215466
9
02701057 (^0)31040171
10 11
^\
.^'?*[l*.^'f.''liiP"*' \' "i"'?*"- 12. and 168, than 20. m„UI.
pz^ ^y wici^nu figure in the Multiplier, adding to the ProdZt
the back Figure to that you miiUinlied. ^ ^'^
B3
\8
MULTIPLICATION OF INTEGER*.
(^')5710502 (' = )6107252 ('3)7663210 (,»*) 02067165
13 14 16 16
(") 6251721
17
('«) 9215324
18
(*') 2571341
19
('«) 3592104
20
When the Multiplier consists of several Figures, there must
be as many products as there are Figures in the Multiplier, ob-
serving to put the first figure of every Product under that Figure
you mu tiply by. Add the several Products together, and their
feum will be the total Product.
( ' ') Multiply 271041071 by 5147.
(' ° ) Multiply 62310047 by 1668,
C ') Multiply 170925164 by 7419.
(22) Multiply 9500985742 by 61379.
(2 3) Multiply 1701495868567 by 4708756.
il!}M^u-^-P^'T ^'"^ P^^,'^^ between the significant Figures ih
the Multiplier, they may be omitted ; but great care must be taken
hat the next Figure must be put one place more to the left hand,
t. e, under the Figure you multiply by.
(s *') Multiply 571204
By
ST-
OOD
5140836
3998428
1142408
Prodact 15427f)4883G
(' ') Multiply 7501240325 by 57002.
(2«) Multiply 562710931 by 590030.
When there are Ciphers at the end of the Multiplicand or Mul-
tiplier, they may be omitted, by only multiplying by the rest of
tne l<igures, and settinsr down on the rio-ht h^r^A of t^t^ *-*-^
rroductas many Ciphers as were omitted.
DIVISION OF INTEGERS.
v")MulUnly 1379500
3400
w
55180
41385
4690300000
(2 8) Multiply 7271000 by 62600.
(»») Multiply 74837000 by 975000.
When the Multiplier is a composite Number, i. e. if any two
Figures being multipHed together, will make that Number, then
multiply by one of those Figures, and that Product being multi-
plied by the other will give the Answer.
(3 0) Multiply 771039 by 35, or 7 times 5.
7 X 5=35
5397273
•5'
2G986365
('>)Multiply921563by32.
(32) Multiply 715241 by 56.
(' ») Multiply 79&4956 by 144.
DIVISION
Teacheth to find how often one Number is contained in another ;
or, to divide any Number into what parts you please.
In this Rule there are three numbers real, and a fourth acci-
dental : viz.
1. The Dividend, or Number to be divided:
2. The Divisor, or Number by which you divide :
3. The Quotient, or Number that shows how often the Divisor
is contained in the Dividend :
4. Or accidental Number, is what remains when the work is
finished, and is of the same name as the Dividend.
Rule. When the Divisor is less than 12, find how often it is
contained in the first Figure of the Dividend ; set it down under
the Figure you divided, and carry^the Overplus (if any) to the
next in the Dividend, as so many Tens ; then find how often the
Divisor is contained therein, set it down, and continue the sani«
90
DIVISION OF INTEGERS.
till you have gone through the Line; but when, the Divisor is
more than 12, multiply it by the Quotient Figure ; the Product
subtract from the Dividend, and to the Remainder brine down
the next Figure in the Dividend and proceed a» before, till the
Figures are all brought down. . " «
Proof. Multiply the Divisor and Quotient together, adding
rJ.® . ,*'T''^'^^^» (^^ »"y») a»<l th« Pi-oduct will b^ the same as the
Uividend.
Dividend. Rem. .
(») Divisor 2)725107(1
(«) 3)7210479(
Cluotient
Proof
362553
2
725107
{*) 5)7203287(
») 4)7210416(
(«) 6)5231037(
(«) 7)2532701(
(») 8)2547325(
') 9)25047306(
Divisctf. Dividend, duotient.^^
(9) 29)4172377(143875
29
2P
127
116
.112
87
.253
232
.217
303
.14?
145
1294875
287750
2 rem.
4172377 Proof.
Rem.
(i») Divide 7210473 by 37.
Ans. 194877**-
( » » ) Divide 42749467 by 3-17.
(1 8 ) Divide 734097143 by f»743.
(13) Divide 1610478407
by i>4716.
(!♦) Divide 4973401891
by 510834.
(» 6) Divide 51704567874
by 4765043
(» •) Divide 17453798946123741 '
by 31479461.
^ When^there are Ciphers at the -^nd of the Divisor, they may
^e cut On, and as many places from oft the Dividend, but thev
must be annexed to the Remainder at last.
tAllLSS Ot MONEY.
21
{\y) 271|00V254rJ2l21(939 (i s) 6721 100)72534721 16(13e?7
( I •) 3731000)75247^1729(2017 (a oj 2l5|(k)0)6326l04|997(
29419
When the Divisor is a composite Pumber, i. e. if any two Fi-
ffUres, being multiplied together, will make that Number, then, by
dividing the Dividend by one of those Figures, and that Quotient
by the other, it will give the Quotient required. Bat as it some-
times happens, that there is a Remainder to each of the Quotients,
and neither of them the true one, it may be found by this
Rule. Multiply the first Divisor into the last Remainder, to
that Product add the first Remainder, which will give the true
one.
(SI) (9 9)
Div. 3210473 by 27. 7210473 by 35.
(9 8)
6251043 by 42.
(9 4)
5761034 by 54.
118906 11 rem. 206013 18 rem. 148834 15 rem. 106685 44 rem.
MONEY.
Marked
i Farthing 4 Farthings make 1 Penny d.
t Halfpenny 12 Pence 1 Shilling s.
i Three Farthings 20 Shillings 1 Pou»d ?.......£
Farthings
4 = 1 Penny
48 = 12 = 1 Shilling
960 = 240 = 20 = i Pound.
8HILUN08.
8.
20
30
40
60
60
70
80
90
100
IIQ
120
130
£
1
1
2
2
.3
3
4
4
5'
e i I
I
PENCE TABLE.
8.
10
10
10
10
10
10
d.
8.
d.
20 .
• 1
I 8
24 •
' 2
:
30 •
• 2
; 6
36 •
• 3
!
40 •
• 3 .
! 4
48 .
• 4 i
60 •
• 4 i
2
60 ..
6 :
70 ..
5 :
10
72 ..
o ;
u
80 ••
6 :
8
^4 ..
7 J
d.
00
06
100
108
110
120
130
132
140
144
150
160
8.
d.
7
! e
8
:
8
s 4
t
s 2
10
!
10
! 10
11 i
11 :
8
12 i
12
C2
TABLES OF WElOIfTg.
24 O
raing mi
THOY WEIGHT.
...I Pennyweight.
Marl (^
20 Pennyweirhli ....1 Ounce oT
^•-^ ^«nces 1 pt,und ".'.'.'.lb'
\»rains
9A s: 1 Pennvw^iffht
5?(,0 240 = 12 = 1 Pound
By this Weight are wrlghed Gold, Silver, Jewels, Electuaries
and all Liquors.
N. B. The Standard for Gold Coin is 22 Carats of fine Gold
and Z Carats of Copper, melted together. For Silver, is 1 1 oi
4 dwts. of fine Silver, and 10 dwts. or Copper.
25 lb. is a quarter of 100 lb. 1 cwt.
20 cwt. 1 Ton of Gold or Silver.
AVOIRDUPOIS WEIGHT. Marked
16 Drams make 1 Ounce
I? ^""'^^s 1 Pound lb
-^ 1^0"" ^^ I Quarter '"qr
4 Quan rs or 112 lb 1 Hundred Weight ",lwt
ed Weight 1 Ton ton
^dr.
S oz.
20 Hun 'r
.Drams
16 =
256 =
7168 =
28672 =
1 Ounce
16 = 1 Pound
448 -= 28 = 1 Quarter
n^Q^^A o32?^ " "^ = ^ = 1 Hundredweight
573440 = 35840 = 2240 = 80 = 20 = 1 Ton.
There are several other Denominations in this Weight thai
tre used m some pa ticular Goods, viz.
lb. . Ij,
A Firkin of Butter 56 A Stone of Iron, Shot or } ,
*A B 1 . '"^P ^"^ Horseman's wt I ^"^
A Barrel of Anchovies 30 Butcher's Meat... 5
^oap 2.56 A Gallon of Train Oil... . 74
Raisins 112 A Truss of Straw 36
A Puncheon of Prunes. JJ20 New Hay 60
urn liav 56
qrs.
A)
Tru
!?.«es a
Load
ay.
i^-.
4 Nails
i^
Marl o4
lb.
Electuaries
)f fine Gold
er, is 1 1 oz
Marketf
>dr.
) oz.
lb.
qr-
..,....cwt.
ton.
TABLES OF WElOHTi.
Cheese and Butter.
. «' . c n. ..^ ^'"''*' "^ Half Stone, 8 lb
A \\«y m Snn.lk, > lb. A Way in Essex,
J^Uovea, or J 2&6 3iiCluros,or
. ^, ^b. A Wey is ti Tods and
^9'^^^ '3' 1 Stone, or
^ ,^^7^ 14 A Sack is 2 Woys, or
^ *"" 28 A Last is 12 Sacks, or 4369
By this Weicrht is wf^ighed anything of a coarse or drossy na-
ture ; as ull Grocery ami (Chandlery Wares; Bread, and all Me-
tals but Silver aed (lold.
Note. One Pound Avoirdupois is equal to 14 oz. 11 dvvts. 15i
grs. Troy ^
$330
nb,
S 182
304
APOTHECARIES' WEIGT.
Marked
3
It
5
.., lb
20 Grains make 1 Scruple
3 Scruples i Dram
,5 J""^"^' 1 Ounce .*;;
13 Ounces i YowxiA
Graias
20 = 1 Sruple
r>0 = 3 = 1 Dram
480 = 24 = 8 = 1 Ounce
5760 = 288 = 96 = 13 = 1 Pound.
Note. The Apothecaries mix their Medicines bv this Rule,
but buy and sell their commodities by Avoirdupois Weight.
OnT^^ iP*'*^^^"^ ' P«"»d a»^ Ounce, and the Pound and
Ounce Troy, are the same, only differently divided and subdivi-
OLOTH MEASURE.
4 Nails make ...l
Marked
Quarter of a Yard
4 g"*^^^''^ 1 Flepnsh Ell :.F1. E.
4 Quarters i v^„i
> Quarters , ^ ,. . — z
'> Q.uarterfi..,
* • * •««.««
■ 1 English Ell E. E.
1 French Ell Fr. E
24
TABLES OF MEASURES.
Inuhes
2i = 1 Nail
9 = 4 = 1 auarter
36 = 16 = 4 = 1 Yard
aI =1? = 3 = 1 FlemishEU
45 = ^ = 5 =, 1 EnglishEU
54 = 24 = 6 = i FrenchEU.
LONG MEASURE.
< 1
Marked
3 Barley Corns. make l Inch > bar. c.
12 Inches... , „ lin.
3 Feet?!;.- :;:•:;;::•• I ?S -St
6 Feet J ^wd j
5* Yards ;;•• - } p!?'^'-,- n* * u' ^h.
40 Poles • ; Rod P^le or Perch rod, p.
SFuriongs...... J S?r'°°g fur "^
3xMile8.T... • ; f*^^ mile.
^ I^egree j^.
Barley Corns
^3 = 1 Inch
36 = 12 = 1 Foot
108= 36= 3= lYard
594 = 198 = 164= i_ 1 p^,
iS - S = ..^ = ^ = ^ = ' ^-long
lyuObO = 63360 = 5280 = 1760 = 320 = 8=1 Muf
WINE MEASURE.
i> n. Marked
^ ^"*« n«Ae 1 auart ) pt«.
iJ 9SSf; 1 GaUon ""^^
18 gZI::: j Anker of Bra,id>:::::::::S*.
42 Gallons..... * -Half an Hogshead jhhd.
63 Gallons .' , « "if';'"' ^er.
2 pip^or4Hog8'h;«is'.'.::::;::::} tZ^'.T::.::::::: f-"®-
Marked
} bar. c.
) in.
..feet
..yd.
..fth.
.rod, p.
..fur.
..mUe.
..lea.
lOUgh com
Bs, or any
Marked
•Jqts.
...gal.
. . .anjt*
...ran.
• ..} hhd*
> . . tier.
. . . una.
. ..P. or B.
TABLES OP MEASURES. 4jg
Inches*
28|= 1 Pint
571= 2= 1 Quart
oSJ = oo®= 4= 1 Gallon
9702 = 336= 168= 42=1 Tierce
iS = S2i= 2^2= 63=lj=i Hogshead
19404 = 672= 336= 84=2 =l*-i Punchpon
29106 =1008= 504=126=3 =2 = U=i P^'°"
58212 =2016=1008=252=6 =4 =3 =2=l^un
,„:^n-?'^"^''''' ®P'"?' ^^"5^' ^^^«^' Mead, Vinegar, Honev
.fat ?u^; :u:to~i;' '' ^'^^ "^^^^-^^ ^ ^^ ^^- ^"^^ -^ ^x
ALE AND BEER MEASURE.
2 Pints
make. lauart
&t:::;::::::;: ip£„fAV-'-
Firkins, or 2 Kilderkins.::::::;} bS
4
8
9
2
• • • • • •
Barrels, or 2 Hogsheads / : : : : : : i Butt .
Marked
>pt8.
•5qt8.
.gal.
.A. fir.
.B.fir.
.kil.
.bar.
.hhd
.pun.
.butt.
_, BEERa
Cubic Inches
35i= iPint
70i= 2= lauart
2538 = 72= 36= 9= 1 Firkin
iS =iM= J?= 18= ^Joderkin
10152 =288=144= 36= 4=2-1 BanS
15228 =432=216- 54- 6-tii i w u ,
20304 =576=4= jt ld-2*-u?fcl
30456 =864=432=108=12=6=1 =2*=lj=TBr
rt ,. ALE.
Cubic Inches
35i= 1 Pint
JOh= 2= 1 Quart
2^ = 8= 4= 1 Gallon
!I?S =ii= ^2= 8=1 Firkin
4513 =128= 64=16=2=^1 Kilderkin
9024 =256=128=32=4=2=1 BaS
13536 =384=192=48=6=3=U=YHo.sh.ad.
* By a ip.te Act of ParliamAnf »h« -o^^-.-,: i-.u. ,,.; ^ ~
S«U'm*"""«' '^^^^ been "ri"(inced to 'o7e Standard p!!^ '""^ ^'^ *'"* ^«"' «""» "»•
hese Measures, with the old stamlard^Ieasures thp ^f,!^?/ ,"■" «""'•'»'« comparison of
the "/n.p«nai Measures," at tlie bSig o^the work " ''^'^"'^ '" *^« ^*'''« <
26 TABLES OF MEASURES.
In London they compute but 8 gallons to the firkin of Ale,
and 32 to the barrel ; but in all other parts of England, for ale,
strong beer and small, 34 gallons to the barrel, and 8^ gallons
to the firkin.
N.B.— A barrel of salmon, or eels, is 42 gallons,
A barrel of herrings 32 gallons.
A keg of sturgeon 4 or 5 gallons.
A firkin of soap 8 gallons.
DRY MEASURE.
Marked
2 Pints make 1 Quart } P**'
f. ^ ' S qts.
2 Quarts 1 Pottle .pot.
2 Pottles 1 Gallon Jal.
2 Gallons ^,...1 Peck Jk.
4 Pecks 1 Bushel bu.
2 Bushels 1 Strike strike.
4 Bushels 1 Coom cooai.
2 Cooms, or 8 Bushels 1 duarter qr.
4 Quarters 1 Chaldron ....'..• ! ."chal.
5 Quarters 1 Wey wey.
2 Weys I Last .laat
In London, 36 bushels make a chaldron.
Solid Inches
268t= 1 Gallon
537f = 2= 1 Peck
4= 1 Bushel
215af= 8=
4300f= 16= S= 2= 1 Strike
8601f= 32= 16=
4= 2= 1 Coom
17203i= 64= 32= 8= 4= 2= 1 Quarter
86016 =320=160=40=20=10= 5=1 Wey
172032 =640=320=80=40=20=10=2=1 Last.
The Bushel in Water Measure is 5 Pecks.
A score of coals is 21 chaldrons.
A sack of coals 3 bushels,
A chaldron of coals 12 sacks.
A load of corn 5 bushels.
A cart of ditto 40 bushels.
ihis measure is applied to ail dry goods.
The standard Bushel is 18^ inches wide, and 8 inches deep
■I
TABLES OP MEASURES.
27
TIME.
60 Seconds make....l Minute....
60 Minutes 1 Hour
^ Hours 1 Day
J Jays 1 Week
,o J:®®¥ 1 Month
U Months, 1 day, 6 hours . . 1 Julian Year
Marked
) m.
hour.
day.
week.
.mo.
.yr.
Seconds
60= 1 Minute
3600= 60= Hour
86400= 1440= 24= 1 Day
604800= 10080= 168= 7=1 Week
2419200= 40320= 672= 28=4= 1 Month.
d. h. w. d. h.
31557600=525960=8766=365 : 6=52 : 1 : 6=1 Julian Year
o... d. h. m. "
31556937=525948=8765=365 : 5 :48 : 57=1 Solar Year.
To know the days in each month, observe,
Thirty days hath September,
April, June, and November,
February hath twenty-eight alone.
And all the rest have thirty and one ;
Except in Leap- Year, and then's the time
February's days are twenty and nine.
SQUARE MEASURE.
*^ {»<^^» make 1 Foot
,n? £""! •• 1 Yard.
^*F^ :::::::::;;• •-•} |2«'«««ffloom*
40 Rods ...'.V.V.V.V.V.V.'.*"* 1 rS
4 Roods, or 160 Rods, or 4840 vaids-V" ' * ' " i A^^\f i-«;
640 Acres
30
-'sv z^z 2eu£u«
t:Z 1 Squaw MUe.
^^ Acres V.V.V.'.Vl Hide
C3
1 Yard of land,
of land.
.88 ADDITION OF MONET.
Inches
144= 1 Foot
1296- 9 = 1 Yard
39204= 272|= 30^ 1 Pole
1568160=108<.)0 =1210 = 40=1 Rood
6272^=43560 =4840 =160=4=1 Acre.
By this measure are measured all things that have length and
breadth ; such as land, painting, plastering, flooring, thatching,
plumbing, glazing, &c.
SOLID MEASURE.
1728 Inches make 1 Solid Foot.
27 Feet 1 Yard, or load of earth.
40 Feet of round timber, ) . , rr-^^ „, t „„,i
Or, 50 Feet of hewn timber, \ '* ^ ^°" °' ^'^•
108 Solid Feet, i. e. 12 feet in length, 3 feet in breadth, and 3
deep, or, commonly, 14 feet long, 3 feet 1 inch broad, and 3 feet
1 inch deep, is a stack of wood.
128 Solid Feet, i. e. 8 feet long, 4 feet broad, and 4 feet deep,
is a cord of wood.
By this measure are measured all things that have length,
breadth, and depth.
ADDITION OF MONEY, WEGHTS, AND MEASURES.
Rule. Add the first row or denomination together, as in In-
tegers, then divide the Sum by as many of the same denomination
as make one of the next greater, setting down the Remainder
under the row added, and carry the Quotient to the next superior
denomination, continuing the same to the last, which add as in
simple Addition.
MONEY.
(») («) («) ^ (*)
£ s. d. £ s. d. £ s. d. £ s. d.
2 .. 13 .. 54 27 .. 7 .. 2 35 .. 17 .. 3 75 .. 3 .. 7
7 . . 9 . . 4* 34 . . 14 . . 7i 59 . . 14 . . 7i 54 . . 17 . . 1
5 .. 15 .. 4i 57 .. 19 .. 2i 97 .. 13 .. 5i 91 .. 15 .. 4^
8 .. 17 .. 6i 91 .. 16 .. 1 37 .. 16 .. 8t 35 .. 16 .. 5|
7 .. 16 .. 3 75 .. 18 ., 71 97 .. 15 .. 7 29 .. 19 ..7*
5 .. 14 ,. 71 97 .. 13 .. 5 59 .. 16 .. 5i 91 .. 17 .. 3i
ADDITION OF WEIOHTSi'
2J>'
MONEY.
length and
thatching,
£
257
734
695
159
207
798
n
s.
1 ..
3 ..
5 ..
14 ..
5 ..
16 ..
d.
6i
7f
3
7i
4
7i
£
525
179
250
975
254
379
n
s.
.. 2
.. 3
.. 4
,. 3
,. 4
d.
4*
5
7i
5i
7
51
£
21
75
79
57
26
54
<')
s.
14 .
16 .
2,
16 .
13 .
2 .
d.
7*
4i
5i
8J
7
£ s.
73 .. 2
25 . . 12
96 . . 13
76
97
54
17
14
11
H
5i
3i
li
7i
idth, and 3
, and 3 feet
I feet deep,
ve length,
ASURES.
', as in In-
lomination
[lemainder
Kt superior
1 add as in
£ :
127 .. 4 ,
(•)
525
271
624
379
215
3
9
4
5
• • ^C • c
{')
oz.
(iwt.
5
.. 11
7
.. 19
3
.. 15
7
.. 19
9
. 18
8-
. 13
d.
7i
5
5
1
3i
8i
£
261
379
257
184
725
359
8.
.. 17 ,
..13
,. 16 ,
.. 13 ,
. 6 .
d
1*
5
71
5
3i
5
£
31
75
39
97
36
24
{'')
1
13
19
d.
n
1
7i
17.. 3i
13 .. 5
16 .. 34
TROY WEIGHT.
. (')
Sf-
lb. oz. dwt.
4
7 .. 1 .. 2-
21
3 .. 2.. 17
14
5 .. 1 .. 15
23
7 .. 10 .. 11
15
2 .. 7 .. 13
12
3 .. 11 .. 16
£
27
16
9
15
37
56
«.
. 13 .
. 12 .
. 13 .
. 2 .
. 19 .
. 19 .
d.
5i
9i
3i
7i
1
If
lb. oz. (Iwt, gr.
5 .. 2 .. 15 .. 22
3 .. 11 .. 17 .. 14
3 .. 7 .. 15 .. 19
9 .. 1 .. 13 .. 21
3 ..' 9.. 7 .. 23
5 .. 2 .. 15 .. 17
AVOIRDUPOIS WEIGHT.
(*)
s.
d.
. 3 ..
7
. 17 ..
1
. 15 ..
4*
. 16 ..
5}
. 19 ..
7i
. 17 ..
3*
(')
lb. oz. dr.
162 .. 15 .. 15
272 . . 14 . . 10
303 .. 15 .. 11
255 . . 10 . . 4
173 . . 6 . . 2
635 . . 13 . . 13
C)
cwt, qrsi lb.
t.
25 . . 1 . . 17
7
7i . . 3 . . 26
5
M .. 1 .. 16
2
24 .. 1 .. 16
3
17 .. .. 19
7
55 . . 2 . . 16
8
(»)
cwt. qrs.
II).
17.. 2 .
12
5 .. 3 .
. 14
4 .. 1 .
. 17
18 . . 2 .
19
9 .. 3 .
.20
C3.
30
ADDITION OF MEASURES.
APOTHECARIES' WEIGHT.
lb.
17
9
27
9
37
49 .
(0
oz.
dr.
scr.
10 ••
7 .
• 1
5 ••
2 .
• 2
11 ..
1 ..
2
6 ••
6 ••
1
10 ..
6 ..
2
..
7 ..
(^)
Fl.E
qr. n
127 ..
2 .. 1
15 ••
1 •• 3
237 ..
•• 2
52 ..
1 .. 3
376 ••
2 .. 1
197 •.
1 •• 3
(»)
yd.
feet
m
bar.
■ 225
• • 1 « .
9
•• 1
171
• • ••
3
•• 2
62
•• 2 • •
3
•• 2
397
• • • •
10
•• 1
164
.. 2 ..
7
•• 2
137
• • 1 • •
4
•• 1
(^)
lb.
7 ..
OZ. dr. scr. «.
2 .. 1 .. ..12
3 ••
1 •• 7 .. 1 .. 17
9 ••
10 .. 2 .. .. 14
7 ..
5 " 7 .. I .. ifi
3 ..
9 •• 5 .. 2 .. 13
7 ..
1 •• 4 .. 1 .. 18
CLOTH MEASURE.
yd.
135
70
95
176
26
279
LONG MEASURE.
(')
qr. n.
E.E.
3 •• 3
272 .
2 •• 2
152 .
3 ••
79 .
1 .. 3
166 •
.. 1
79 .
2 .. 1
164 .
qr. n.
2 •• 1
1 •. i
.. I
2 ••
3 •• 1
2 •• 1
lea. m. far. no.
72 .. 2 .. 1 .. ii9
27 .. 1 .. 7 .. 22
35 .. 2 .. 6 .. 31
79 .. .. 6 .. 12
51 •• 1 .. 6 .. 17
72 .. .. 6 .. 21
(»)
a.
r. p.
726
•• I .. 31
219
.. 2 •• 17
1455
•« 3 .. 14
879
.. 1 .. 21
1195
•" 2 .. 14
LAND MEASURE.
(«)
a.
r.
1232
1
327
131
2 ■
1219
1 .
459
2 .
p
14
19
15
18
17
ADDITION OF MEASURES.
WINE MEASURE.
31
(f)
tlr. scr.
^y.
1 •• ..
12
7 .. 1 ..
17
2 •• ..
14
7 •. 1 ..
Ifi
6 •• 2 ..
13
4 •• 1 ..
18
2.E.
i72
.52
79
56
79
54
in
qr.
n.
• • 2 ♦•
1
• . 1 . .
3
• • ••
1
.« 2 ..
.. 3 ..
1
• . 2 ••
1
(»)
hhds.
gals.
qts.
31 .
. 57.
. 1
97
. 18.
. 2
76 .
. 13.
. 1
55
. 46 .
. 2
87 .
. 38 .
. 3
55 .
. 17.
. I
t, hhds. gals. qts.
14.. 3 .. 27.. 2
19.
.2
.. 56 .
. 3
17.
.
.39 .
. 3
79 .
. 2
.. 16 .
. 1
54
. 1
.. 19 .
. 2
97.
. 3
..54.
. 3
ALE AND BEER MEASURE.
(»)
A.B. fir.
ftal
25 . . 2 .
.7
17.. 3 .
. 5
96 . . 2 .
. 6
75 . . 1 .
. 4
96 . . 3 .
. 7
75 . . .
. 5
(2)
B.B.
fir.
gal.
37.
. 2.
. 8
54.
. 1 .
. 7
97.
. 3.
8
78.
. 2.
5
47.
. 0..
7
35-
• 2 ..
5
(»)
hhds.
gals.
qts
76 .
. 51 .
. 2
57.
. 3 .
. 3
97.
. 27 .
. 3
23.
. 17.
. 2
32.
. 19 .
. 3
65.. 38. .3
lur. po.
•• 1 •• 19
•• 7 .. 22
•• 6 .. 31
.. 6 .. 12
. • 6 .. 17
.. 5 .. 21
(«)
r.
P
.. 1 ..
14
.. ..
19
.. 2 ..
15
.. 1 ..
18
.. 2 ..
17
ch.
75 ,
41
29 ,
70,
54 ,
79 ,
(0
bu.
pks
. 2
. 1
. 24
. 1
. 16.
. 1
. 13
. 2
. 17
. 3
. 25
. 1
(M
w.
d. h.
71
.. 3 ,. 11
51
. . 2 . . 9
76
.. .. 21
95
. . 3 . . 21
79
. . 1 . . 15
DRY MEASURE.
TIME.
(»)
last. wey. q. bu.
38 .. 1 .. 4 .. 5
pks
.. 3
47 . . 1 . . 3 . . 6
.. 2
62 . . . . 2 . . 4
.. 3
45 . . 1 . . 4 . . 3
.. 3
78.. 1.. 1 ..2
.. 2
29 .. 1 .. 3 .. 6
.. 2
. C^)
w.
d. h. m.
»»
57
. . 2 . . 15 . . 42 . .
41
95
.. 3 .. 21 .. 27..
51
76
.. .. 15 •• 37..
28
53
.. 2.. 21 .. 42..
27
9H
= = 2 . . 18 . , 47 . .
as
32
ADDITION.
THE APPLICATION.
of ag^™*" """ *""■" '" *" y*" '''^' «'••«" "-i" he be 47 year.
nineteen Dom,;), LlT? '' *'^ " i* = }"' ■""* <■<»"• ^eor* and
he lend in^X ' ■'"'f-'-S'""^''' ""d » «h"ling. How much did
4. What is the estate worth per annu^.l^hen'^^e ia™
31 guineas, the neat income 8 score, £19 : 14?
5. There are three numbers : the first i, ai'^'^t' ^^^ '}^\^
andthe third is as much as the'clt^'^o:' ^fe^^'ot
6. Bought a parcel of goods, for which I naid 1^4 .\w
7. There are two numbers, the least whefeTfif 4V tWr^dif
t^^'o'f bothT'^^ '" """^^ -'^' " "•« ^-'- — J:a1i^-
a A gentleman left his ellTda^Vh?ef il5W mL'^.b"'";.
younger, and her fortune was 11 thoS.ll h^nleLnd Vn
What was the elder sister's fortune, and what did Sfetthe"'] fav,
Ans. Elder sister's fortune, £1361 1.
Q A 1.1 , , . Father left them £25722.
9. A nobleman, before he went out of town, wa7dSrn,„ ,f
paying all his tradesmen's bills, and upon inZirThe found th/,
he owed 82 guineas for rent ; to his wine-merSt £7? 5 O
10 his confectioner, £12 : 13 : 4 ; to his draper £47 -iV. 9. , '
his tailor, £110 : 15 : 6 ; to his coach-make? £157 S '• n W°
jallow-chandler £8 : 17 : 9 ; .0 his cor^.ch;„d,er,£I70 '• 6 s"
his brewer £52 : 17 : 0; to his butcher,£I22 • 11 • 5'. tohl'
d.',L^\= ^ •■ "'.^""^ '" '•'^ ^"™"'«' <■" wage , £53 :'l8
ie'"reH'",1"Z '!!!l!"r-?_''^''.»i '" ™- in the who.;. whe"n
with him"' ""■"'" ' •^'""' '"^"f "« ^''hed to take
• ^»s. £1032. 17: 3.
ADDITION.
33
10. A father was 24 years of age (allowing 13 months to u
vcar, aild 28 days to a month) when his first chiltl was born ;
between the eldest and next born was I year, H months, I i
days ; between the second and third were 3 years, 1 month, and
15 days >etwcen the third and fourth were 2 years, 10 months,
and 25 (la> ; when the fourth was 27 years, 9 months, and 12
Jays bid, how old was the father ?
, '. , , , >lw,9. ,5S years, 7 months, 10 days.
11. A banker s clerk having been out with bills, brino-s hom?.
an account, that A paid him £7 : 5 : 2, B £15 : Is": 6i C
£150 : 13 : 2^, D £17 : : 8, E 5 guineas, 2 crown pieces, 4
half-crowns, and 4s. 2d., F paid him only twenty groats, G £7t$
15 : 9i, and H £121 : 12 : 4. I desire to know how much the
whole amounted to, that he had to pay ?
,o A ,1 1 . .1715. £396 : 7 : 6|.
12. A nobleman had a service of plate, wliich consisted of
twenty dishes, weighing 203 oz. 8 dwts. ; thirty-six plates, weigh-
ing 408 oz. 9 dwts. ; five dozen of spoons, weighino- 1 12 oz. 8
dwts. ; six salts, and six pepperboxes, weighing"?! oz. 7dwt8. ;
knives and forks, weighing 73 oz. 5 dwts. ; two large cups, a
tankard, and a mug, weighing 121 oz. 4 dwts. ; a tea.kettle and
lamp, weighing 131 oz. 7 dwts. ; togc'.her with sundry other
small articles, weighing 105 oz. 5 dwts. I desire to know the
weight of the whole ?
,„ ., ^ , ^715. 102 lb. 2 oz. 13 dwts.
13. A hop-merchant buy? five bags of hops, of which the first
weighed 2 cwt. 3 qrs. 13 lb. ; the second, 2 cwt. 2 qrs. 11 lb. •
the third, 2 cwt. 3 qrs. 5 lb. ; the fourth, 2 cwt. .3 qrs. 12 <b •
the fi.th, 2 cwt. 3 qrs. 15 lb. Besides these, he purchased two
pockets, each weighing 84 lb. I desire to know the weio-ht of
the whole ? °
1/1 A TAr- « ^1«.'?. 15 cwt. 2 qrs.
^ 14. A, of Vienna, owes to B, of Liverpool, for roods received
m January, the sum of £103 : 12 : 2 ; for gootls received in Fe-
bruary, £93 : .3 : 4 ; for goods received in M-irch, £121 • 17 •
for goods rccdved in April, £142 : 15 : 4 ; for goods received in'
May, £171 : l.j : 10; for goods received in June, £143 : 12 • () •
but the latter six months of the year, owinir to the fallin.r ok'il
the demands for the articles in which he donit, tho amou'it was
only £^.0o : 7 : 2. I desire to know the amount of the whoh^
years bill ?
*
.A/:^. £im : 3: 1.
34
SUBTRACTION.
SUBTRACTION OF MONEY, WEIGHTS & MEASURED
Rule. Subtract as in Integers ; only when any of the lower
denominations are greater tlien the upper, borrow as many of
that as make one of the next superior, adding it to the upper,
from which take the lower ; set down the difference, and carry
1 to the next higher denomination from what you borrowed.
Proof. As in Integers.
£
Borrowed 715
Paid 476
Proof 715
s.
2
3
Remains to pay 238 .. 18
MONEY.
d.
8J
10}
7i
£
Lent 316
Received 218
s. d.
• . 3 . . 5^
. 2 .. If
£> ». d.
87.. 2.. 10
79 .. 3.. 74
(*)
£ s. d.
3.. 15 .. U
1 .. 14 .. 7
(«)
£ *. d.
25 . . 2 . . 5^
17 . . 9 . . 8i
£ a. d.
37..3..4J
25.. 5.. 2i
£ ». d
321 .. 17.. U
257 .. 14. .7
£ 8. d,
59 . . 15 . . 3i
36 .. 17.. 2
(•)
£ a. d.
71 .. 2.. 4
19 .. 13 .. 7*
(10)
£ a. d,
527.. 3 .. 6|
139 .. 5 .. 7J
£ s. d.
Borrowed 25107 . . 15 . . 7
375 ..
5 ..
5i
Paid 259 ..
2 ..
7*
at 359 . .
13 ..
4}
different 523 ..
17 ..
3
times 274 ..
15 ..
7*
325 ..
13 ..
5
Paid in all
Remains to pay
(IS)
£ a. d.
Lent 250156 .. 1 .. 6
7i
3
9«
3i
5
271 ..
13
Received 359 . .
15
at 475 . .
13
several 527 ..
15
payments 272 ..
16
150 ..
\ie lower
many of
e upper,
nd carry
wed.
d.
SUBTRACTION.
TROY WEIGHT.
(I) B*>"ght52..1. 7..2 0) 7.. a.. 2. .^7
Sold 39 . . . . 15 . . 7 5 . . 7 . . 1 . . 5
Unsold
AVOIRDUPOIS WEIGHT.
lb oz. dr. cwt. qra. lb. t. cwt. qrs. lb.
^ ^ S-- J2--S <") 35..!.. 21 (8) 21..1..^2..7
29 .. 12 .. 7 25 .. 1 .. 10 9 .. 1 .. 3 .. 5
APOTHECARIES WEIGHT.
,,, 't o^- <!'• «". lb. oz. dr. 8cr. gr.
<•) ^-f-i"? («) 9. .7. .2..!.. 13
2 • 5..2.. 1 5 .. 7..3.. 1 .. 18
35
(•)
s.
3
^ 1
1
CLOTH MEASURE.
yd. qr. n.
(2) 71.. 1..2
3 .. 2.. 1
>' H^D
..5..
Fl.E. qr. n.
(») 35. .2. .2
17.. 2.. 1
E.R t qr. n.
(») 35.. 2.. 1
14 . 3 . . 2
1
(10)
. 3 ..
d 1
7» ■
1
.5..
yds. ft, in.
(>) 107. .2. .10.
78 .. 2.. 11 .
LONG MEASURE.
bar.
.2 '
lea. nu. fur. po.
147.. 2.. 6.. 29
58 . . 2 . . 7 . . 33
. 6
1
1
. 3*
. 9f
i
H
.
a. r. p.
(^) 175.. l..§7
59..0..27
LAND MEASURE,
a. r. p.
(«) 325.. 2.. 1
279.. 3,. 5
n
*
11
!■
3o
t^vtM nxrrios.
WINL .MKASUUE.
hlid. gal. qts. pt.
(«) 47.. 47.. iJ .. 1
28 . . 59 . . 3 . .
tun. hlid. gal. qt
(8) 42.. 2. .^7. .2
17.. 3. .49. .3
ALE AND REER MEASURE.
A.B. fir. gal.
(>) 25.. 1 .. 2
21 .. 1 .. 5
BR. nr. gal.
( ' ^ :>7 . . '2 . . 1
25 . . 1 . . 7
hhd. gal. q '
(8) 27 .. 27 .. 1
12 . . 50 . . 2
qu. bu. p.
(1) 72 .. I .. 2
CD • . /O . . <>
DRY MEASURE.
(2) 05
bu.
, 2 ,
2.
P-
1
3
eh. bu. p.
(3) 79 .. 3 ..
54.. 7.. 1
yrs. «no, w. <.lg,
(>) 79 .. 8 .. 2.. 4
23.. 9 .. 3
5
TIME.
ho. min.
(8) 24.. 42.. 45
19.. 53.. 47
THE APPLICATION.
1. A man \va« born in the year 1723, what was I^s age in the year 1781 1
Ans. 58.
2. What vi the (iiflfcience between the age of a man born in 1710, and an-
other born in iToG 1
Ans. 56.
8. A McrclKsnt hud five debtors, A, B, C, D, and E, who together owed hira
£1156; B, C, D, and £, owed him £737. What was A.'s debf?
ilns. £419.
4. When an rstatc of £300 [ut annum, is reduced, on the paying of taxcn
to 12 score and i- 14 : i> What is the lax ]
Ans. £45 : 14.
COMPOUND iMULTIPMCATIOX.
31
5. What U the dinbrcncc between £9164, aiui the amount of £754 acKlod lo
£305?
Ana. £8095.
G. A horse in his furniture is worth £37: 5; out of it, 14 guineas ; how much
docs the price of the furniture exceed that of the horse 1
Ans. £7 : 17.
7. A merchant, at his out-scttino; in trade, owed £750; he had in cash,
commodities, the stocks, and good debts, £12510: 7; he' cleared, the first
year, by commerce, £452 : 3 : 6 j what is the neat balance at tae twelve montlis'
endl
ilnj. £12212: 10:6,
8. A gentleman dying, left £452^17 between two daughters, the younger
was to have 15 thousand, 15 hundred, and twice £15. What was the elder
sister's fortune ']
Ans. £28717.
9. A tradesman happening to fail in business, called all his creditors to-
gether, and found he owed to A, £63 : 7 : 6 ; to B, £105 : 10 : to C, £34 : 5 :
•2 ; toD, £28 : 16 : 5; to E, £14 : 15 : 8; to F, £112 : 9; and to G, £143 :
l-i : 9. His creditors found the value of his stock to be £212 : 6, and that he
had owing to him, in good book debts, £112 : 8 : 3, besides £21 : 10: 5 mo-
ney in hand. As his creditors took all his effects into their hands, I desire to
know whether they were losers or gainers, and how much 1
Ans. The creditors lost £146: 11 : 10.
10. My correspondent at Seville, in Spain, sends me the following account
of money received, at different sales, for goods sent him by me, viz : Bees-
wax, to the value of £37 : 15 : 4; stockings, £37 : 6 : 7 ; tobacco, £125 : 11 :
6; hneu cloth, £112:14:8; tin, £115:10:5. My correspondent, at the
same time, informs me, that he has shipped, agreeably to my order, winps
to the value of £250 : 15 ; fruit to the value of £5l : 12 : 6 ; figs, £19 : 17 : 6 •,
oil, £19 : 12 : 4 ; and Spanish wool, to the value of £115 : 15 : 6. I desire to
know how the account stands between us, and who is the debtor 1
Ans. Due to my Spanish correspondent, £28 : 14 : 4.
MULTIPLICATION OF SEVERAL DENOMINATIONS.
Rule.— Multiply the first Denomination by the quantity given, divide the
product by as many of that as make one of the next, set down the remainder,
a.nd add the quotient to the next superior, after it is multiplied.
If the given quantity is above 1^ multiply by any two numbers, which raul-
jp>iru t.ogcttier whi maKe tue same nutubcr ; but if no two numbers multipiit^.ti
together will make the exact number, then multiply the top Une by as many «s
m wanting, adding it to the last product.
D
38
COMPOUND MULTIPLICATION.
Proof. By Division.
£ s. d.
35: 12: 7}
2
71: 5:2J
per yard.
9x2=18
£ s. d.
75:]3:H
3
(3) (♦)
£ s. d. £ «. d,
62:5:4i 57 : 2 : 4f
4 5
1, at 9s. 6d.
9
2. 26 lb. of tea, at £1 : 2 : 6
per lb. 8
ftvS-l- —26
4:5:6
2
^ 9:0:0
3
8: 11:0
27 : ;
Top line X 2 = 2 : 5 :
29 : 5 :
3. 21 ellsofHolland, at7s. 8|d. perell.
Facit, £8:1: 10^.
4. 36 firkins of butter, at 15s. 3^(1. per fii^kin.
Facit, £26 : 15 : 2|.
5. 15 lb. of nutmegs, at 7s. 2^d. per lb.
Facit, £27 : 2 : 21.
6. 37 yards of tabby, nt 9s. 7d. per yard.
^ Facit, £17 : 14 : 7.
7. 97 cwt. of cheese, at £1 : 5 : 3 per cwt. ^,^„ . _
Facit, £122 : 9 : 3.
8. 43 dozen of candles, at 6s. 4d. per doz. „ ,^ .
Facit, £13 : 12 : 4.
9. 127 lb. of Bohea tea, at 12s. 3d. per lb. ^^^ _ ^
Facit, £77 : 15 : 9.
10. 135 gallons of rum, at 7s. 5d. per gallon.
" Facit, £50 : 1 : 3.
11. 74 ells of diaper, at Is. 4|d. per ell. . ^^ . ^
Facit, £5:1:9.
12. 6 dozen pair of gloves, at Is. lOd. per pair.
Facit, £o : 1-5.
When the given quantity consists of i, i, or ^.
Rule. Dlvitle the given price (or the price of one) by 4 for i, by 2 for h and
for i,
j»ro.iuo
first divide by 2 tor i, then divi<1e that quotient by 2 for J, add them to tho
t. and Cicir sum will he thc^ niiswor rctumw
COMPOUND MULTIPLICATION.
13. 25i ells of holland, at 3 : 4^d. per ell.
5_ 5X5=25
16 : 10^
6_
4:4: 4|=25
0:1: 8^=^
39
4:6: 0^=25^
14. 75i ells of diaper, at Is. 3d. per ell.
Facit, £4:14:4i
15. 19A ells of damask, at 4s. 3d. per ell.
Facit, £4:2: lOJ.
16. 354 ells of dowlas, at Is. 4d. per ell.
Facit, £2:7:4.
17. 7i cwt. of Malaga raisins, at £1 : 1 : 6 per cwt.
Facit, £7:15:10^.
18. 64 barrels of herrings, at £3 : 15 : 7 per barrel.
Facit, £24:11 :3^
19. 354 cwt. double refined sugar, at £4 : 15 : 6 per cwt.
Facit, £169 : 10 : 3.
20. 1544 cwt. of tobacco, at £4 : 17 : 10 per cwt.
Facit, £755:15:3.
21. 117i gallons of arrack, at 12s. 6d. per gallon.
Facit, £73:5: 7i.
22. 851 cwt. of cheese, at £1 : 7:8 per cwt.
Facit, £118:12:5.
23. 291 lb. of fine hyson tea, at £1 : 3 : 6 per lb.
Facit, £34 : 7 : 4^.
24. 171 yards of superfine scarlet drab, at £1 : 3 : 6 per yard.
Facit, £20:17:1^.
25. 374 yards of rich brocaded silk, at 12s. 4d. per yard.
Facit, £23 : 2 : 6.
26. 56f cwt. of sugar, at £2 : 18 : 7 per cwt.
Facit, £166:4 :7i.
27. 964 cwt. of currants, at £2 : 15 : 6 per cwt.
Facit, £267 : 15 : 9.
2a 451 lb. of Belladine silk, at 18s. 6d. per lb.
bushels of wheat, at 4s. 3d. per bushel.
87|
per
D2
Facit, £18:12: lU
40
COMPOUND MULTIPLICATION.
30. 1205 cwt. of hops, at £4 ; 7 : G per cwt.
Facit, £528 : 5 : 7^.
31. 407 yards of cloth, at 3s. 9^d. per yard.
_ Facit, £77 : 3 : 2^.
32. 729 ells of cloth, at 7s. 7^d. per ell.
Facit, £277 : 3 : 6^.
33. 2069 yards of lace, at 9s. 5^d. per yard.
Facit, £977 : 19 : 10.
THE APPLICATION.
1. "What sum of money must be divided amongst 18 men, so
that each man may receive £14 : 6 : 8^ ?
Ans. £258 : : 9.
2.^ A p- ivatcer of 250 men took a prize, which amounted to
£125 : 15 : 6 to each man ; what was the value of the prize ?
^«5. £31443: 15
3. What is the difference between six dozen dozen, and half a
dozen dozen ; and what is their sum and product ?
Ans. 792 diff. Sum 936, Product 62208.
4. What difference is there between twice eight and fifty, and
twice fifty-eight, and what is their product ?
Ans. 50 diff 7656 Product.
5. There are two numbers, the greater of them is 37 times
45, and their difference 19 times 4 ; their sum and product are
required? ^tis. 3254 Sum, 2645685 Product.
6. The sum of two numbers is^ 360, the less of them 144 ;
what is their product and the square of their difference ?
Ans. 31104 Product, 5184 Square of their difference.
7. In an army consisting of 187 squadrons of horse, each 157
men, and 207 battalions, each 560 men, how many effective sol-
diers, supposing that in 7 hospitals there are 473 sick ?
Ans. 144806.
8. What sum did that gentleman receive in doAvry with hif<
wife, whose fortune was her wedding suit; her petticoat haviuir
two rows of furbelows, each furbelow 87 quills, and in cacli quiO
21 guineas ? Ans. £3836 : 14 : 0.
9. A merchant had £19118 to begin trade with ; for 5 years
toorether he cleared £1080 a year ; tlje next 4 years he made good
£2715 : 10 : a year ; but the last 3 years he was in tradc"^ he
had the misfortune to lose, one year with another, £475: 4:6a
year ; wliru v/a:! IiIb real fortune at 12 years' end?
' ^n«?. £33984 : 8 : 6.
COMPOUND MULTIPLICATION.
41
10. -In some parts of the kingdom, they weigh their coals by a
machine in the nature of a steel-yard, waggon and all. Three
of these draughts together amount to 137 cwt. 2 qrs. 10 lb., and
the tare or weight of the waggon is 13 cwt. 1 qr. ; how many
coals had the customer in 12 such draughts ?
Ans. 391 cwt. 1 qr. 12 lb.
11. A certain gentleman lays up every year £294: 12: G,
and spends daily £1 : 12 : 0. I desire to know what is his an
nual income ? Ans. £887 : 15 : 0.
12. A. tradesman gave his daughter, ^ a marriage portion, a
scrutoire, in which there were twelve drawers, in each drawer
were six divisons, in each division there were £50, four crown
pieces, and eight half-crown pieces , how much had she to her
^<''*J"«-, . . ^ws. £3744.
13. Admitting that I pay eight guineas and half-a-crown for a
quarter's rent, and am allowed quarterly 15s. for repairs, what
does my apartment cost me annually, and how much in seven
y^a^s ? Ans. In 1 year, £31 : 2. In 7, £217 : 14.
14. A robbery being committed on the highway, an assessment
was made on a neighbouring Hundred for the sum of £386 : 15 :
6, of which four parishes paid each £37 : 14 : 2, four hamlets
£31 : 4 : 2 each, and the four townships £18 : 12 : 6 each ; how
much was the deficiency ? Ans. £36 : 12 : 2.
15. A gentleman, at his decease, left his widow £4560 ; to a
pubhc charity he bequeathed £572 : 10 ; to each of his four ne-
phews, £750: 10; to each of his four nieces, £375: 12: 6; to
thirty poor housekeepers, ten guineas each, and 150 guineas to
his executor. What sum must he have been possessed of at the
time of his death, to answer all these legacies ?
,_ . , . Ans. £10109: 10: 0.
16. Admit 20 to be the remainder of a division sum, 423 the
quotient, the divisor the sum of both, and 19 more, what was the
number of the dividend? Ans. 19544«.
EXAMPLES OF WEIGHTS AND MEASURES.
(») Multiply 9 lb. 10 oz. 15 dwts. 19 grs. by 9.
(') Multiply 23 tons, 9 cwt. 3 qrs. 18 lb. by 7.
(3) Multiply 107 yards, 3 qrs. 2 nails, by TO.
(*) Multiply 33 ale bar. 2firk, 3 oal. bv 11. '
(5) Multiply 27 beer bar. 2 firk. 4 gal.'3 qts. by 12.
(') Multiply no miles, 6 fur. 26 poles, by 12.
ii
I
!|
ll
42
DIVISION.
DIVISION OF SEVERAL DENOMINATIONS.
Rule. Divide the first Denomination on the left hand, and if
any remains, multiply it by as many of the next less as make
one of that, which add to the next, and divide as before.
Proof. By Multiplication.
£ s. d.
2)25:2: 4(
£ s. d.
3)37 :»7 : 7(
£ 5. d.
4)57 : 5 : 7(
n
£ s. d,
5)52 : 7 : 0(
12: 11 :2
(«) Divide £1407 : 17 : 7 by 243.
(s) Divide £700791 : 14 : 4 by 1794.
(■') Divide £490981 : 3 : 7^ by 31715.
(8) Divide £19743052 : 5 : 7^ by 214723.
THE APPLICATION.
1. If a man spends £257 : 2 : 5 in twelve months* time, what
is that per month ? Ans. £21 : 8 : 6^.
2. The clothing of 35 charity boys came to £57 : 3 : 7, what
is the expense of each 1 Ans. £1 : 12 : 8.
3. If I ga-e £37 : 3 : 4^ for nine pieces of cloth, what did I
give per piece ? Ans. £4:2:11.
4 If 20 cwt. of tobacco came to £27 : 5 : 4^, at what rate
is that per c« t. ? Ans. £1 : 7 : 3.
5. What is the value of one hogshead of beer, when 120 are
sold for £164 : 17 : 10 ? . Ans. £1:5: 9^.
6. Bought 72 yards of cloth for £85 : 6 : 0. I desire to know
at what rate per yard ? Ans. £1:3: 8^.
7. Gave £275 : 3 : 4 for 36 bales of cloth, what is that for 2
bales '. Ans. £15 : 5 : 8^.
8. A prize of £7257 : 3 : 6 is to be equally divided amongst
500 sailors, what is each man's share ?
Ans. £14 : 10 : 3^
9. There au 2545 bullocks to be divided amongst 509 men, 1
desire to know how many each man had, and the value of each
man's share, supposing every bullock worth £9 : 14 : 6.
Ans. 5 bullocks each man, £48 : 12 : 6 each share.
DIVISION.
13
id, and if
as make
e.
?. d.
:0(
ne, wliftt
8:6f.
: 7, what
12:8.
hat did I
2: 11.
hat rate
:7:3.
I 120 are
5:9f
to know
hat for 2
3:8J.
amongst
3 : 3^
9 men, 1
3 of each
S.
share.
10. A gentleman has a garden walled in, containing 9625
yards, the breadth was 35 yards, what was the length?
Ans. 275.
11. A club in London, consisting of 25 gentlemen, joined for
a lottery ticket of £10 value, which came up a prize of £4000.
I desire to know what each man contributed, and what each
man's share came to ?
lo A J ^^^' ^^^^ contributed 8s., each share £160.
12. A trader cleared £1156, equally, in 17 years, how much
did he lay by m a year ? ^^5. £68
^ 13. Another cleared £2805 in 7^ years, what was his vea'rlv
increase of fortune ? J J
tA ^TTi. , ^^^* £374.
. oVo, ^* number added to the 43d part of 4429, will raise it
to ^40? "^ Ans.^37.
15.^Divide 20s. between A, B, and C, in such sort that A may,
have 2s. less than B, and C 2s more than B ?
-^ _ , ^715. A 4s. 8d., B 6s. 8d., C 8s. 8d.
10. 11 there are 1000 men to a regiment, and but 50 officers^
how many private men are there to one officer ?
Ans. 19.
17. What number is that, which multiplied by 7847, will
make the product 3013248 ? Jns. 384.
18. The quotient is 1083, the divisor 28604, what was the'di-
vidend if the remainder came out 1788?
Ans. 30979920.
19. An army, consisting of 20,000 men, took and plunderen
a city of £12,000. What was each man's share, the whole
being equally divided among them ?
Ans. 12s>
a }^i ^^i P"^^^' '^"^ ^Tf^oney, said Dick to Harry, are worth 12s.
8d., but the money is worth seven times the purse. What did
the purse contain ? ^^^^ Us, ij,
21. A merchant bought two lots of tobacc*, which weighed
12 cwt. 3 qrs. 15 lb., for £114 : 15 : 6. Their difference, in
point of weight, was 1 cwt. 2 qrs. 13 lb., and of price, £7 : 15 :
o. 1 desire to know their respective weights and value.
Ans. Less weight, 5 cwt. 2 qrs. 15 lb. Price, £53 : 10.
n- • ?^®^^®^ weight, 7 cwt. 1 qr. Price, £61 : 5 : 6.
22. Diviae 1000 crowns in such a manner between A. B. and
C, that A may receive 129 more than B, and B 178 less'than C.
^7?5. A360, B 231, C 409.
44
BILLS OF PARCELS..
EXAMPLES OF WEIGHTS AND MEAflVRE»..
1 . Divide 83 lb. 5 oz. 10 dwts. 17 gr. by 8.
2. Divide 29 tons, 17 cvvt. qrs. 18 lb. by 9.
3. Divide 114 yards, 3 qrs. 2 nails, by 10.
4. Divide 1017 miles, 6 fur, 38 poles, by 11.
5. Divide 2019 acres, 3 roods, 29 poles, by 26.
G. Divide 117 years, 7 months, 3 weeks, 5 days, 11 hours, 2T
piinutes, by 37.
BILLS OF PARCELS.
4
12
15
2
14
35
HOSIERS.
(') Mr. John Thomas,
Bought of Samuel Green. Mity 1,18^*
s, di
8 Pair of worsted stockings, at.. .4 : 6 per pair £
5 Pair of thread ditto 3 : 2
3 Pair of black silk ditto 14 :
6 Pair of milled hose 4 : 2
4 Pair of cotton ditto 7 : 6....
2 Yards of fine flannel 1 : 8 per yard
£7:12:2:
mercers'.
(•) Mr. Isaac Grants
Bought of John Sims.
5. d.
May 3, 18
15
18
12
16
13
23
Yards of satin ...at.. .9 : 6 per yard£
Yards of flowered silk 17 : 4.
Yards of rich brocade 19 : 8
Yards of sarsenet 3 : 2
Yards of Genoa velvet 27 : 6 ,
Yards of lutestring 6 : 3
£62 : 2 : 5
18
5
12
2
4
17
18
15
16
25
17
■ j'u
urs, ^
1,18" 1
:12:2:
BILLS OF PARCELS.
LINEN drapers'.
45
(') Mr. Simon Surety,
Bought of Josiah Short.
s. d.
June 4, 18
4 Yards of cambric at.. .12 : 6 per yard £
12 Yards of muslin 8: 3
15 Yards of printed linen 5 : 4
2 Dozen of napkins 2 : 3 each
14 Ells of diaper 1 : 7 per ell..
35 Ells of dowlas 1 : l^..
£17:4:6i
June 14, 18
MILLINERS*.
(*) Mrs. Bright,
Bought of Lucy Brown.
£ s. d.
18 Yards of fine lace at...O : 12 : 3 per yard £
5 Pair of fine kid gloves : 2 : 2 per pair
12 Fans of French mounts : 3:6 each
2 Fine lace tippets 3 : 3:0
4 Dozen Irish lamb : 1 : 3 per pair.
6 Sets of knots, : 2 : 6 per set..
£23 : 14 : 4
5, IS
1:2:5
June 20, 18
WOOLLEN drapers'.
(») Mr. Thomas Sage,
Bought of Ellis Smith.
£ s. d.
17 Yards of fine serge at...O : 3 : 9 per yard £
18 Yards of drugget ,,.., : 9:0
15 Yards of superfine scarlet 1 : 2:0
16 Yards of black : 18 : ,
25 Yards of shalloon : 1 : 9 ..,.
17 Yards of drab .0 : 17 : 6
£59 : 5 :
46
bills of parcels,
leather-sellers'.
(^) Mr. Giles Harris,
Bought of Abel Smith.
s. d.
July I 18
27 Calfskins at...,3 : 9 per skin £
75 Sheep ditto 1 : 7
36 Coloured ditto 1 : 8
15 Buck ditto 11 : 6
17 Russia Hides 10 : 7
120 Lamb Skins.... 1 : 2^
£3S : 17 : 5
GROCERS
{') Mr. Richard Groves,
Bought of Francis Elliot. July 5, 18
s. d.
25 lb. of lump sugar at...O : 6i per lb. £
2 loaves of double refined, ) • \\l
weight 15 lb. ) *
14 lb. of rice : 3
28 lb. of Malaga raisins : 5
15 lb. of currants 0: 5^
7 lb. of black pepper , 1 : 10
£3:2: 9^
CHEESEMONOERS\
(') Mr. Charles Cross,
Bought of Samuel Grant.
s, d.
July 6, 18
8 lb. of Cambridge butter at...0 : 6 per lb. £
17 lb. of new cheese : 4
^ Fir. of butter, wt. 28 lb : 5^..
5 Cheshire cheeses, 127 lb : 4
2 Warwickshire ditto, 15 lb : 3 .,
12 lb. of cream cheese : 6
£3:14:7
REDUCTION.
n
CORN-CI> ^*ni>LERS\
C) Mr. Abraham Doyley.
Bought of Isaac Jones.
Tares, 19 bushels at...l
Pease, 18 bushels 3
Malt, 7 quarters 25
Hops, 15 lb 1
Oats, 6 qrs 2
Beans, 13 bushels 4
July 20, 18
d.
10 per bushel £
9^
per quarter
5 per lb
4 per bushel
8
£23 : 7 : 4
REDUCTION
Is the bringing or reducing numbers of one denomination into
other numbers of another denomination, retaining the same value,
and is performed by multiplication and division.
First, All great names are brought into small, by multiplying
with so many of the less as make one of the greater.
Secondly, All small names are brought into great, by dividing
with so many of the. less as make one of the greater.
A TABLE OF SUCH COINS AS ARE CURRENT IN ENGLAND.
£ a. d.
Guinea. 1: i:0
Half ditto : 10 : 6
Sovereign 1 : 0:0
Half ditto 0: 10:
Crown 0: 5:0
Half ditto 0: 2:6
Shilling 0: 1:0
Note. There are several pieces which speak their own
value ; such as sixpence, fourpence, threepence, twopence,
penny, halfpenny, farthing.
rl. In £8, how many sjiillings and pence ?
20
160 shillings.
1920
^
REDUCTION.
2. in £12, how many shillings, pence, and farthingi? ?
Alls. 240s. 2880d. 11520 far
3. In 311520 farthings, how many pounds ?
Ans. £324 : 10.
4. How many farthings are there in 21 guineas ?
Ans. 21168.
6. In £17 : 5 : 3^, how many farthings ? Aiis. 16573.
6. In £25 : 14 : 1, how manv shillings and pence ?
Ans. 514s. 6169d.
7. In 17940 pence, how many crowns ? Ans. 299.
8. In 15 crowns, how many shillings and sixpences ?
Ans. 75s. 150 sixpences
9. In 57 half-crowns, how many pence and farthings ?
Ans. 1710d. 6840 farthings.
10. In 52 crowns, as many half-crowns, shillings, and pencftj
how many farthings ? Ans. 21424.
11. How many pence, shillings, and pounds, are there in
.17280 farthings ? Ans. 4320d. 360s. £18.
12. How many guineas in 21168 farthings ?
Ans. 21 guineas.
13. In 16573 farthings, how many pounds ?
Ans. £17 : 5 : 3^
14. In 6169 pence, how many shillings and pounds ?
Ans. 514s. £25 : 14 : 1.
15. In 6840 farthings, how many pence and half-crowns ?
Ans. 1710d. 57 half-crowns.
16. In 21424 farthings, how many crowns, half-crowns, shil-
■lings, and pence, and of each an equal number ? Ans. 52.
17. How many shillings, crowns, and pounds, in 60 guineas ?
Ans. 1260s. 252 crowns, £63.
18. Reduce 76 moidores into shillings and pounds ?
Ans. 2052s. £102 : 12.
19. Reduce £102 : 12 into shillings and moidores ?
Ans. 2052s. 76 moidores.
20. How many shillings, half-crowns, and crowns, are there
in £556, and of each an equal number?
Ans. 1308 each, and 2s. over.
21. In 1308 half-crowns, as many crowns and shillings, how
many pounds ? Ans. £555 : 18.
22. Seven men brought £15 : 10 each into the mint,^to be ex-
changed for guineas, how many must they have in all ?
Ans. 103 guineas, 7s. over.
REDUCTION.
49
23. If 103 guineas and seven shillings are to be divided
amongst seven men, how many pounds sterling is that each ?
Ans, £15 : 10.
24. A certain person had 25 purses, and in each purse 12 gui-
neas, a crown, and a moiilorc, how many pounds sterling had he
in all ?
Ans. £355.
25. A gentleman, in his will, left £50 to the poor, and ordered
that -^ should be given to ancient men, each to have 5s. — ^ to
poor women, each to have 2s. 6d. — ^ to poor boys, each to have
Is. — }■ to poor girls, each to have 9d. and the remainder to the
person who distributed it. I demand how many of each sort
there were, and what the person who distributed the money had
for his trouble ?
Ans, 66 men, 100 women, 200 boys, 222 girls,
£2 : 13 : 6 for the person's trouble.
TROY WEIGHT.
26. In 27 ounces of gold, how many grains ?
Ans, 12060.
27. In 12960 grains of gold, how mar.y ounces ?
Ans, 27.
28. In 3 lb. 10 oz. 7 dwts. 5 gr. how many grains ?
Ans. 22253.
29. In 8 ingots of silver, each weighing 7 lb. 4 oz. 17 dwts.
16 gr. how many ounces, pennyweights, and grains ?
Ans. 711 oz. 14221 dwts. 341304 gr.
30. How many ingots, of 7 lb. 4 oz. 17 dwts. 15 gr. each, are
there in 341304 grains ? Ans. 8 ingots.
31. Bought 7 ingots of silver, each containing 23 lb. 5 oz. 7
dwts. how many grains ? Ans. 945336.
32. A gentleman sent a tankard to his goldsmith, that weighed
60 oz. 8 dwts. and ordered him to make it into spoons, each to
weigh 2 oz. 16 dwts. how many had he ?
Ans. 18.
33. A gentleman delivered to a goldsmith 137 oz. 6 dwts. 9
gr. of silver, and ordered him to make it into tankards of 17 oz.
16 dwts. 10 gr. each; spoons of 21 oz. 11 dwts. 13 gr. per doz..
•alts of 3 oz. 10 dwts. each; and forks of 21 oz. 11 dwts. 13 gr.
perdoz. and for every tankard to have one salt, a dozen of spoons,
and a dozen of forks ; what is the number of each he must have T
Ans* 2 of each sort, 8 oz. 9 dwts. 9 gr. over.
m
M
M
if
I !
Iji.
If
fiO JIEDUCTIOK.
AVOIRDUPOIS WEIGHT.
NoTB.— There are several sorts of silk which are wcij^hcJ by a (jreal
pound of 24 oz. others by the coninion pound of 10 oz. ; thcrctorc,
To bring great pounda into common, multiply by 3, and divide by 2, or add
one half.
To bring small pounds into great, multiply by 2, and divide by 3, or subtrM
ope third.
lyings bought and sold by the TaU.
12 Pieces or things moke 1 Dozen.
12 Dozen 1 Gross.
12 Gross, or 144 doz 1 Great Gross.
24 Sheets 1 auire.
20 Cluires I Ream.
2 Rt^ams 1 Bundle.
I Dozen of Parchment.. 12 Skins.
12 Skins 1 Roll.
34. In 147G9 ounces how many cwt.! o^n o^ n. i «.
Ana. 8 cwt. qr. 27 lb. I en.
36. Reduce 8 cwt. qrs. 27 lb. I oz. into qwarters, Pounds and ouncw.
Ans. 32 qrs. 923 lb. 147b9oz.
if
36 Bought 32 bags of hop, each 2 cwt. 1 qr. 14 lb. and anothey of 150 lU.
i»ow many cwt. in the whole t ^^ ^^ ^^^ ^ ^^ ^^ ^^
37. In 34 ton, 17 cwt. 1 qr. 19 lb. how many pounds 1 ^^ TgUlIb.
88. In 547 great pounds, how many common pounds 1 ^^^ ^^ ^^ ^ ^
39. In 27 cwt >f raisins, how many parcels of 18 lb. each 1 ^^^ ^^
40. In 9 cwt. 2 qrs. 14 lb. of indigo, how many pounds 1 ^^^ ^^ ^^
41. Bought 27 bags of hops, each 2 cwt I qr. 15 lb. and one bag of 187 lb.
how many cwt in the whole f ^^^ ^^ ^^ 2 ^^ ^q ^^
43. How many pounds in 27 hogsheads of tobacco, each weighing neat 8t
*wt.1 ilns. S64CO,
43. In 552 common pounds of silk, how many great pound* 1 ^^^g^g
. . /• </< tv o ,_ ..«« <tiara in IG CWt 1 QT.
44. How man^ parceis oi fiugar oi lu i;.. - ---. «. ^.. —
^ ^''^ Ans. 113 parcels, and 13 lb. 14 oi. ovef.
KF.DIJCTION.
61
3, or iul<?
r «ubtr«e
APOTHECARIES' WEIGHT.
46. In 27 lb. 7 oz. 2 dr. 1 scr. how many grains I
Ans. 159022.
46. ilow many lb. oz. tlr. acr. are there in 159022 frruina ?
A7ts. 27 lb. 7 oz. 2 dr. 1 scr.
lb. 1 08.
mcee.
1769 ofc
of 150 Ik
r. 10 lb.
8111 Ih.
ib.8<n.
ns. iQBl
10781b
of 187 lb.
rs. 10 lb.
ng neat 8|
?. 36460,
[ns. 368.
cwt 1 or.
o%. owe».
CLOTH MEASURE.
47. In 27 yards, how many nails ? Ans. 432.
48. In 75 English ells, how many yards ?
Ans. 93 yard?, 3 qrs.
49. In 93| yards, how many English ells ? Ans. 75.
60. In 24 pieces, each containing 32 Flemish ells, how many
English ells ? Ans. 460 English ells, 4 qrs.
61. In 17 pieces of cloth, each 27 Flemish ells, how many
yards? Ans. 344 yards, 1 qr.
62. Bought 27 pieces of English stufT, each 27 ells, how many
yards? Ans. 911 yards, 1 qr.
53. In 911^ yards, how many English ells ?
Ans. 729.
54. In 12 bales of cloth, each 25 pieces, each 13 EngliHh ells,
how many yards ? Ans. 562f
LONG MEASURE.
66. In 57 miles, how many furlong iid poles?
A71S. HM? furlongs, 18240 poles.
66. In 7 miles, how many feet, inches, arul barley-corns ?
Ans. 36960 ft. 413520 in. 1330560 b. corns.
67. In 18240 poles, how mar\y furlonirs and miles?
Ans. 456 furlongs, 57 miles.
58. In "i 2 leagues, how many yards? Ans. 380160.
59. In 380160 yards, how many miles and leagues ?
Ans. 216 miles, 72 leagues
60. If from London to York be accounted 50 leagues, I de-
mand how many miles, yards, feet, inches, and barley-corns ?
Ans. 150 miles, 264000 yards, 792000 feet,
9504000 inches, 28512000 barlry-corns.
61. How often will the wheel of a coach, that is 17 feet in
circumference, turn in 100 miles ?
Ans. 31068j^ times round.
c2
m
REDUCTION.
19
62. How many barley-corns will reach round the world, the
circumference of which is 360 degrees, each degree 69 miles and
a half? iln5. 4755S01000 badey-corns.
LAND MEASUItE.
63. I'i 27 acres, how many roods and perches ?
Ans. 108 roods, 4320 perches.
64. In 4320 perches, how many acres? Ans^, 27*
66. A person having a piece of ground,'containing 37 acires, 1
Sole, has a mind to dispose of 15 acres to A. I dedre to knovir
ow many perches he will Iwtve left?
Ans. %1U
66. There are four fields to be dii^ded into shai-es of 75 perches
each ; the first fieM containing 5 acres ; the second, 4 acres, 2
poles ; the third, 7 acres, 3 roods $ and the fourth, 2 acres, 1 rood.
I desire to know how many shares are contained therein?
Ans. 40 shares, 42 perches rem.
WllSnS MEASURE.
67. iBought 5 tuns of port wine, how many gallons and pints ?
Ans. 1260 gallons, 10080 pints.
68. In 10080 pints, how many tuns ? Ans. 5 tuns.
69. In 5896 gallons of Canary, how many pipes and hogs-
heads, and of each an equal number ?
Ans. 31 of each, 37 gallons over-
70. A gentleman ordered his butler to bottle off f of a pipe
of French wine into quarts, and the rest into pints. I desire to
know how many dozen of each he had ?
Ans. 28 dozen of each.
ALE AND BEER MEASURE.
71. Ih 46 barrels of beer, how many pints .
Ans. 1324a
79. In 10 barrels of ale, how many gallons and quarts ?
Ans. 320 gals. 1280 qts.
*^ In 72 hogsheads of ale, how many barrels ?
Ans. iOS.
ti. In 108 barrels of ale, how many hogsheads ?
Ane. 1%
rid, the
lies and
orns.
SINGLE RULE OF THttEB DiaKOT.
DRY MEASURE.
53
ches*
acfes, 1
know
perches
Acres, 2
1 rood,
n?
rem.
i pints ?
pints,
tuns.
i hogs-
over.
r a pipe
lesire to
each.
75. In 120 quarters of wheat, how many bushels,. pecks, igal
Ions, and quarts ?
Ans. 960 bushels, 3840 pecks, 7680 gallons, 30720 qts.
76* In 30720 quarts of corn, how many quarters?
Ans. 120
77. In 20 chaldrons of coals, how mdny pecks?
Ans. 2880.
78* In 273 lasts of corn* how many pecks?
Ans. 8736a
TIME.
79. In 72015 hours, how many weeks ?
Ans. 428 weeks, 4 days, 15 hours.
80. How many days is it since the bhrth of our Saviour, to
<3hristmas, 1794 ? Ans. 655258^.
81. Stowe writes, London was built 1108 years before our
Saviour's birth, how many hours is it since to Christmas, 1794 ?
Ans. 25438032 hours.
82. From November 17, 1738, to September 12, 1739, how
many day 8? ^Tis. 299.
83. From July 18, 1749, to December 27 of the same year
how many days? Ans. 162.
84. From July 18, 1723, to April 18, 1750, how many years
Mid days ? Ans. 26 years, 9770^ days,
reckoning 365 days 6 hours d yean
THE SINGLE RULE OF THREE DIRECT,
324a
ts?
Oqts.
. lOS.
e. 72.
Teacheth by three numbers given to find out a fourth, in such
proportion to the third, as tlie' second is to the first,
Rule. First state the question, that is, place the numbers in
such order, that the first and third be of one kind, and the second
the same as the number required ; then bring the first and third
numbers into one name, and the second into the low>3st term men-
tioned. Multiply the second nnd third numbers together, and
e3
54
8INGLE RULE OV THREE I^IRECT.
divide the product by the first, and the quotient will be the an-
swer to the question in the same denomination you left the second
number in.
EXAMPLES.
1. If 1 lb. of siigar cost 4j, what cost 54 lb. 1
1:44 ::54
4 18
— Ana. £1:0: Z.
18 4)972
12)243
20s. 3d.
3. If a eallon of beer cost lOd., what is that per barrel 1
^ Ans. £1 ; 10. .
3. If a pair of shoes cost 4s. 6(1., what will 12 dozen come to %
Ans. £32 : a
4. If one yard of cloth cost 158. 6d,, what will 32 yards cost at the sazna
rate 1 -Aws- £24 : 16.
5. If 32 yards of cloth cost £24 : 16, what is the value of a yard 1
Ans. 15s. 6d.
6. If I ffive £4 : 18 for 1 cwt. of sugar, at what rate did I buy it per lb. 1
Ans. lOjd.
7. If I buy 2a pieces of cloth, each 20 ells, for 12s. Od. per ell, what is the
▼olue of the whole 1 Ans. £250.
8. What will 25 cwt. 3 qrs. 14 lb. of tobacco come to, at I5jil. per lb. 1
Ans. £187 : 3 : 3.
9. Bou'Tht27j yards of muslin, at 6s. 9 id. per yard, what does it amount
Ijq'I " Ans. £i) : 5 : 0}, 3 rem.
10 Bought 17 cwt. 1 or. 14 lb. of iron, at 3id. per lb., wliat docs it come
tol " Ans. £20:11:01
11. If coffee is sold for 5id. per ounce, what must be given for 2 cwt. 1
yln«. £82 : 2 : 8.
12. How many yards of cloth may l>e bought for £21 : 11 : li, when 3|
yards cost £2 : l4 : '3 ? Ans. 27 yards, 3 qrs. 1 nail, 84 rem.
%fi Tf 1 nmf nf nh*^«hire cheese cost £1 : 14 : 8. what must I ffive for 3i
Ibl
Ans. Is. Id.
14. Bouffht I cwt. 24 lb. 8 oz. of old lead, at 9s. iier cwt., what docs it come
tol " Ans. 10s. lUd. 113 rem.
SIKOLt; RVLB OF THREE DIRECT.
as»
13. \i » g. nneman's income is £500 a year, and ho spcnck 19«. 44- per day,
liow much does he lay by at the year's end 1 Ans. £147 : 3 : 4.
16. If I buy 14 yards of cloth for 10 guineas, how many Flemish ella can I
buy for £ii83 : 17 : 6 at the same rate 1
Ans. 504 Fl. ells. 2 qr».
17. If bOi Flemish ells, 2 quarters, cost £283 : 17 : 6, at what rate did I y&j
for 14 yards ]
Ans. 10s. lOd.
18. Gave £ 1 : 1 : 8 for 3 lb. of coffee, what must bo given for 29 lb. 4 oz 1
Ans. £10: 11 : 3,
19. If one English ell 2 qrs. cost 48. 7d. what will 39i yards coet at the same
ratcl
Ans. £5:3: 5^, 5 rem.
'20. If one ounce of gold is worth £5:4:2, what is the worth of one grain 7
ilns. 2jd. 20 rem.
'21. If 14 yards of broad cloth cost £9 : 12, what is the purchase of 75 yeards 1
iln*. £51 :8:6|,erom.
22. If 27 yards of Holland cost £5 : 12 : 6, how many ells English can I buy
for £1001 ilns.384.
23. If 1 cwt. cost £12 : 12 : C>, what must I give for 14 cwt. 1 qr. 19 lb. 1
Ans. £182:0: llj, 8rem.
34. Bought 7 yards of cloth for 178. 8d. what must be given for 5 pieces, each
containing 274 yards 1
iln«. £17 : 7 : 0}, 2 rem.
25. If 7 oz. 11 dwts. of g' ' ■ h^ worth £35, what is the value of 14 lb. 9 oi
12 dwts. 16 gr. at the same ,. I
Ans. £833 : & : 3}, 552 rem.
26. A draper bought 420 yards of broad cloth, at the rate of 148. lOjd. per ell
English, how much did he pay for the whole 1
Ans. £250 : 5.
27. A gentleman bought a wedge of gold, which weighed 14 lb. 3 oz. 8 dwts.
for the sum of £514 : 4, at what rate did he pay for it per oz. 1
Ans. £3.
28. A grocer bought 4 hogsheads of sugar, each weighing neat 6 cwt. 2
qrs. 14 lb. which cost him £:i: 8 : 6 per cwt.; what is the value of the 4
hogsheads 1
Ans. £64 : 5 : 3.
29. A draper bought 8 packs of cloth, each containing 4 parcels, each })arcel
10 pieces, and each piece 2() yards, and gave after the rate of £4 : 16 for 6 yards ;
I desire to know what the 8 packs stood him to 1
Ans. £G65t5.
30. If 24 lb. of Kusins cost 68. 6d. what will 18 fraib cost, each weighing ueai
3 qrs. 18 lb. 1
Ans. £SM ; 17 : 3.
31. If I oz. of silver t)e worth 5s. what is the price of 14 ingots, cnch wei|:h-
ing 7 lb. 5 oz. 1 ) dwts. 1 Ans. £313 : 5.
32. What is the price of a pack of wool, weighing 2 cwt. 1 qr, 19 lb. at 8fc.
6d. i>er stone 1
Ans. £8:4: G}, 10 rem.
QT PrftTtrvKf M /•«»♦ # #iiHj OA IK >n.f fr\\\ari*f\ of CO.' 17 • A TtnY rviri • trKnt line*
it coi^c to ^
Ans.£llk.Z:li 80 rem.
56
RULE OF THREE INVERSE.
34. Bought 171 tons of lead, at £14 per ton; paid carnage
and other incident charges, £4 : 10. I require the value of the
lead, and what it stands me in per lb. ?
Ans. £2:398 : 10 value ; l^d. 433 rem. per lb.
35. If a pair of stockings cost 10 groats, how many dozen may
I buy for £43 : 6 ?
Ans. 21 dozen, 7^ pair.
36. Bought 27 dozen 5 lb. of • andles, after the rate of 17d.
per 3 lb. what did they cost me ?
Ans, £7:15 : 4^, 1^ rem.
37. If an ounce of fine gold is sold for £3 : 10, what come 7
ingots to, each weighing 3 lb. 7 oz. 14 dwts. 21 gr.^ at the same
price ? Ans. £1U71 : 14 : 5^.
39. If my horse stands me in 9^d. per day keeping, what will
be tlie charge of 1 1 horses for the year ?
Ans. £159 : 18 : 6^.
39. A factor bought 86 pieces of stuff, which cost him £617 :
19 : 4, at 4s. lOd. per yard ; I demand how many yards there
were, and how many ells English in a piece ?
Ans. 2143^ yards, 56 rem. and 19 ells, 4 quarters,
2 nails, 61 rem. in a piece.
40. A gentleman hath an annuity of £896 : 17 per annum.
I desire to know how much he may spend daily, that at the yearns
end he may lay up 200 guineas, and give to the poor quarterly
40 moidores? Ans. £1 : 14 : 8, 176 rem.
THE RULE OF THREE INVERSE.
Inverse Proportion is, when more requires less, and less re-
quires more. More requires less, is when the third term is great-
er than the first, and requires the fourth term to be less than the
second. And less requires more, is when the third term is less^
than the first, and requires the fourth term to be greater thfui:
tlie second.
Rule. — Multiply the first and second terms together, and di-
vide the product by the third, the quotient will bear such propor
tion to the second as the first does to the thiid..
RUI.fi or TBREB INTEMi'
m
EXAMPLES.
h l( 8 men can do a piece of work in 12 days, hovr many
days can 16 men perform the same in ? 4n9* 6 dtiy«.
8 . 12 . . 16 . e
8
16)96(6 days.
2. If 54 men can build a house in 90 days, how many can do
Ihe same in 50 days ?
Ans, 97^ men.
3. If, when a peck of wheat is sold for 28., the penny loaf
weighs 8 oz., how much must it weigh when the peck is worth
but Is. 6d. ?
Ans. lOf oz.
4. How many pieces of money, of 20s. value, are equal to
240 pieces of 128. each ? Ans. 144.
5. How many yards, of three quarters wide, are equal in mea-
sure to 30 yards, of 5 quarters wide ? Ans. 50.
6. if I lend my friend £200 for 12 months, how long ought
he to lend me £150, to requite my kindness ?
Ans. 16 months.
7. If for 24s. I have 1200 lb. carried 36 miles, how many
pounds can I have carried 24 miles for the same money ?
Ans. 1800 lb.
8. If 108 workmen finish a piece of work in 12 days, how
nany are sufficient to finish it in 3 days ?
Ans. 432.
9. An army besieging a town, in which were 1000 soldiers,
with provisions for 3 months, how many soldiers departed, when
the provisions lasted them 6 months ?
Ans. 500.
10. If £20 worth of wine is sufficient to serve aft ordinary of
100 men, when the tiiu is sold for £30, how many will £20
worth suffice, when the tun is sold but for £24 ?
An!^. 125.
11. A courier makes a journey in 24 days, when the day is
but 12 hours long, how many days will he be going the same-
journey, when the day is 10 aours long?
Ans. 18 days...
58
DbVBLG RULE OF THREE.
12. How much plush is sufficient for a cloak, which has in it
4 yards, of Tquaiters wide, of stuff, for the lining, the plush beiag
but 3 quarters wide ?
Ans. 91- yards.
13. If 14 pioneers make a trench in 18 days, how many dayt
will 34 men take to do the same ?
Ans. 7 days, 4 hours, 50 min. -,-V, at 12 hours for a day.
14. Borrowed of my friend £()4 for 8 months, and he had oc-
casion another time to borrow of me for 12 months, how much
must I lend him to requite his former kiridness to me ?
Ans. £42 : 13 : 4.
15. A regiment of soldiers, consisting of 1000 men, are to have
new coats, each coat to contain 2A yards of cloth, 5 quarters wide,
and to be lined with shalloon of 3 quarters wide ; I demand how
many yards of shalloon will line them ?
Ans. 41(50 yards, 2 qrs. 2 nails. 2 rem
THE DOUBLE RULE OF THREE,
Is so called because it is composed of 5 numbers given to find a
6th, which, if the proportion is direct, mupt bear such a proportion
to the 4th and 5th, as the 3d bears to the 1st and 2d. But if in-
verse, the 0th number must bear such pro])ortion to the 4th and
5th, as the 1st bears to the '2d and lid. The three first terms are
a supposition; the two Uif^t, a demand.
Rule 1. Let the principal cause of loss or gain, interest or
decrease, action or passion, be put in tlie first place.
2. Let that wliich betokenctli time, distance of place, and the
like, be in the second place, and the remaining one in the third!
3. Place the other two terms under tlieir like in the supposi-
tion.
4. If the blank falls under the third term, multiply the first and
second terms for a divisor, and the other three for a dividend.
But,
5. If the blank falls under the first or second term, multiply
♦}w> fl»ii«/l niul fourth terms for a divisor, ?ind the other three fo?
the dividend, and the quotient will be the answer.
Proof. By two single rules of tlirec.
DOUBLE RULE OF THREE.
09
EXAMPLES.
1 . If 14 horses eat 5G bushels of oats in 16 days, how many busheb will b»
sufficient fur 20 horses for 24 days 1
By two single rules. ^ or in one stating, worked thus ;
hor. bu. hor. Iiu. | hor. days. bu.
bu.
1. As 14 . 50 . . 20 . 80
days. bu. days. bu.
2 As IC . 80 . . 24 . 120
14.16.56 56X20X24
20.24.— =120
14X16
2. If 8 men in 14 days can mow 112 acres of grass, how many mea must
there be to mow 2000 acres in 10 daysl
acres, days, acres, days.
1. As 112 . 14 . . 2000 . 250
days. men. days. men.
2. As 250 . 8 . . 10 . 200
men. days, acres.
8 . 14 . 113 . 8 X 14 X 2000
=200
- . 10 . 2900 112X10
3. If £100 in 12 months gain £G interest, how much will £75 gain kt 9
months 1 Ans. £3:7: 6.
4. If a carrier receives £2 : 2 for the carriage of 3 cwt. 150 miles, how much
ought he to receive for tbis carriage of 7 cwt. 3 qrs. 14 lb. for 50 miles 1
Ans. 1 : 16 : 9.
5. If a regiment of soldiers, consisting of 136 men, consume 351 quarters of
wheat in 108 dajs, how many quarters of wheat will 11232 soldiers consume in
56 days ]
Ans. 15031 qrs. 864 rem.
6. If 40 acres of grass be mowed by 8 men in 7 days, how many acres can
be mowed by 24 men in 28 days 'i Ans. 480.
7. If 40s. will pay 8 men for 5 days' work, how much will pay 32 men fur
84 days' work 1 Ans. £38 : 8.
8. If £100 in 12 months gain £6 interest, what principal will gain £3:7:
6 in 9 months 1 Ans. £75.
9. If a regiment, consisting of 939 soldiers, consume 351 qrs. of wheat in 168
days, how many soldiers will consume 1404 qrs. m 56 days 1
Ans. 11968.
10. If a family consisting of 7 persons, drink out 2 kilJerkins of beer in 12
lays, how many kilderkins will another family of 14 persons drink out in 8
daysl Ans. 2 kil. 12 gal.
11. If the carriage of GO cvrt. 20 miles, cost £14 : 10, what weight can I
Lave carried 30 miles for £5 : 8 : 9, at the same rate of carriage 1
Ans. 15 cwt.
12. If 2 horses cat 8 bushels of oats in 16 days, how many horses will eat up
3000 quarters in 24 days 1
Ana. 4000.
13. If £100 in 12 inonlbs gaiii £7 inU^rcsl, wba 'm thi^ iuiiirtfit of £571 fo*
6 years 1
Ans. £239; 16:41,20 rem.
60'
fRACTICE.
14. If I pay 10s. for the carriage of 2 tons 6 miles, whatmiui
I pay for the carriage of 12 tons, 17 cwt. 17 miles?
Ans. £9 i2:0^.
PRACTICE,
Is so called from the general use thereof by all persons concern
ed in trade and business.
All questions in this rule are performed by taking aliquot, ov
even parts, by which means many tedious reductions are avoided ,
the table of which is as follows : —
Of
10:
6:
5:
4:
3:
2:
2:
1:
a Pound.
d.
\j • • •IS*** 2
a i
i
4
i
X
••••6
6 i
0.
8.
1
-JL.
13
Of a shilling.
d
4
3 i
2
H
1
JL
3
J.
6
JL
8
-J-
13
Of a Ton.
cwt.
5. i
4.
3i
2
X
6
X
8
10
Of a Hundred.
ors. lb.
2 or 56 is f
1 or 28 i
14 i
Of a Quarter.
14 lb i
7 i
4 4
3^ i
Rule 1. When the price is less than a penny, divide by the
aliquot parts that are in a penny ; then by 12 and 20, it will be
the answer.
(J.)iisi)57041b. at 4:
12)1426
2|0)ni&:10
Facit,£5:18: 10
(2) 7695 at ^
Facit, £16:0: 7^
(3) 5470 at?.
Facit, £11 :7:11
(4) 6547 at I
Facit, £20 : 9 : 2i
(S)4573at|
Facit, £14 : 5 : 9^
Rule 2, When thn price is less then a shillinff, take the ali-
quot part or parts that'ure in a shilling, add them together, and
divide bv 20, as before
PRACTICE.
61
i
r.
i
i
JL
'7
JL
8
(»)is-iV764Tatld.
2|0)63|8:11
Facit, £31 :8: U
(«)lis-iV3751atlid
fisi 312:7
78: 1|
3|0)3910 : 8^
Facit, £19: 10 ;8J.
(^) 54325 at Hd.
Facit, £339: 10: 7^.
(«)6254atHd.
Facit, £45: 12:0^;
(5)2351 at 2d.
Facil, £19: 11 : 10.
(«)7210at2id
Facit, £67:11:10^.
(')2710at2^d.
Facit, £28:4: 7.
(8)3350 at 2^d.
Facit, £37 : 4 : 9^.
(9) 2715 at 3d.
Facit, £33 : 18 : 9.
(^»)7062at3id.
Facit, £95 : 12 : 1^.
(»')2147at3id.
Facit, £31 : 6 : 2|^.
(»-^)7000at3H
Facit, £109 : 7 : 6.
(>»)3257at4d.
Facit, £54 : 6 : 8.
('♦)2056at4^d.
Facit, £36 : 8 : 2.
(»°)3752at4id.
Facit, £70: 7:0.
(»'»)2107at4|d.
Facit, £41: 14 :0i.
(»')32I0at5d.
Facit, £66: 17:6.
(»«)2715at5^d.
Facit, £59 : 7 : 9^.
(»»)3120at5id.
Facit, £71 : 10:0.
(«'»)7521 atSH
Facit,£180:3:9i
(2 1)3271 at6d.
Facit, £81 : 15:6.
(2 2) 7914 at 6H
Facit, £206: 1:10A.
(2 3)3250ut6^d.
Facit, £83 : : 5.
(2 *) 2708 at Of d.
Facit, £76 : 3 : 3.
(2'-')3271 at7d.
Facit, £95 : 8 : 1.
(2«)3254at7id.
Facit, £98:5: 11|.
(2 7)2701 at7<^d.
Facit, £84:8: 1|.
F
(i8)37l4at7|d.
Facit,£119:18:7i.
(2»)2710at8d.
Facit, £90 : 6 : 8.
(3 0)35l4at8id.
Facit, £120: 15: 10^.
(3')2759at8id.
Facit, £97 : 14 : 3J.
(»2)9872at8|d.
Facit, £359:8:4.
('9)5272 at 9d
Facit, £197 : 14 : 0.
(^*)G325at9id.
Facit, £243: 15 :6i.
(»«)7924at9^d.
Facit, £313:13:2.
(3«)2150at9|d.
Facit, £87 : 6 : 10^.
(3-)r)32oat lOd.
Facit, £263: 10: 10.
(3s)572-4atlO:Jd.
Facit, £244 : 9 : 3.
(3 3)6327atlOid.
Facit, £270 : 4 : 3|.
(*«)3254atlOJd.
Facit, £142 : 7 : 3.
(^')729latl0|d.
Facit, £326: 11: 6^.
(*2) 3256 at lid.
Facit, £149: 4:8.
69<
PHACTlCtJ.
i*')??^^! allied. |(**)3754atnid. \r'^)rm^tUid
Facit, £340 : : 7i. | Faeit, £179 : l| : 7. | Facit! S^?5 ! U.
Rule 3. When the price is more than one shilling, and less
than two, take the part or parts, with so much of^ie Vyel
price as 18 more than a shilling, which add to the given L^^^^^^
and divide by 20, it will give the answer ^ quantity,
(')iTV210(Jatl2|d.
43 : 10^
2|0)21 1|9 : 10^
(')i«V37]5atl2^d.
154 : 9i
2|0)3S6i9 : 9^^
(0 2712 at 12|d.
Facit, £144 : 1 : 6.
Facit, £107 : 9 : 10^. I Facit, £193 ; 9 : 9^.
(0 3215 at Is. Hd.
Facit, £177:9: lOi
(0 2790'itls. I^d7
Facit, £156 : 18 : 9.
7904 at Is. l^d.
Facit, £452 : 16 : 8.
r03254atls.3|d.
Facit, £213: ).0: 10^.
CO 2915 at Is. 4d~
Facit, £194:0:8.
(0 2107 at Is. Id.
Facit, £114:2: 7.
(0 3750 at Is. 2d.
Facit, £218 : 15 : 0.
CO 3270 at Is. 4fd.
Facit, £221 : 8 : 1^.
C0 7103atls.6|d.
Facit, £540 : 2 . 5|.
('^03254atld.6^d.
Facit, £250 : 16 : 7.
CO 7925 at Is. 6fd.
Facit, £619 ; 2 : 9|.
(0 3291atls. 2id.
Facit, £195:8 : 0:^
("^)925l"^ir2^d~
Facit, £559: I : H.
("^0^725071172^17
Facit^£4l5;ll;5j.
C0 75"977T77k
Facit, £474 : 8 : 9.
CO 6325 at Is. 3^d!
Facit, £401 : I8:0|.
(J ' )^7Jun73H
CO 7059 at Is. 4^d.
Facit, £485 : : 1^.
CO 2750 at Is. 4|d.
Facit, £191: 18:0^.
(^0 37257tll"5dir
Facit, £263 : 17 : 1.
CO 7250 at U.&Jd.
Facit, £521 : 1 : 10|.
{' 'T25977rrsT5idT
Facit, £189 : 7 : 3.1.
(-0 ^271 at Is. 7d.
Facit, £733 : 19 : 1.
('^0 72I0atls. 7H
Facit, £578:6: 0|.
(^OSSlTatlTTid;
Facit, £187 : 13 : 9.
COssoTTls. 7|d.
Facii, £206 : 1:2.
('07l727tTr8d.''
Facit, £596 : : 0.
C ' ) 72 10 at 1 s. 5id. j ( 3 2905 at I s. 8^d.
I;ac^t^£533 : 4 : 9^ Facit, £245 : 2 : 2^.
niACTlOB,
63
[*\^n^ ft W. I(*«) 1071 at l8. lOd. I(*M2105atl8 lUA
('"')3l04atls. 9(1.
Facit, £184 : 2 : 0.
(*')5300atls.l04d.
Facit, £482 : 1 : 8.
(•')2571atl3.9id.
Facit, £227 : 12 : 9|.
(»»)2104atls.9^(L
Facit, £188 : 9 ; 8.
(•»)7506atl8. 9H
Facit, £680 ; 4 : 7f
(*'^)21l7atl8.10^d.
Facit, £198 : 9 : 4^.
r^) 1007 at Is. 10^
Facit, £95 : 9 : Ij.
(**)500pat Is. lid.
Facit, £479 : 3 : 4.
(^MlOOOatls.lUd.
Facit, £98 : 10 : K
(*02705atl8.11|d.
Facit, 267 : 13 : 7if.
(^«75000atl8.1Ud,
Facit, £489: 11:8.
(*'')4000atls.llfd.
Facit, £395 : 10 : 8.
2750 at 2s.
Facit, £275 : : 0.
(»)3254at4s.
Facit, £050 : 16 : 0.
P2102atl08. 1(^)1075 at IBs.
Facit, £1051 ; ; . j Facit, £860 : : 0.
(')2101 at 12^.
Facit, £1260:12:0.
2710 at 6s.
Facit, £813 : : 0.
{*) 1572 at 8s.
('")l621atl8s.
Fat t, £1458: 18:0.
Note. When the
(')527I at 14s.
Facit, £3689 : 14 : 0. price is lOs. take half
of the quantity, and
if any remains, it is
10s.
(«) 3123 at 16s.
Facit, £628 : 16 : 0. i Facit, £24{)8 : 8 : 0.
Rule 5. When the price consists of odd shillings, multiply
the given quantity by the price, and divide by 20, the quotient
will be the answer.
( ' ) 2703 at Is.
Facit, £135 .3:0.
(=) 3270 at 3s.
3
2|0)981|0
Facit, £490 : 10 :
P2
(3)3271 at 5s.
Facit, £817 : 15 . a
64
PRACTICE.
(«)2715at78.
Facit, £950 : 6 : 0.
(»)3214 at 98.
Facit, £1446 : 6 : 0.
(')3179atl3«.
Facit, £3066 : 7 : 0.
(8) 2150 at 15s.
Facit, £1612:10:0.
(•)2710at lis.
Facit, £1490:10:0.
(»»)2160att98.
Facit, £2042: 10 :l»
(»')7l57atl98.
Faeit, £6799 : 3 : i'
(») 3142 at 178.
Facit, £2670: 14:0.
Note. When the price is 5s., divide the quantity by 4, ani
if any remain, it is 5s. '
Rule 6. When the price is shillings and pence, and they the
aliquot part of a pound, divide by the aliquot part, and it will
give the answer at once ; but if they are not an aliquot part,
then multiply the quantity by the shillings, and take parts for
the irest, add them iygcther, and divide by 20.
(»)7614at48. 7d.
Facit, £1721 : 19:2.
6:8
2
2j0
i
i
(•)2710at6s. 8d.
Facit, £903 : 6 : 8.
('*)3150at39. 4d.
Facit, £525 : : 0.
(»)2715at2». 6d.
Facit, £339 : 7 : 0.
(«)7150atls. 8d.
Facit, £595 : 16 : 8.
(«)3215at ls.4d.
Facit, £214:6:8.
('')7211 at Is. 3d.
Facit, £450 : 13 : 9.
('r2710"at3s. 2d.
3
8130
451 :8
85Sil :8
Facit £429
1 :8.
(») 2517 at 5s. 3d.
Facit, £660 : 14 : 3.
(,0)
Fac
{'')
1 1
Fac
Fac
(13)
Fac
Fac
(16)
Fac
(la)
Fac
Fac
2547 at 7s. S^d.
t, £928: 11: 10^.
3271 at 5s. 9^d.
t, £943: 16:4i
2103 at 15s. 4^d.
t, £1616: 13: 7^.
7152 at 17s. 65d
t, £6280 : 7 : 0.
2510atl4:7ild.
t, £1832: 16: 5^.
3715 at 9s. 4 id.
t, £1741 :8:"U,.
2572atl3:7^d.
t, £1752 : 3 : 6.
72.51 at Hs.8id.
t, £5324: 19 0%
l^RACTIOE.
<V5
|(»») 3210 at 158. 73d.
|Facit,£2511.3.y.
|(»«)27!0atl98. 2i<i
iFacit. £2002.14.7.
RtLG 7. Ist, When the price is pounds and shillings, multiply
the quantity by the pounds, and proceed with the shillings, il
they are even, as the fourth rule ; if odd, take the aliquot parts^
add them together, the sum will be the answer.
2d!y, When pounds, shillingj*, and pence, and the shillings and
pence the aliquot parts of a pound, multiply the quajitity by the
pounds, and take parts for the re^t.
3dly, When the price is pounds, shillings, pence* and far*
things, and the shillings and pence are not the ali juot parts of a
pound reduce the pounds and shillings into shillings,, multiply
the quantity by the shillings, take parts f^.. 1? *^ rcst^add them:
together, and divide by 20.
Note. When the given quantity co.:s:-t9ci' no more than,
tliree figures, proceed as in Compound Mu ^wi^ation.
«. d
2.01
\
(») 7215 at £1.4.0
7
60505
1443
£51948
JL
8
(«)2104at£5.a.O
i
10520
263
52.12
£10835.12
() 2107 at £2. 8.0.
Facit, £5050 . 10 . 0.
(<) 7156 at £5. 0.0.
Facit, £37926. 16.0.
&
li
h
a|Oj
1^3
(»)2730at£2.3.7i..
43
116530.
1.355
338. »:
11822|3.9
Pack, £5911.3.0.
(*)3215at£1.17.0-
Facit, £5947 . 16 0.
(.')2107at£1.13.0.
Facit, £3476. IKO.
(«) 3215 at £4. 6. 8.
Facit, £13931. 13. 4.
(9) 2154 at £7. 1.3.
Facit, £15212. 12. «.
m
PRACTICE,
(»»)2701at£2.3.4.
Facit, £585JJ .3.4.
('»)2715at£1.17.2i.
Facit, £5051 .0.lh.
(»2)2157at£3.15.2i.
Facit, £8108. 19.5^.
(»')3210 at £1.18.61.
Facit, £6180 . 5 . 1^.
(»«)2157at£2.7.4|.
Facit, £5100. 7. 10^.
(»»)l42at£1.15.ai.
Facit, £250 . 2 . 6^.
('«)Vi5at£15.14.7|.
Facit, £1494 . 7 . 4|.
(")37at£1.19.5i
Facit, £73.0.' 8|.
(»«)2175at£2.15.4i.
Facit, £6022 . . 7^.
(»»)2150at£17.16.1^
Facit, £38283.8.0,
Rule 8. When the price and quantity given are of several
denominations, multiply the price by the integers, and take parts
with the parts of the integers for the rest.
I. At £3.17.6 per cwt., what is the value of 25 cwt. 2 qrs. 14 lb. of tobacco 1
£3.17.6
5X5=25
lb.
14
19. 7.6
5
96.17.6
1.18.9
9.8J
99.5. Hi
2. At £1 . 4 .9 per cwt., what comes 17 cwt. 1 qr. 17 lb. of
cheese to? ylns. £21 . 10.8.
S. Sold 85 cwt. 1 qr. 10 lb. of cheese, at CI . 7 . 8 per cvi't,
what does it come to ? Arts. £1 18 . 1 . 0|.
4. Hops at £4 . 5 . 8 per cwt., what must be given for 72 cwt
1 qr- IS lb.? 7l7i5. £310.3.2.
5. At £1 . 1 . 4 per cwt., lyhat is the value of 27 cwt, 2 qrs,
15 lb. of Malaga raisins ?
^7Z5. £29.9.6i.
fi. Rr»iia-f»f 7Q rnrt Q n\-a TO IK nC m.,>~
cwl., what did I give for the whole ?
^ns. £227.14.
uixis, ai, v~.>-.^ . 1 * . ;? pur
TARE AND TRET.
W
it. Sold 56 cwt. 1 qr. 17 lb. of sugar, at £2 : 15 : 9 the cwu.
what cioes it come to? Ans. £157 : 4 : 44.
S. Tobacco at £3 : 17 : 10 the cwt., what is the wcyrth of 07
cwt. 15 lb. ? Ans. £378 : : 3.
9. At £4 : 14 : 6 the cwt., what is the value of 37 cwt. 2 qrs.
13 lb. of double refined sugar 1
Ans. £177 : 14 : 8^
10. Bought sugar at £3 : 14 : 6 the cwt., Avhat did I give for
15 cwt. 1 qr. 10 lb. ? Ans. £57 : 2 : 9.
11. At £4 : 15 : 4 the cwt., the value of 172 cwt. 3 qrs. 12 lb.
of tobacco is required? Ans. £823 : 19 : 0^.
12. Soap at £3 : 11 : 6 the cwt., what is the value of o3 cwt.
171b.? ^ws. £190 : : 4.
TARE AND TRET.
The allowances usually made in this Weight, are Tare^ TVcf,
and Cloff,
Tare is an allowance made to the buyer for the weight of the
box, barrel, bag, &c., which contains the goods bought, and ia
either
At so much per box, bag, barrel, &.c.
At so much per cwt., or
At so much in the gross weight.
Tret is an allowance of 4 lb. in every 101 lb. for waste, dust,
&.C., made by the merchant to the buyer.
Cloff is an allowance of 2 lb. to the citizens of London, on
every draught above 3 cwt. on some sort of goods.
Gross weight is the whole weight of any sort of goods, and
that which contains it.
Suttle is when part of the allowance is deducted from the gross.
Neat is the pure weight, when all allowances are deducted.
Rule 1. Wh^n the tare is at so much nor hnv. barrel, &C.,
multiply the number of bags, barrels, &c. l)y the tare, and sub-
tract the product from the gross, the remainder is neat.
06
TARE AND TRET.
Note. To reduce Pounds into Gallons, multiply by ^ and
divide by 15.
1. In 7 ffaiN of raisins, each weighing 6 cwt. 2 qrs. 51b. gross,
tare at 23lb. per frail, how much neat weight?
Arts. 37 cwt 1 qr. 14 lb.
23 ft. 2. 5- or, 5. 2. 5
7 7 S3
4
58)161(5 38.3. 7=gro6». 6.1.10
140 1.1.2l=tare 7
1.1
21 37.1.14=neal 37.1.14
3. What is the neat weight of 25 hogsheads of tobacco, weigh-
ing gross 163 cwt. 2 qrs. 15 lb., tare 100 lb. per hogshead?
Ans. 141 cwt. 1 qr. 7 lb.
3. In 16 bags of pepper, each 85 lb. 4 oz. gross, taic per bag
3 lb. 5 oz. how hiany pounds neat ? Ans, 1311.
Rule 2. When the tare is at so much in the whole gross
weight, subtract the given tare from the gross, the remainder if
neat.
4. What is tlie neat weight of 5 hogsheads of tobacco, weigh-
ing gross 75 cwt. 1 qr. 14 lb., tare in the whole 752 lb. ?
Ans. 68 cwt. 2 qrs. 18 lb.
5. In 75 barrels of figs, each 2 qrs. 27 lb. gross, tare in the
whole 697 lb. how much neat weight ?
Ans. 50 cwt. 1 qr.
Rule 3. When the tare is at so much per cwt., divide the
gross weight by the aliquot parts of a cwt., which subtract from
the gross, the remainder is neat.
Note. 7 lb. is -jV, 8 lb. is -^, 14 lb. is i, 16 lb. is -f.
6. What is the neat weight of 18 butts of currants, each 8 cwt
2 qr;?. 5 lb., tare at 14 lb. per cwt. ? /
8.2.5
9x^13
76
3 . 17
2
4=i 153 .3. 6
19 . . 25}
134 . 2 . 8|
tARB AND TRET.
83
t. In 25 barrels ot figs, each 2 cwt. 1 qr. gross, tare per cwt,
16 lb., how much neat weight ?
Ans. 48 cwt. qr. 24 lb.
8. What is the neat weight of 9 hogsheads of nutmegs, each
treighing gross 8 cwt. 3 qrs. 14 lb., tare 16 lb. per cwt. ?
Ans. 68 cwt. 1 qr. 24 lb.
Ruti 4. When tret is allowed with tare, divide the poundt
suttic by 26, the quotient is the tret, which subtract from the aut-
tie, the remainder is neat.
9. In 1 butt of currants, weighing 12 cwt 2 qrs. 24 lb. gross,
tare 14 lb. per cwt, Iret4 lb. per 194 lb., how many pounds neat?
13 . 8 . ^
4
50
28
14=1 1424 grom,
178 tare.
86)1246 sutUe.
47 tret.
1199 neat.
iO. In 7 cwt 3 qrs. 27 lb. gross, tare 361b., !tret4 lb. per 104
lb., how many pounds neat ?
-Atos. 8261b.
11. In 152 cwt 1 qr. 3 lb. gross, tare 101b. per cwt, tret 4 lb.
per 104 lb., how much neat weight ?
H Ans, 133 cwt 1 qr. 12 lb.
Rdlb 5. When cloff is allowed, multiply the cwts. suttle by
2, divide the product by 3, the quotient will be the pounds clofli
which subtract from the suttle, the remainder will be neat
12. What is the neat weight of 3 hogsheads of tobacco, weigh-
Sug 2i; ewt. o qrs. ^ Ih. gross, tare 7 ib. per cwt, tret 4 lb per
m
U)., doff 21b. for 3 cwt 7
Ans. 14 cwt 1 qr. 3 Ib.
TO
INTBRS8T.
7=|V 15 . 3 . 20 grow.
3 . 27itare.
26)14 . 3 . 20i suttle.
y 2.8 tret.
14 . 1 . 12^ suttle.
9i cloff.
14 . 1 . 3
13. In 7 hogsheads of tobacco, each weighing gross 5 ewt. d qn. 7 Vt ,
tare 8 lb. per cwt., tret 4 lb. per 104 lb., doff 2 lb. per 3 cwt., how much ne»*
weight 1 Ana. 34 cwt. 2 qrs. 8 lb.
SIMPLE INTEREST,
b the Profit allowed in lending or forbearance of any sum of money for a
determined space of time.
The Principal is the money lent, for which interest is to be received.
The rate per cent, is a certain sum agreed on between the Borrower and
the Lender, to be paid for every £100 for the use of the principal 12 months.
The Amount is the principal and interest added together.
Interest is also applied to Commission, Brokage, Purchasing of Stoclu^
and Insurance, and are calculated by the same rules.
To jind the Interest of any Sum of Money for a Year.
Rule 1. Multiply the Principal by the Rate per cent,, that Product divi-
ded by 100, will give the interest required.
For several Years,
2. Multiply the interest of one year by the number of years given m the
question, and the product will be the answer.
3. If there be parts of a year, as months, weeks, or days, work for th«
months by the aliquot parts of a year, and for the weeks and days \3y the
Rule of Three Direct.
EXAMPLES.
1. What is the interest of £375 for a year, at 5 per cent, per annoEal
5
18175
20
15100
Ans. £18 . 15 . 0.
2. What is the interest of £368 for 1 year, at 4 per cent, per annum 1
Ana. £10 . 14 . 4|.
3. What is the interest of £945 . 10. for a year, at 4 per cent, per annum 1
Ana. 3T. 16 . 4|.
INTEREST.
71
4. What is ihc interest of £547 . 15, at 5 per cent, per annum, for 3 years 1
Ans. £82 .3.3.
5. What is the interest of £254 . 17 . 6, for 5 years, at 4 per cent, per an-
'^"^ ^ Ans. £50 . 19 . 6.
G. What ia the interest of £556 . 13 . 4, at 5 per cent, per annum, for 5
y^'^^^ iln*. £139.3.4.
/•''iiS^ *^°O^P°"''ent writes me word, that he has bought goods to the amount
of £ /54 . lb on my account, what does his commission come to at 2^ per cent. ]
^n*. £18.17. 4i.
8. If I allow my factor 3| per cent, for commission, what may he demand on
the laymg out £876 . 5 . 10 ? Ans. £32 . 17 . 2j.
9. At I10{ per cent., what is the purchase of £2054 . 16. South Sea Stock 1
Ans. £2265 .8.4.
10. At 101| per cent. South Sea annuities, what is the purchase of 1797 . 14 1
ilns. £1876.6.111.
11. At 96} per cent., what is the purchase of £577 . 19 Bank annuities!
^ns. £559 . 3 . 3|.
la At £124| per cent, what is the purchase of £758 . 17 . 10, India Stock!
Ans. £945 . 15 . 4*.
BROKAGE,
Is an allowance to brokers, for helping merchants or factors to persons, to buy or
•ell them goods.
RuLR. Divide the sum given by 100, and take parts from the quotient with
tne rate per cent.
13. If I employ a broker to sell goods for me, to the value of £2575 . 17 . G.
what IS the brokage at 4s. per cent. 1
25|75 ,, 17 . 6
20 . 4s.=|25.15.2
15|17
12
2110
Ans. £5 . 3 . Oi
14. When a broker sells goods to the amount of £7105 . 5 . 10, what may ho
lemand for brokage, if he is allowed 5s. 6d. per cent. ?
^ns.£19. 10.9}.
c}^r 'J^^^'ojei'ls employed to buy a quantity of goods, to the value of
£>\)lo .0.4, what is the brokage, at Gs. 6d. per cent. 1
Ans. £3.3. 4j.
16. What is the interest of £547 .2.4, for 5j years, at 4 per cent, per an-
"""^ * Ans. £120 . 7 . 3fc.
- ■- -.^=»tt, 1= uic inicresi oi s,;io/ . D . i, ai 4 per cent., ior a year and three
quarters
Ans, £18 . . \\.
18. Whatia the interest of £479 . 5 for 5* years, at 5 per cent, per annum 1
ilns. £125. 16.0J.
72
INTEREST.
19. What is the interest of £576 : 2 : 7 Corl^ years, at4i P^
cent, per annum ?
Ans. £187 : 10 : 1^.
20. What is the interest af £279 : 13 : 8 at 5^ per cent, per
annum, for 3^ years ?
Ans. £51 : 7 10.
When the interest is required for uny nunber of Weeks.
Rule. As 52 weeks are to the Interest of the given sun^ for
« year, so are the weeks given for .the interest required.
21. What is the interest of £259 : 13 : 5 for 20 we* Its, at 5
per cent, per annum ?
Ans. £4 : 19 lOi.
22. What is the amount of £375 ; 6 : 1 for 12 weeks, at %
per cent, per annum ? Ans. £379 : 4 : 0|.
When the Interest is fur at:-^ mimhsr of days*
RvLE. As 365 days are to Ihj? i^tiereat of the given sum for &
7««r, so are the days giv^sn ia the intere&t required.
23. At 5^ per cent, per annum, what is the interest of £965 .
2 . 7 for is> years, 127 davs?
Ans. £289 . 15 . 3.
24. What is the interest of £2726 . 1 . 4 at 4^ per cent, per
annum, for three years, 154 days ?
Ans. £419 . 15 . 6^.
When the Amount^ Time, and Rate per cent, are given tofin6
the Principal.
Rule. As the amount of £100 at the rate and time given : is
io £100 : : 80 is the amount given : to the principal required.
25. What principal being put to interest, will amount to £402
10 in 5 years, at 3 per cent, per annum ?
3 X 5+ 100=£115 . 100 . . 402 . 10
20 20
2300
8050
1AA
2W
S3HX^}''050|00(£350 Aiu.
INTEREST.
73
at 4^ per
9:U.
cent, per
:710.
^eeks.
sum lor
eks, at 5
9 10i.
ks, at 4^j
4:0i.
um for &
15.3.
eent. per
5.6|.
71 to find
riven : is
[uired.
; to £402
26 What principal being put to interest for 9 years, will
amount to £734 : 8, at 4 per cent, per annum 1
Ans. £540.
37. What principal being put to interest for 7 years, at 5 per
cent, per annum, will amount to £334 : 16 ?
Ans. £248.
When the principal, Rate per cent., and Amouat are given,
to find the Time,
Rule. As the interest of the principal for 1 year : is tol year : :
«o is the whole interest : to the time required.
28. In what time will £350 amount to £402 . 10, a4 3 per cent,
per annum ?
350
3
Asl0.10:l::52.10:5
20 20
10|50
20
210 2ll0)105|0(5yean.
105
iifw. 402.10
350.
10|00 52.10
29. In what time will £540 amount to £734 r 8, at 4 per cent
per annum 1 Ans. 9 years.
30. In what time will £248 amount to £334 : 16, at 5 per
cent, per annum ? Ans. 7 years.
When the Principal, Amount, and Time, are given, to find the
Rate per cent.
Rule. As the principal : is to the interest for the whole time : :
so is £100 : to the interest for the same time. Divide that in-
terest by the time, and the quotient will be the rate per cent.
31. At what rate per cent, will £350 amount to £402 : 10 in
5 years' time ?
350
52.10
Ab350:52.10::100:£15
20
1050
100
32. At what rate per cent
7 years' time ?
35|0)10500|0(3008.=£15-i-5=3 per cent
ill £248 amount to £33"
10 in
Ans. 5 per cent
74
INTEREST.
33. At what rate per cent, will £640 amount to £734 : 8 in 9
years' time ? Ans. 4 per cent.
COMPOUND INTEREST,
Is that which arises both from the principal and interest ; that
is, when the interest on money becomes due, and not paid, the
same interest is allowed on that interest unpaid, as was on the
principal before.
Rule 1. Find the firstyear's interest, which add to the princi-
pal ; then find the interest of that sum, which add as before, and
flo on for the number of years.
2. Subtract the given sum from the last amount, and it will
give the compound interest required.
EXAMPLES.
1. Wl»t is the compound interest ^of £500 forborne 3 years,
at 5 per cent, per annum I <
26. .5
500 500
5 25
25100 5^5= l#t year.
26125
5^
551 . . 5=2d year.
5
551.. 5
27156.. 5 27. 11.. 3
20
11125
12
578.16..3=3dyear.
5Q0 prin. sub
3100
78 . 16 . . 3=intere8tforSyeaw.
3. What is tbe amount of £400 forborne 3^ years, at^-p^r
cent, per annum, compound interest ?
Ans. £490 : 13 : lU-
3. What will £650 amount to in 5 ye^rs, at 5 per cent, per
annum, compound intereiSt? Ans. £839 : 11 : 7^.
4. What is the amount of £550 : 10 for 3 years and 6 months,
at (3 per cent, per annum, compound interest ?
^»s. £675 : 6 : 5.
5. What is tlie compound Interest of £764 for 4 years and 9
months, at 6 per cent, per annum ?
Ans. £343 : 18 : 8.
6. What ifi the compound interest of £57 : 10 : 6 for 5 years,
7 months, and 15 days, at 5 per cent per annum ?
Ans. £18 : 3 : 8^.
REBATE OR DISCOUNT.
75
7. What is the compound interest of £259 : 10 for 3 years, 9
months, and 10 days, at 4^ per cent, per annum ?
Ans. £46 : 19 : 10^.
REBATE OR DISCOUNT,
Is the abating of so much money on a debt, to be received be-
fore it is due, as that money, if put to interest, would gain in the
same time, and at the same rate. As £100 present money would
discharge a debt of £105, to be paid a year to come, rebate being
made at 5 per cent.
Rule. As £100 with the interest for the time given : is to
that interest : : so is the sum given : to the rebate required
Subtract the rebate from the giveii sum, arid the remainder
will be the present worth.
EXAMPLES.
1. What is the discount and present worth of £487 : 12 for 6
months, at 3 per cent, per annum ?
3
100
103
487 : 13 prindpaL
14 : 4 rebate.
Ail03:0::487:12
aO 20
2060
9752
3
£«.
Ans. £473 : 8 present wortn
20610)292516(14.4 rebate.
206
IS
824
2. What is the present payment of £357 : 10, which wag
agreed to be paid 9 months hence, at 5 per cent, per annum ?
^ns. £344 : 11 : 7.
3. \Yhat is ihe discount of £275 : 10 for 7 months, at 5 per
cent, per annum? Ans, £7 : 16 : If.
Q3
w
EQUATION OF PAYMENTS.
4. Bought goods to the value of £109 : 10, to be p lid at nine
months, what present money will discharge the same, if I am al-
lowed 6 per cent, per annum discount?
Ans. £10^: 15 : 8^.
6. What is the present worth of £527 : 9 : 1, payable 7 month*
hence, at 4^ per cent. ? Ans. £514 : 13 : lOf^.
6. What is the discount of £85 : 1^', ^hm September thr 8th,
this being July the 4th, rebate at 5 ^^ei C(*'i , ..er annum?
Ans. 15s. 3fd.
7. Sold goods for £875 : 5 ; C, to be paid 5 months hence,
what is the present worth at 4^ per cent. ?
Ans. £859 : 3 : 4.
8. What is the present worth of £500, payabl^^ i.». ki, i.iciths,
at 5 per cent, per annum ? Ans. £480.
9. How much ready money can I receive for a note of £75,
due 15 mon'ihs hence, at G per cent. ?
Ans. £70 : 11 : 9^.
10. Whiit will be tlse present worth of £150, payable at 3
four months, i.e. one tLird at four months, one third at 8 months,
and one third at 12 months, at 5 per cent, discount ?
A71S. £145 : 3 : 8^.
11. Sold goods to the value of £575 : 10, to be paid at 2 three
months, what must be discounted for present payment, at 5 per
cent; ? Ans. £10 : 1 1 : 4f .
12. What ifl the present worth of £500 at 4 per cent., £100
being to be paid down, and the lest at 2 six months ?
Ans. £488 : 7 : 8^
EQUATION OF PAYMENTS,
Is when several sums are due at different time to fird a mean
time for paying the whole debt ; to do which thi ^s t- common
RvLB. Multiply eaclii term by its time, and div ide the sum
of the products by iMe whole debt, ihe quotient is accounted the
inea*- time.
ii
I \l
at nine
[ am al-
:8i.
months
lOf.
he 8th,
3^(1.
hence,
?:4.
-ic'iths,
C480.
of £75,
ble at 3
months,
i:8i.
, 2 three
at 5 per
t., £100
:8^
a mean
ommon
the sum
nteu the
EQUATION OF PAYMENTS.
EXAMPLES.
t/
1. A owes B £200, whereof £40 is to be paid at 3 months,
£60 at 5 months, and £100 at 10 months ; at what time may the
whole debt be paid together, without prejudice to either ?
£ m.
40
X
3 =
120
60
X
5 =
300
too
X
10 =
2 00)
1000
14 20
7 months
1 6
2. B owes C £800, whereof £200 is to be paid at 3 months,
£100 at 4 months, £300 at 5 months, and £200 at 6 months ;
but they agreeing to make but one payh^at of the whole, I de-
mand what time that must be ?
Ans. 4 months, 18 days.
3. I bought of K a quantity of goods, to the value of £360,
which was to have been paid as follows : £120 at 2 months, and
£200 at 4mo'?iths, and the rest at 5 months ; but they afterwards
agreed to hav c it pai'^ at one mean time ; the time is demanded.
Ans. 3 months, 13 days.
4. A merchar ought goods to the value of £500, to pay £100
at the end of 3 ionth«' '15( at the end of 6 months, and £250 at
the end of 12 months , i alter ards they agreed to discharge
the debt at one payment ; u. vhat time was this payment made ?
Ans. 8 months, 12 days.
5. H is indebted to L a certain sum, which is to be paid at 6
different payments, that is, [ at 2 moi.< s, f at 3 months, f 1
m( nths, ■}- at 5 months, -i- at 6 months, an.j the rest at 7 months ;
bu! they agree that the whole should be paid at one equated time i
wiiat is that time ?
Ans. 4 lonths, 1 qu-^rter.
6. A is indebted to B £1*30, whertoi | is to be paid at 3
months, 4^ -t « months, a^ 1 the rest st 9 months h
equated time of the whole payment ?
IS. 5 nonths days.
G3 ^
IS iii8
78
:
BARTER.
BARTER
Is the exchanging of one commodity for another, and informi
the traders so to proportionate their goods, that neither may
sustain loss.
Rule 1st. Find the value of that commodity whose quantitj
is given ; then find what quantity of the other, at the rate pro
posed, you may have for the same money,
2dly. When one has goods at a certain price, ready money,
but in bartering, advances it to something more, find what the
other ought to rate his. goods at, in proportion to that advance,
and then proceed as before.
EXAMPLES.
1. What quantity of chocolate, at
As. per lb. must be delivered in barter
for 2 cwt., of tea, at 98. per lb. 1
2 cwt.,
112
"224 lb.
9 price.
4)2016 the value of the tea.
5041b. of chocolate.
2. A and B ])arter ; A hath 20 cwt.
of prunes, at 4d. per lb. ready money,
but in barter will have .5d, per lb. and
B. hath hops worth 328. per cwt.,
ready money whai ottght B to rate
his hops at in barter, and what quan-
tity muist, bo given for the 20 cwt., of
prunes 1
112 As 4: 5:: 32
20 6
8.
40
12
2240
5
-cwt. qr. lb.
4)160
408.
4810)112010(23 . 1 . 9|f .An*.
96
160
144
16=1 qr. 9 lb. ||.
3. How much tea, at 93. per lb. can I have in barter for 4 cwt., 2 qrs. of
chocolate, at 4s, per lb. 1 , « .
' *^ Ans. 2 cwt.
4. Two merchants barter ; A hath 20 cwt. of cheese, at 21s. 6d. per cwt. ;
B hath 8 pieces of Irish cloth, at £3 . I4s. per piece : I desire to know who must
receive the difference, and how much *? ^ «. « ^o «
Ans. B must receive of A x-o . ».
r>. A and B barti^r •. A hath 3l lb. of nepper at I3id. per lb. ; B hath gin-
ger at I5td. per lb.; how much ginger must he deliver m barter for thr
^^^' - Ans. 3 lb. 1 oz. l\.
PROnX AND LOSS.
70
6 How many dozen of candles, at 5b. 2d. per dozen, must bo delivered in
barter for three cwt. 2 qrs. 16 lb. of tallow, at 378. 4d. per^cwt.^ ^^ ^ ^^
7. A hath 608 yards of cloth, worth Us. per yard, for which B riyeth him
£125 . 12. in ready money, and 85 cwt. 2 qrs. Jt lb. of bcca'-wax. The ques-
tion is. what did B rockon his bees'- wax e.t per cwt. 1 , ^o i n
8. A and B I irter ; A hath 320 dozen of candles, at 43. 6tl. per dozen; for
which B giveth him £30 in money, and the rest in cotton, at 8d. per lb. ; 1 dcsiro
to know how much cotton B gave A besides the money 1
Ans.ll cwt. 1 qr.
9. If P. hath cotton, at Is. 2d per lb., how much must he give A for 114 lb. of
tobacco, at 6d. per lb. 1 . ^o n i •?
10. C hath nutmegs worth 7s. Od. per lb. ready money, but in barter will
have 8s. per lb.; and D hath leaf lobacco worth 9d. per lb. ready raciicy;
how much must D rate his tobacco at per lb. that hia profit may be equivalent
PROFIT AND LOS&
Is a Rule that discovers what is got or lost in the buying or selling
of goods, and instructs us to raise and lower the price, so as to
gain so much per cent, or otherwise.
The questions in this Rule are performed by the Rule of Three.
EXAMPLES.
1. If ayar.' of cloth is bought for 2. If 60 ells of Holland cost £J8
lis. and sold for I'is, 6d. what is the
gain per cent. 1
As 11 : 1 : G : : 100
12 20
18
12.6
11.0
2000
18
11)30000
12)3273^.
2I'0)27I2 . 8
Ans. £13 . 12 . S^^.
what must 1 ell be sold for to gain 8
per cent. 1
As 100 : 18 : : 103
108
1 100)19144
20
8|80
12
9160
4
12X5=60
12)19. 8.9i
5)1 . 12.41
0. 6.51
2j40
-Ans Gs. 5 id.
so
FELLOWSHIP.
ii
'%
2 If 1 lb. of tobacco cost I6d. and is sold for 20d. what is the gain per cent. 1
Ans. £25.
4. If a parrel of cloth be sold for £560, and at 12 per cent, gain, wha^Wai
the prime cost-? , ,, . ^ ./""'A^ii.
5. If a yard of cloth is bought for iSs. 4d. and sold again for 16s. what is the
gain percent.'? ^ ,^ ^ 4ns. £^.
6. If 112 lb. of iron cost 27s. 6d., what must 1 cwt. be sold for to gam 15 per
(jgjjt^ 1 Ans. £1 , 11 . 7i.
7. If 375 yards of broad cloth be sold for £490, and 20 per cent, profit, what
did it cost per yard 1 ^"*- £1 • 1 • 9i-
8. Sold 1 cwt. of hops, for £6 . 15, at the rate of 25 per cent, profit, what
wouid have been the gain per cent, if I had sold them for £8 per 'cvit. 7
Ans. £48 . 2 . llj.
9. If 90 ells of cambric cost £60, how much must I sell it per yard to gain 18
per cent 1 -^^- ^^^- '^"•
10. A plumber sold 10 fother of lead for £204 . 15, (the fother being 19J
cwt) and gained after the rate of £12 . 10 per cent. ; what did it cost him per
cy/fi Ans. 18s. 8d.
11. Bought 436 yards of cloth, at the rate of 8s. 6d. per yard, and sold it for
10s. 4d. per yard j what was the gain of the whole 1 „«« , « ^
Ans. £o9 . 19 . 4.
12. Paid £69 for one ton of steel, which is retailed at 6d. per lb. ; what is the
profit or loss by the sale of 15 tons 1 , Ans. £182 loss.
13. Bought 124 yards of Uaen, for £32 ; how should the same be retailed
per yard to gain 15 per cent. 1 . - , , i a a
^ ^ ^ ^ Ans. 5s. nd.-ffT'
14. Bought 249 yards of cloth, at 3s. 4d. per yard, retailed the sams at 4s. 2d.
per yard, wkat is the profit in the whole, and how much per cent. ^
Ans. £10 . 7 . 6 profit, and £25 per cent
FELLOWSHIP
Is when two or more join their stock and trade together, so to
determine each person's particular share of the gain or loss, in
■ •ioportion to his principal in joint stock.
By this rule a bankrupt's estate many be divided amongst his
creditors ; as alr.o legacies may be adjusted when there is a defi-
ciency of assets or effects.
FELLOWSHIP IS EITHER WITH OR WITHOUT TIME.
FELLOWSHIP WITHOUT TIMK
RuLF. As the whole stock : is to the whole gain or loss : : so
is each man's share in stock : to his share of the gain or loss.
Proof. Add all the shares together, and the sum will be equal
*/^ *V.o trUron nrain nr \i)ea lint thp. SlirPSt WftV is. aS the wholo
gain or loss : is to the whole stock : : so is each man's share o<
the gain or loss : to his share in stock.
FELLOWBHrP.
81
EXAMPLES,
1. Two merchants trade together; A puts into stock £20, ood B £40, they
gained £50 ; what is each persoi.'s share thereof f
A 60: 50:: 20
20
As 60 : 50 . : 40
40
610)200
£33 . 6 . 8
33. 6 . 8, B's share.
16 . 13 . 4, A's.
610)10010
£16 13.4
50. O.Oproofl
2. Three merchants trade together, A, B and C ; A IJ^t in £20 B £30,
and C £40 ; they gained £180 : what is -ch^-- PJ^ of ^he^|-n ^^ ^^
q A B and C enter 'ntc partnership; A puts in £364, B £4^, and C
£500ranrtfey gained £867; what isWh man's share in proportion to to.
"""^^ ■ Ans. A £234 . 9 . 3i-rem. 70 ; B £310 . 9 . 5^rem. 248 ; C
£322 . 1 . 3J— rem. 1028.
A Four merchants B C, D. and Emake a stock; P put in £227, C £349,
D £m, LTe £^9 ; in tmding th^ gained £428 : 1 d.maUd each merchant's
*'"'''*^'^""%n..B£85..19.6j-690; C £132 3 . 9-120 ; D £43.
11 . i|_250 ; E £166 . 5 . 6i— 70.
5. Three persons, D,E, and F,join in company; D's stock wm £750, E's
£460 and F^ £500 ; and at the end of 12 months they gained £684 : what is
each man's particular share of the gainf ^^^ ^ ^^^^ ^ ^^^^ ^^ p ^2^
6. A merchant is indebted to B £275 . 14, to C,£304 .7, to D £152, and
to E £104 . 6; but upon his decease, his estate is found to be worth but
£675 . 15 : how must it be divided among his creditors 1
Ans. B's share £222 . 15 . 1-6584 ; C's £2^ 18 -^^^^^ >
D'c £122 . 16 . 2J— 12227; and E's £84 . 5 . 5-15620.
7 Four persons trade together in a tomt stock, of which A has^, B i", C i
and D*T and at the end of 6 months tiey gain £100: what is each nan's share
of the said gain 1 ^ ^^^ ^ ^_^^^^ ^ ^^6 . 6 . 3J-36; C £21 . 1 . OJ
—120; and D £17 . 10 . lOj— 24.
8. Two persons purchased an estate of £1700 per annum, fr«^;J;"W, for
£27,200, when money was at 6 per cent, interest, and 4s. per pound, »^nci-tMC ,
whereof b paid £15,800, and E the rest ; sometmve after, t^e ^nte'f ?iJ^,Itr^
nev fallinff to 5 per cent, and 28. per pound land-tax, the; sell the said estate for
24-years' purchase : 1 desire to know each V^^'^'^^J^' ^^^ g ^^g gog..
sz
F£LL0w3Ht
J'^. • .iJ?^ ^' i""'.^ ^^^''^ ^*°^^^ ^^ *ra<^e 5 t^ie amount of their
stocks IS £647, and they arc in proportion as 4, 6, and 8 are to
one another, and the amount of the gain is equal to D's stock :
what is each man's stock and gain ?
Ans. D's stock £143 . 15 . 6^1 gain, 31 . 19 . (m.
f^ 215.13.4 47.18.6|f.
F « 287 . 11 . lA 63 . 18 . (V^.
10. D, E, and F, join stocks in trade; the amount of their
s ock was £100; D's gain £3, E's £5, and F's £8 : what was
each man's stock ?
^^7^5. D's Stock £18 . 15; E's £31. 5 ; and F'» £50,
FELLOWSHIP WITH TIME. '
i'.,^J''''''\^fi!^''' V? ^^*^^ products of each man's money and
time . IS to the whole gam or loss : : so is each man's product :
to his share of the gain or loss. prouuci
Proof. As in fellowship without timtj.
EXAMPLES.
months, and E £75 for four months ; and they gained £70 •
what IS eacli man's share of the gain ? '
Ans. D £20, E £50,
40x3=120
75X4=300
As 420 : 70 : : 120
120
As 420 : 70 : : 300
300
420
42|0)840|0(20
'840
42|0)2100|0(50
2100
14 r T"" '"^'•^^^''\"t^ m^ i« company ; D puts in stock £195 .
;f-o. . 14 . 10, for 1 1 months ; they gained £364 . 18 : what is
each Hian's part of the gain?
Ans. IVs £102 . .4—5008; E's £148 . 1 . IJ-
4S'iS02 ; and F's £114 . 10 . (5|— 14707."
▲LLIOATION.
«3
It of their
d 8 are to
►'s stock :
: of their
t^hat was
)ney and
Jroduct :
3. Three merchants join in company for 18 months ; D put in
£500, and at five months' end takes out £200 ; at ten months*
end puts in £300, and at the end of 14 months takes out £130 :
E puts in £400, and at the end of 3 months £5:70 more ; at 9
months he takes out £140, but puts in £100 at the end of 12
months, and withdraws £99 at the end of 15 months : F puts in
£900, and at 6 months takes out £200; at the end of 11 months
puts in £500, but takes out that and £100 more at the end of 13
months. They gained £200 ; I desire to know each man's share
of the gain ?
Ans. D £50 : 7 : 6—21720 ; E £62 : 12 : ^^-29859 : and
F £87:0:0^—14167.
4. D, E, and F, hold a piece of ground in common, for which
they are ^o pay £36 : 10 : 6. D puts in 23 oxen 27 days ; E 21
oxen 35 ^' /s ; and F 16 oxen 23 days. What is each man to
pay of the said rent ?
Ans. D £13 : 3 : 1^-624 ; E £15 : 11 : 5—1688 ; and F
£7 ; 15 : 11—1136.
4'
3r three
id £70 :
I £50.
): :300
)0
010(50
}
c £195 .
and F
what is
[ . IJ-
707.
ALLIGATION
ALLIGATION IS EITHER MEDIAL OR ALTERNATE.
ALLIGATION MEDIAL
Is when the price and quantities of several simples af« g4ven
to be mixed, to find the mean price of that mixture.
Rule. As the whole composition : is to its total value : : so
is any part of the composition : to its mean price.
Proof. Find the value of the whole mixture at the mean rate,
and if it '^n'^'^^^s «m<1> tiin ♦a^m »-"1"- -f ^i-- - i .••
their respective prices, tlic work is right.
:t si
'84
ALLIGATION.
EXAMPLES.
1. A farmer mixed 20 bushels of wheat, at 5s. per bushel, and
36 bushels of rye, at 3s. per bushel, with 40 bushels of barley,
at 2s. per bushel. I desire to know the worth of a bushel of
this mixture.
As 96 : 288 : : 1 : 3
Ans. 3s.
20X5 =
100
36x3 =
108
40x2 =
80
96
288
2. A vintner mingles 15 gallons of canary, at 8s. per gallon,
with 20 gallons, at 7s. 4d. per gallon, 10 gallons of sherry, at 6s.
8d. per gallon, and 24 gallons of white wine, at 4s. per gallon.
What is the worth of a gallon of this mixture?
Ans. 6s. 2^d.
6 9'
3. A grocer mingled 4 cwt. of sugar, at 56s. per cwt. with 7
cwt. at 43s. per cwt. and 5 cwt. at 37s. per cwt. I demand the
price of 2 cwt. of this mixture. Ans. £4.8.9.
4. A maltster mingles 30 quarters of brown malt, at 28s. per
quarter, with 46 quarters of pale, at 30s. per quarter, and 24
quarters of high-dried ditto, at 25s. per quarter. What is the
value of 8 bushels of this mixture ?
Ans. £1 . 8 . 2^d. °
5. If I mix 27 bushels of wheat, at 5s. 6d. per bushel,*with
the same quantity of rye, at 4s. per bushel, and 14 bushels of
barley at 2s. 8d. per bushel, what is the worth of a bushel of this
»"ixture? Ans. 4s. S^d.^.
6. A vintner mixes 20 gallons of port at 5s. 4d. per gallon,
with 12 gallons of white wine, at 5s. per gallon, 30 gallons of
Lisbon, at 6s. per gallon, and 20 gallons of mountain, at 4s. 6d
per gallon. What is a gallon of this mixture worth ?
Ans. 5s. 3|d.-f4.
7. A refiner having 12 lb. of silver bullion, of 6 oz. fine, would
melt it with 8 lb. of 7 oz. fine, and 10 lb. of 8 oz. fine; required
the fineness of 1 lb. of that mixture ?
Ans. 6 oz. 18 dwts. 16 gr.
8. A tobacconist would mix 50 lb. of tobacco, at lid. per lb.
with 30 IK at 14d. per lb. 25 lb. at 22d. per lb. and 37 lb. at 2s
per lb. What will 1 lb. of this mixture be worth I
Ans. 16|d.||f
AT.LIOATION.
86
ALLIGATION ALTERNATE
(s when the price of several things are given, to find such quanti*
ties of them to make a mixture, that may bear a price pro-
pounded.
In ordering the rates and the given price, observe,
1. Place them one under the other, 18 M
and the propounded price or mean «^20
rate at the left hand of them, thus,
23
24-
28-
.6
.4
.2
2. Link the several rates together by 2 and 2, ahva , observ-
ing to join a greater and a less than the mean.
3. Against each extreme place the difference of the mean and
its yoke fellow.
When the prices of the several simples and the mean rate are
given without any quantity, to find how much of each simple is
required to compose the mixture.
Rule. Take the difference between each price and the mean
rate, and set them alternately, they will be the answer required.
Proof. By Alligation Medial.
EXAMPLES.
1. A vintner would mix four sorts of wine together, of 18d.,
20d., 24d., aiid 28d. per quart, what quantity r^ each must he
have, to sell the mixture at 22d. per quart ?
or thus. Proof.
18 6 of 18d. = 108d.
2 of 20d. = 40
2 of 24d. = 48
4 of 28d. = 112
22'
Answer.
Proof.
18 _2 of 18d.
= 36d.
20-.
6 of 20d.
= 120
24_
4 of 24d.
= 96
28
2 of 28d.
= 56
1
4
)308
22d.
22^—1
24j
28
14
)30S
22d.
Note. Queations in this rule admit of a great variety of an-
swers, according to the manner of linking them.
2. A grocer would mix sugar at 4d., 6d., and lOd. per lb., »o
as to sell the compound Ibv 8d. per lb. ; what quantity of each
Ans. 2 lb. at 4d., 2 lb. at 6d., and 6 lb. at lOd,
H
I
r
86
ALLIOATION PARTIAL.
3. I desire to know how much tea, at 16s., 14s., 9s., and 89
per lb., will compose a mixture w^orth 10s. per lb. ?
Ans. 1 lb. at IGs., 2 lb. 14s., 6 lb. at 9s., and 4 lb. at 8s.
4. A farmer would mix as much barley at 3s. 6d. per bushel,
rye at 4s. per bushel, and oats at 2s. per bushel, as to make a
mixture worth 2s. 6d. per bushel. How much is that of each
sort?
Ans. 6 bushels of barley, 6 of rye, and 30 of oats.
5. A grocer would mix ra?sins of the sun, at7d. per lb., with
Malagas at 6d., and Smyrnas at 4d. per lb. ; I desire to know
what quantity of each sort he must take to sell them at 5d. per lb. ?
Ans. 1 lb. of raisins of the sun, 1 lb. of Malagas,
and 3 lb. of Smyrnas.
6. A tobacconist would mix tobacco at 2s., Is. 6d., and Is. 3d.
per lb., so as the compound may bear a price of Is. 8d. per lb
What quantity of each sort must he take ?
i ! An.<f, 7 lb. at 2s., 4 lb. at Is. 6d., and 4 lb. at Is. 3d.
ALLIGATION PARTIAL
I
Is when the prices of all the simples, the quantity of but on©
of them, and the mean rate are given to find the several quanti-
ties of the rest in proportion to that given.
Rule. Take the difference between each price and the mear
rate as before. Then,
As the diiTerence of that simple whose quantity is given : tc
the rest of the differences severally : : so is the quantity given : ti
the several quantities required.
EXAMPLES.
1. A tobacconist being determined to mix 20 lb. of tobacco
at 15d. per lb., with others at 16d. per lb., 18d. per lb., and 22d.
per lb. ; how many pounds of each sort must he take to make
one pound of that mixture worth 17d. ?
Answer. Proof.
15 5 20 lb. at 15d. = 300d. As 5 : 1
,^16--^ 1 41b. atUid. = 64d. As 5 : 1
* 'l8— I 1 4 lb. at 18d. = 72d. As 5 : 2
22 2 8 lb. at 22d. = 17()d.
20: 4
20: 4
20:8
Ans. 36 lb.
C12d. :: 1 lb. 17d.
ALLIGATION TOTAL.
87
2. A farmer would mix 20 bushels of wheat at COd. per bush-
el, with rye at 36d., barley at 24d - aad oats at 18d. per bushel.
How much must he take of each sort, to make the composi-
tion worth 32d. per bushel ?
Ans. 20 bushels of wheat, 35 bushels of rye, 70 bushels
of barley, and 10 bushels of oats.
3. A distiller would mix 40 gallons of French Brandy, at 12s.
per gallon, with English at 7s., and spirits at 4s. per gallon.
What quantity of each sort must he take to afford it for 8s. per
gallon ?
Ans. 40 gallons French, 32 English, and 32 spirits.
4. A grocer would mix teas at 12s., 10s., and Os., with 20 lb.
at 4s. per lb. How much of each sort must he take to make
the composition worth 8s. per lb. ?
Ans. 20 lb. at 4s., 10 lb. at 6s., 10 lb. at 10s., 20 lb. at 12s.
5. A wine merchant is desirous of mixing 18 gallons of Ca-
nary, at 6s. 9d. per gallon with Malaga, at 7s. 6d. per gallon,
sherry at 5s. per gallon, and white wine at 4s. 3d. per gallon.
How much of each sort must he take that the mixture may be
sold for 6s. per gallon ?
Ans. 18 gallons of Canary, 31 1 of Malaga, 13^ of Sherry,
and 27 of white wine.
v»„
■K\
ALLIGATION TOTAL
Ift when the price of each simple, the '{Jintity to be compound-
ed, and the mean rate are given, to fmJ hov much of each sort
will make that quantity.
Rule. Take the difference between each price, and the
mean rate as before. Then,
As the sum of the differences : is to each particular differ-
ence : : so is the quantity given : to the quantity required.
EXAMPLES.
1. A grocerhas four sorts of sugar, viz., atT2d., lOd., Od.. and
— — " " -jlLlt?:; -Ji z'X'^ ;:.-. ir •-•; s.sj •..•ti.
>-» T-» r~\ c
per lb. I desire to know what quantity of each lie must take?
H
■ f!
POSITION, OR THE RULE OF FALSE.
Answer. Proof.
12 . 4 : 48 at 12d. 576=As 12 : 4 : : 144 : 48
2 : 24 at lOd. 240=As 12 : 2 : : 144 : 24
2 : 24 at 6d. 144=As 12 : 2 : : 144 : 24
4 : 48 at 4d. 192=As 12 : 4 : : 144 : 48
^'l3
12 144 )1152(8d.
2. A grocer having four sorts of tea, at 5s., 6s., 8s., and 9s.
per lb., would have a composition of 87 lb., worth 7s. per lb.
What quantity must there be of each ?
Ans. 14| lb. of 5s., 29 lb. of 6s., 29 lb. of 8s., and 14^ lb. of 9s.
3. A vintner having four sorts of wine, viz., white wine at 4s.
per gallon ; Flemish at Os. per gallon ; Malaga at 8s. per gal-
lon ; and Canary at 10s. per gallon ; and would make a mixture
of 60 gallons, to be worth 5s. per gallon. What quantity of
each must he take ?
Ans^ 45 gallons of white wine, 5 gallons of Flemish, ^
5 gallons of Malaga, and 5 gallons of Canary.
4. A silversmith had four sorts of gold, viz., of 24 caratf
fine, of 22, 20, and 15 carats fine, and would mix as much of
each sort together, so as to have 42 oz. of 17 carats fine. How
much must he take of each ?
Ans. 4 oz. of 24, 4 oz of 22, 4 oz. of 20, and 30 oz.
of 15 carats fine.
5. A druggist having some drugs of 8s., 5s., and 4s. per lb.,
made them into two parcels ; one of 28 lb. at 6s, per lb., the
other of 42 lb. at 7s. per lb. How much of each sort did he
f^ke for each parcel 1
Ans. 12 lb. of 8s.
8 lb. of 5s.
8 lb. of 48.
30 lb. of 8s.
6 lb. of 5s.
6 lb. of 4s.
28 lb. at 6s. per lb.
42 lb. at 7s. per lb.
POSITION, OR THE RULE OF FALSE,
ha a rirtc that by false or supposed numbers, taken at pleasure
discovers the true < ne required. It is divided into two pall^^
SiKoLE and Double.
ifosiriofi, OR the rule op false.
SINGLE POSITION
Is, by using one supposed number, and working with it as the
true one, you find the real number required, by the following
Rule. As the total of the em r? : is to the true total : : so is
the supposed number : to the true one required.
Proof. Add the several parts of the sum together, and if \i
agrees with the sum it is right.
EXAMPLES.
1. A schoolmaster being asked how many scholars he had, said,
If I had as many, half as many, and one quarter as many more,
I should have 88. How many had he ?
Suppose he had... 40 As 110 : 88 : : 40
as many 40 40
half as many 20
} as many.... 10
110
11|0)352|0(32
33
22
22
Ans. 32.
32
32
16
8
88 proof.
2. A person having about him a certain number of Portugal
pieces, said, If the third, fourth, and oth of them were added
together, they would make 54. I desire to know how many he
had ? Ans. 72.
3. A gentleman bought a chaise, horse, and harness, for £60,
the horse came to twice the price of the harness, and the chaise
to twice the price of the horse and harness. What did he give
for each ?
Ans, Horse £13:6: 8, Harness £6:18: 4, Chaise £40.
4. A, B, and C, being determined to buy a quantity of goods
which would cost them £120, agreed among themselves that B
should have a third part more than A, and C a fourth nart more
than B. I desire to know what each man must pay?
Ans. A £30, B £40, C £50.
H3
00
POSITION, OR THE RULE OF FALSE.
5. A person delivered to another a sum of money unknown, to
receive interest for the same, at 6 per cent per annum, simple 'i-
terest, and at the end of lO years received, for principal and in-
terest, £300. What was ilie sum lent? Ans. £187 : 10.
DOUBLE POSITION
I :
Is by making use of two supposed numbers, and if both prove
false, (as it generally happens) they are, with their errors, to
be thus ordered : —
Rule 1. Place each error against its respective position.
2. Multiply them cross-ways.
3. If the errors are alike, i. e. both greater, or both less than
the given number, take their difference for a divisor, and the
difference of the products for a dividend. But if unlike, take
their sum for a divisor, the sum of their products for a dividend,
the quotient will be the answer.
EXAMPLES.
1. A,B, and C, would divide £200 between them, so that B
may have £6 more than A, and C £8 more than B ; how much
must each have ?
Suppose A had 40
Tlien B had 4G
and C 54
j'hf n suppose A had 50
tiuiii B must have 56
2),.n<l C 64
1 40 too little by tO
sup. ei ors.
40 v^O
SO'^SO
.SOOO 1200
1200
60
30
30 divisor.
3i0)180|0
60 Ans. for A.
170 too little by 30;
60 A
66 B
74 C
200 proof.
2. A man had two silver cups of unequal weight, having one
cover to both, of 5 oz , now if the cover is put on the less cup,
it will double the weight of the greater cup ; and set on th«
^.^*^_ «,,^ :* ..rm v.« ♦Vi>.{/i« oe. Tiooirxr pQ flip Inss Min Whai
is the weight of each cup ?
Ans, 3 ounces less, 4 greater
BXCHANOE.
01
3. A genOeman bouglit a joiist, witli a garden, and ahorse in
the staMe, i^r £500 ; now he paid 4 times the price of <hr horse
for the garden, and 5 times the price of the garden for ousc.
What was the value of th« .ouse, grarden, and horse, ^. ?
Ans, horse £'^ jrarden £80, huus
j\f»
4. Three pi rsons discoursed conc(rning their ages : tsays If,
I am 30 years of age ; says K, I am as old as H and -J-of L ; and
Bays L, I am ab old a^ you '>ota. What was the age of each
person ?
Ans. II 30, K 50 and L 80.
5. D, E, and F, playing at cards, staked 324 crowns : but dis-
puting about the tri ^k.!*, each man took as many ' uld : D
got a certain numb* '" • E as many as D, and 15 ii and F got
a fifth part of both thtir ims added together. many did
each get?
Ans. D 127^, E 14^^, and F 54..
6. A gentleman g ? into a garden, meets with some ladies,
an'^ says to them, Gv . moniing to you 10 fair maids. Sir, you
•'listake, answered o le of them, we ar not 10; but if we weie
twi^e as many more as we aro, weshou. 1 be as manv above 10
as we are now under. How many were they?
JLtis. 5.
EXCHANGE
Is receiving money in one country for the same value paid in
another.
The par of exchange is always fixed and cc'-tain, it being the
intrinsic value of foreign money, com ared /ith sterling ; but
the course of exchange rises and falls upo' various occasions.
I. FRANCE.
They keep -heir : ccounts at Paris, Lyons, and Rouen, inlivres,
sols, and deniers, and exchange by the crown=4s. 6d. at par.
Note. 12 denisid make 1 sol.
20 sols 1 livre.
3 livers 1 crown.
■>%,
.ail
IMAGE EVALUATION
TEST TARGET (MT-3)
1.0
I.I
1.25
| 4S
m
Hi
■ 40
2.:
22
20
1.8
1.4 III 1.6
V]
//.
v:
%%
//^
'/
Hiotographic
Sciences
Corporation
33 WEST MAIN STREET
WEBSTER, NY. MSSO
(716) 872-4503
^
>^
rV
^
:\
,v
\
4
<h
W^\j
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M
EXCHANGE.
To change French into Sterling.
Rule. As 1 crown : is to the given rate : : so is the French
sum : to the sterling required.
To change Sterling into French.
Rule. As the rate of exchange : is to 1 crown : : so is the
sterling sum : to the French required.
EXAMPLES.
1. How many crowns must be paid at Paris, to receive ia
London £180 exchanged at 4s. 6d. per crown ?
d. c. £
As 54 : 1 : : 180 : 800.
240
54)43200(800 crowns.
432
f0.
How much sterling must be paid in London, to receive in'
t'aris 758 crowns, exchanged at 56d. per crown ?
Ans. £176 : 17 : 4.
3. A merchant in London remits £176 : 17 : 4, to his corres-
pondent at Paris ; what is the value in French crowns, at 56d.
per crown
Ans. 758.
4. Change 725 crowns, 17 sols, 7 deniers, at 54 |d. per crown,
into sterling, what is the sum? Ans. £164 : 14 : (Hd-f^-?^.
5. Change £164 : 14 : 0^ sterling, into French crowns, ex-
change at 54^d. per crown ?
Ans. 725 crowns, 17 sols, 7 tVo deniers.
n. SPAIN.
They keep their accounts at Madrid, Cadiz and Seville, in
dollars, rials, and maravedies, and exchange by the piece of eight
s=4s. 6d. at par.
Note. 34 maravedies make 1 rial.
8 rials 1 piastre or piece of eight,
10 rials 1 doUar.
Rule. As with France.
EXAMPLES.
fi. A merchant at Cadiz remits to London 2547 pieces of eight,
at 56d. per piece, how much sterling is the sum ?
Ans. £594 : 6.
EXCHANGE. ^
7. How many pieces of eight, at 56d. each, will answer a bill
of £594 : 6, sterling ? Ans. 2547.
8. If I pay a bill here of £2500, what Spanish money may I
draw my bill for at Madrid, exchange at 57^d. per piece of eight ?
Ans. 10434 pieces of eight, 6 rials, 8 mar. ff .
III. ITALY.
They keep their accounts at Genoa and Leghorn, in livrcs,
sols, and deniers, and exchange by the piece of eight, or dollar
=4s. 6d. at par.
Note. 12 deniers make 1 sol.
30 sols 1 iivre.
5 livres 1 piece of eight at Genoa.
6 livres 1 piece of eight at Leghorn.
N. B. The exchange at Florence is by ducatoons; the exchange at Venice
by ducats.
Note. C solidi make 1 gross.
34 gross .... 1 ducat.
Rule. Same as before.
9. How much sterling money may a person receive in London, if he pays im
Genoa 976 dollars, at 53d. per dollar 1 Ans. £315 . 10 . 8.
10. A factor has sold goods at Florence, for 350 ducatoons, at 54d. each;
what is the mlue in pounds sterling 1 Ans. £56 .5.0.
11. If 375 ducats, at 4s. 5d. each, be remitted from Venice to London ; what
is the value in pounds sterling 1 Ans, £60 . 14 . 7.
12. A gentleman travelling would exchange £60 .14.7, sterling, for Venice
ducats, at 4s, 5d. each ; how many must he receive 1
' Ana. ^5.
IV. PORTUGAL.
They keep their accounts at Oporto and Lisbon, in reas, and
exchange by the milrea=6s. 8^d. at par.
Note. 1000 reas make 1 milrea.
Rule. The same as with France.
EXAMPLES.
IS. A gentleman being desirous to remit to bis correspondent in London 2750
milreas, exchange at 69. 5d. per milrea ; how much sterlmg will he be the creditor
for in London f ./"*• ^®^oo^ ' ^®' .
14. A merchant at Oporto remits to LondMi 4366 milreas, and 18d reas, at
5«. 5*d. exchanire per mikea; how much sterling must be paid in London for
thi. remittance f ^ W £119^17 . 6j. 0375
te. iri u:ii ;^ T ryr>A^^ r^f ^11051 17 Ai (V^H^ whflt must I draw for
on my correspondent in Lisbon, exchange at 58. 5f d. per milrea ^
i iln*. 4366 milreas, 183 reM.
94 ^ EXCHANGE.
V. HOLLAND, FLANDERS, AND GERMANY.
They keep their accounts at Antwerp, Amsterdam, Brussels,
Rotterdam, and Hamburgh, some in pounds, shillings, and pence,
as in Fngland ; others in guilders, stivers, and pennings ; and
'exchange with us in our pound, at 33s. 4d. Flemish, at par.
JS^OTE. 8 pennings make 1 groat.
2 groats, or 16 pennings .... 1 stive?.
20 stivers 1 guilder or florin.
ALSO,
12 groats, or G stivers make. . 1 schelling.
20 schcUiiigs, or 6 guilders. . . 1 pound.
To change Flemish into Sterling.
Rule. As the given rate : is to one pound : : so is the Flemish
«um : 10 the sterling required.
To cha7ige Sterling into Flemish. %
Rule. As £1 sterling : is to the given rate : : so is the sterling
given : to the Flemish sought.
EXAMPLES.
16. Remitted from London to Amsterdam, a bill of £754 . 10 . sterling, how
many pounds Flemish is the sum, the exchange at 33s. 6d. Flemish, per pound
sterling '{ Ans. £1263 . 15 . 9, Flenush.
17. A merchant in Rotterdam remits £1263 . 15 . 9 Flemish, to be paid in
London, how much sterling money must he draw for, the exchange being at 338.
Cd. Flemish per pound sterlinff 'J Ans. £754 . 10.
IS. If I pay in London £853 . 12 . 6, sterling, how many guilders must I
draw for at Amsterdam, exchange at 34 schel. 4i groats Flemish per pound
iterling '\ Ans. 8792 guild. 13 stiv. 14i pennings.
19. What must I draw for at London, if I pay in Amsterdam 8793 guild.
13 stiv. 14i pennings, exchange at 34 schel. 4| groats per pound sterling *?
Ans. £852 . 12 . 6.
To convert Bank Money into Current^ and the contrary.
Note. The Bank Money is worth more than the Current.
The difference between one and the other is called agio, and is
generajly from 3 to 6 per cent, in favour of the Bank.
To change Bank into Current Money.
R
«rr «• Acs 1 AA /nii1#lAl*ci
■Rank ? ia to 100 with the awio added ; i
so ia the Bank given : to the Current required.
EXCHANGE*
05
NY.
Brussek,
nd pence^
igs ; and
t par.
3 Flemish
e sterling
l^rling, how
, per pound
Flemish.
) be paid in
leing at 338.
;75l.lO.
tiers must I
per pound
pennings.
8793 guild,
•ling'?
2 . 12 . 6.
irary.
Current.
iO) and is
i
\ A
AUt^A
To change Current Money into Bank.
RtJL£. As 100 with the agio is added : is to 100 Bank : : so is
the Curl at money given : to the Bank required.
20. Change 794 guilders, 15 stivers, Current Money, into Bank
florins agio 4f per cent, t
Ans. 761 guilders, 8 stivers. \\\^ pennings.
21. Change 761 guilders, 9 stivers Bank, into Current Money,
agio 4f per cent.
Ans. 794 guilders, 15 stivers, 4^^ pennings.
VI. IRELAND.
22. A gentlenlan remits to Ireland £575 : 15, sterling, what
will he receive there, the exchange being at 10 per cent. ?
Ans. £633 : 6 : 6.
23. What must be paid in London for a remittance of £633 t
6 : 6, Irish, exchange at 10 per cent. ? Ans. £575 : 15.
COMPARISON OF WEIGHTS AND MEASURES.
EXAMPLES.
1. If 50 Dutch pence be worth 65 French pence, how many
Dutch pence are equal to 350 French pence ?
Ans. 269f|.
2. If 12 yards at London make 8 ells ?\ Paris, how many ells
at Paris will make 64 yards at London ?
Ans. 42^.
3. If 30 lb. at London make 28 lb. at Amsterdam, how many
lb. at London will be equal to 350 lb. at Amsterdam ?
Ans. 375.
4. If 951b, Flemish make 100 lb. English, how many lb. En-
glish are equal to 275 lb. Flemish.
Ans. 289f|.
CONJOINED PROPORTION
Is when the coin, weights, or measures of several countries arc
compared in the same question ; or, it is linking together a varie-
ty of proportions.
When it is required to find how many of the first sort of coin,
weight, or measure, mentioned in the question, are equal to a
given quantity of the last.
9«
PROPORTION.
■I I
'I! I
I
Left.
Right.
20
23
155
180
n
Rule. Place the numbers alternately, beginning at the left
hand, and let the last number stand on the left hand ; then multi-
ply the first row continually for a dividend, and the second for
a diviu r.
Proof. By as many single Rules of Three as the question
requires.
EXAMPLES.
1. If 20 lb. at London make 23 lb. at Antwerp, and 156 lb.
at Antwerp make 180 lb. at Leghorn, how many lb. at London
arc equal to 72 lb. at Leghorn ?
20X155x72=223200
23 X 180 = 4140)223200(53fii.
2. If 12 lb. at London make 101b. at Amsterdam, and 100 lb.
at Amsterdam 120 lb. at Thoulouse, how many lb. at London
are equal to 40 lb. at Thoulouse ?
Ans. 40 lb.
3. If 140 braces at Venice are equal to 156 braces at Leghorn,
and 7 braces at Leg^horn equal to 4 ells English, how many bra-
ces at Venice are equal to 16 ells English 1
Ans, 25^.
4. If 40 lb. at London make 36 lb. at Amsterdam, and 90 lb.
at Amsterdam make 116 at Dantzick, how many lb. at London
are equal to 130 lb. at Dantzick ?
Ans. U^lffA'
When it is required to find how many of the last sort of coin,
weight, or measure, mentioned in the question, are equal to a
quantity of the first.
Rule. Place the numbers alternately, beginning at the left
hand: and let the last number stand on the rio'ht hand ; then mul»
tiply the first row for a divisor, and the second for a dividend.
the left
m multi-
icond for
question
i 156 lb.
London
^•
id 100 lb.
k London
. 40 lb.
Leghorn,
lany bra-
nd 90 lb.
t London
'*4 1 y « •
t of coin,
qual to a
t the left
then mul»
ividend.
rnoGREgflioN. 07
EXAMPLES.
5. If 12 lb. at London make 10 lb. at Amsterdam, and 100 lb.
at Amsterdam 120 lb. at Thoulouse, how many lb. at Thoulouso
are equal to 40 lb. at London ? Ans, 40 lb.
6. If 40 lb. at London make 30 lb. at Amsterdam, and 90 lb.
at Amsterdam 116 ]b. at Dantzick, how many lb. at Dantzick are
equal to 122 lb. at London ? Ans. Hl\^,
PROGRESSION
CONSISTS OP TWO PARTS,
ARITHMETICAL AND GEOMETRICAL.
ARITHMETICAL PROGRESSION
Is when a rank of numbers increase or decrease regularly by the
continual adding or subtracting of equal numbers ; as 1, 2, 3, 4,
3, 6, are in Arithmetical Progression by the continual increasing
or adding of one; 11, 9, 7, 5, 3, 1, by the continual decreasing
or subtracting of two.
Note. When any even number of terms differ by Arithme-
tical Progression, the sum of the two extremes will be equal
to the two middle numbers, or any two means equally distant
from the exteemes : as 2, 4, 6, 8, 10, 12, where 6 -f 8, the two
middle numbers, are=12+2, the two extremes, ana=10+4thc
two means=l4.
When the number of terms arc odd, the double of the middle
term will be equal to the two extremes ; or of any two means
equally distant from the middle term ; as 1, 2, 3, 4, 5, where the
double number of 3=5+ 1=2+4=6.
In Arithmetical Progression five things are to be observed, viz.
1. The first term ; better expressed thus, F.
3. The last term, L.
3. The number of terms, ....,N.
4. TheequaldifTerence, D.
5. The sum of all terms, S.
Any three of which being given, the other two may be found.
The first, second, and third terms given, to find the fifth.
Dnvvi iur..i^:.,%i.. 4i.« _i» At.- A___ . 1 t. «* .t -
a«u2ica i-AUiiipij mc suui ui uiB \wo exiTBTUGs oy naii ine
number of terms, or multiply half the sum of the two extreme!
96
PROOR1.88ION.
/
by the whole number of terms, the product is the totel of «ll the
terms : or thus,
F. F LN arc given to find S.
-N
■ F-fLX— =S.
2
EXAMPLES.
1. How many strokes does the hammer of a clock strike in 12
hours t
12+1=13, then 13x6=79.
2. A man bought 17 yards of cloth, and gave for the first yard
26. and for the last 10s. what did the 17 yards amount to?
Ans, £5 . 2.
3. If 100 eggs were placed in a right line, exactly a yard a«^
under from one another, and the first a yard from a basket, what
length of ground does that man go who gathers up these 100 eggi
singly, and returns with every egg to the basket to put it in ?
Ans, 6 miles, 1300 yards.
The first, second, and third terms given, to find the fourth.
Rule. From the second subtract the first, the remainder divi-
ded by the third less one, gives the fourth : pr thus
II. F L N are given to find P.
L— F
■'• >,.^D. ■ . , . ..-
N— 1
EXAMPLES.
4. A man had eight sons, the youngest was 4 years old, and
the eldest 32, they increase in Arithmetical Progression, what
was the common difierence of their ages ? Ans, 4.
J ,:Ul
then 28T*-&-rl=4 common diflference.
5. A man is to travel from London to a certain place in 12
days, and to go but 3 miles the first day, increasing every day by
|ta equal excess, so that the last day*8 journey may be 58 miles,
PROORBSSION.
90
1 of all the
trike in 12
s first yard
tto?
£5.2.
a yarii as-
sket, what
e 100 egg'i
Qt it in ?
) yards.
I fourth.
inderdivi-
'8 old, and
sion, what
Ans, 4.
le.
lace in 12
ery day by
e 58 mileg,
what is the daily increasef and how many miles distant is that
place from London ? Ans. 5 daily incrraie.
Therefore, as three miles is the first day's journey,
34-6=8 the second day.
84-5=13 the third day, &c. -
Tne whole distance is 366 miles.
The first, second, and fourth terms given, to find the third.
RuLB. From the second subtract the first, the remainder di /ide
by the fourth, -and to the quotient add 1, gives the third ; or thus,
III. F L D are given to find N.
L— F
D
^EXAMPLES.
6. A person travelling into the country, went 3 miles the first
day, and increased every day 5 miles, till at last he went 58 miles
in one day ; how many days did he travel ? Ans, 12.
58— 3=55-»-5=ll+l=12 the number of days.
7. A man being asked how many sons he had, said, that the
youngest was 4 years old, and the oldest 32 ; and that he increas-
ed One in his family every 4 years, how many had he?
Ans. 8.
The second, third, and fourth terms given to find the first
Rule. Multiply the fourth by the third made less by one, the
product subtracted from the second gives the first : or thus,
IV. L N D are given to find F.
L— DxN— 1=F.
EXAMPLES.
8. A man in 10 days went from London to a certain town in
the country, every day's journey increasing the fonner by 4, and
the last he went was 46 miles, what the first ?
Ans. 10 mile?.
4x10—1=36, then 46—36=10, the first day's journey.
r
too
PROOCSSION.
9. A man takes out of his pocket at 8 several times, so many
different numbers of shillings, every one exceeding the former
by 6, the last at 46 ; what was the first i Ans. 4.
The fourth, third, and fifth given, to find the first.
Rule, Divide the fifth by the third, and from the quotient
subtract half the product of the fourth multiplied by the third
less 1 gives the first : or thus,
V N D S are given to find F
S DXN— 1
— F.
N2
EXAMPLES.
10. A man is to receive £360 at 12 several payments, each to
exceed the former by £4, and is willing to bestow the first pay-
ment on any one that can tell him what it is. What will that
jierson have for his pains ? -Ans, £8.
4 X 12—1
360+12=:30, then 30
=£8 the first payment.
The first, third, and fourth, given to find the second.
Rule. Subtract the fourth from the product of the third, mul-
tiplied by the fourth, that remainder added to the first gives the
second : or thus,
VI. F N D are given to find L.
NP— P-f-F=L
EXAMPLES.
11. What is the last number of an Arithmetical Progression,
beginning at6» and continuing by the increase of 8 to 20 places?
Ans. 158.
30X8—8=^152, then 152+6=158, the last number.
GEOMETRICAL PROGRESSION
Is the incieasiiig or decreasing of any rank of numbers by some
common ratio ; that is, by the continual multiplication or division
/. -— 1 —.1.-.— . ^m n A Q ta. iwxMvanaA \\tr t\\tk vnilltlTtllAt
Oi Home OqiSSU JlUinucr i oa .«, •*, «j, *v, iiti^«\jf»ow vj »«»« m..vi»».^——
% an4 IG, 8, 4, 2> decrease by the divisor 2.
fROORKSSIOlV.
19!
so many
} formei
ns. 4.
quotient
he third
, each to
irst pay-
will that
IS. £8.
nent.
ird, mul'
gives the
gressioR,
5 places?
s. 158.
I by some
r division
Tiiilf'irtllAt
Note. "When any number of terms is continued in Geome-
trical Progression, the product of the two extremes will be equal
to any two means, equally distant from the extremes : as 2, 4, 8,
16, 32, 64, where 64x2 are=4x32, and 8X16=128.
When the number of the terms are odd, the middle term multi-
plied into itself will be equal to the two extremes, or any two
means equally distant from it, as 2, 4, 8, 16, 32, where 2X32^
4x16=8x8=64.
In Geometrical Progression the same 5 things are to be obeer
fed as are in Arithmetical, viz.
1. The first term.
2. The last term.
3. The number of terms.
4. The equal difference or ratia
5. The siun of all the terms.
Note. As the last term in a long series of numbers is very
tedious to come at, by continual multiplication ; therefore, for the
reader finding it out, there is a series of numbers made use oJ
in Arithmetical Proportion, called indices, beginning with an
unit, whose common difference is one ; whatever number of in-
dices you make use of, set as many numbers (in such Geomet-
rical Proportion, as is given in the question) under them.
^g 1, 2, 3, 4, 5, 6, Indices.
2, 4, 8, 16, 32, 64, Numbers in Geometrical Proportion.
But if the first term in Geometrical Proportion be different
from the ratio, the indices must begin with a cipher.
^g 0, 1, 2, 3, 4, 5, 6, Indices.
1, 2, 4, 8, 16, 32, 64, Numbers in Geometrical Proportion.
When the Indices begin with a cipher, th^ ^ *m of the indices
made choice of must always be one less than me number of terms
given in the question ; for 1 in the indices is over the second
term, and 2 over the third, «fcc.
Add any two of the indices together, and that sum will agree
with the product of their respective terms.
As in the first table of Indices 2+ 5= 7
Geometrical Proportion 4x32=128
Then the second
13
'Z-\- 4= 6
4x16= 64
i02
FKOOBMSION.
In any Geometrical Progression proceeding from unity, the
ratio being known, to find any remote term, without producing
all the intermediate terms.
Rule. Find what figures of the indices added together would
give the exponent of the term wanted : then multiply the num*
bars standing under such exponents into each other, and it will
give the term required. ^
Note. When the exponent 1 stands over the second term,
the number of exponents Vnust be one less than the number o(
terms.
EXAMPLES.
1. A man agrees for 12 peaches, to pay only the price of the
last, reckoning a farthing for the first, and a halfpenny for the
second, ^c. doubling the price to the last ; what must he give
for them? Ans, £2,^,9,
16=4
0, 1, 2, 3, 4, Exponents 16=4
1, 2, 4, 8, 16, No. of terms.
256::a8
8=a
For 4+4+3=11, No. of terms less 1-
4)2Q48«llNo.offi^.
12)512
2|0)4|2 . 8
£2.2.8
2. A country gentleman going to a fair to buy some oxen,
meets, with a person who had 23 ; he demanded the price of them,
and was answered £16 a piece; the gentleman bids £15 a piece
and he would buy all ; the other tells him it could not be taken ;
but if he would give what the last ox would come to, at a farthing
for the first, and doubling it to the last, he should have all. What
was the price of the oxen ? Ans. £4360 .1.4.
In any Geometrical Progression not proceeding from unity,
the ratio being given, to find any remote term, without produ-
cing all the intermediate terms.
PROORECSION.
103
<#
RvLS. Proceed as in the last, onl/ observoi that erery prodact
rnual be divided by the first term.
EXAMPLE.
3. A sum of money is to be divided among eight persons, the
first to have £20, the next £00, and so in triple proportion ; what
will the last have ? Ans. £43740.
540X540 14580X60
30 20
3+3+1=7, one less than the number of terms.
4. A gentleman dying, left nine sons, to whom and to his exe-
cutors he bequeathed his estate in the manner following : To his
executors £50, his youngest son Was to have as much more as
the executors, and each son to exceed the next younger by as
much more ; what was the eldest son*s proportion?
Ans. £25600.
IChc first tei'm, ratio, and number of termd given, to find the
tsilm of all the terms.
Rut.?:. Find the last term as before, then subtract the first
from it, and divide the remainder by the ratio, less 1 ; to the quo-
tient of which add the greater, gives the eum required.
EXAMPLES.
B. A servant skilled in numbers, agreed with a gentleman to
serve him twelve months, provided he would give him a farthing
for bis first month^s service, a penny for the second, and 4d. for
the third, &e., what did his wages amount to ?
Ans. £6825 . 8 . 5:1.
256X256=65536, then 65536X64=4194304
4194304—1
=1398101, then
0, 1, 2, 3, 4,
1, 4, 16, 64, 250,
4+4+3=11
No. of terms less 1, 4 — 1
1398101+4194304=5592405 farthings.
6. A man bought ahorse, and by agreement was to give a far-
thing for the first nail, three for the second, &.c., there were four
shoes, and in each shoe 8 nails \ what was the worth of the horse ?
4ns. £9651 14681 693- • 1 3 • i.
104
PERMIITATION.
7. A certaii: person married his daughter on New*year*s day,
and gave her husband Is. towards her marriage portion, promis-
ing to double it on the first day of every month for 1 year ; what
was her portion 1
^ns. £204.15.
8. A laceman, well versed in numbers, agreed with a gentle
man to sell him 22 yards of rich gold brocaded lace, for 2 pins
the first yard, 6 pins the second, &.C., in triple proportion ; I
desire to know what he sold the lace for, if the pins were valued
at 100 for a farthing ; also what the laceman got or lost by the
sale thereof, supposing the lace stood him in £7 per yard.
Ans. The lace sold for £326886 .0.9.
Gain £326732 .0 . 9.
PERMUTATION
Is the changing or varying of the order of things.
Rule. Multiply all the given terms one into another, and the
last product will be the number of changes required.
EXAMPLES.
1. How many changes may be rung upon 12 bells ; and how
long would they be ringing but once over, supposing 10 changes
might be rung in 2 minutes, and the year to contain 365 days, 6
hours ?
1X2X3 X4X5X6X7X8X9X 10 XllX 12=479001600
changes, which -f- 10=47900160 minutes ; and, if reduced, is=91
years, 3 weeks, 5 days, 6 hours.
2. A young scholar coming to town for the convenience of a
good library, demands of a gentleman with whom he lodged,
\yiiat his diet would cost for a year, who told him £10, but the
scholar not being certain what time he should stay, asked him
what he must give him for so long as he should place his family,
(consisting of 6 persons besides himself) in different positions,
every day at dinner; the gentleman thinking it would not be
long, tells him £5, to which the scholar agrees. What time did
the^scholar stay with the gentleman?
Ans. 5040 days.
106
ear's day,
n, promis-
ear ; whal
04. 15.
k a gentle
for 2 pins
>ortion; I
ere valued
)st by the
|rard.
k . 9.
1.0,9.
THE
TUTOR'S ASSISTANT.
;r, and the
; and how
10 changes
65 days, 6
479001600
ced, is=9l
lience of a
le lodged,
10, but the
asked him
his family,
positions,
lid not be
at time did
10 days.
PART 11.
VULGAR FRACTIONS,
A PR ACTION is a part or parts of an unit, and written with Iw*
Igures, with a line between them, as -}, f , f , Ac.
The figure above the line is called the numerator, and the un-
Jer one me denominator ; which shows how many parts the
«init is divided into : and the numerator shoves how many of
ihose parts are meant by the fraction.
There are four sorts of vulgar fractions : proper, improper,
compound, and mixed, viz.
1. A PROPER FRACTION is wheu the numerator is less than
the denominator, as f , f , f , -j^, loj., &c.
2. An IMPROPER FRACTION is when the numerator is equal
to, or greater than the denominator, as f , f , ff , J-f^, &c.
3. A COMPOUND FRACTION is the fraction of a fraction, and
known by the word of, as ^ of f of ■Z'^jf 5^ of j*^, &c.
4. A MIXED NUMBER, OR FriACTioN, IS composed of a whol»
number and fraction, as 8^,
2' "a7»
6lc.
106
REDUCTlOBr OF VVLOAR FRACTIONS.
REDUCTION OF VULGAR FRACTIONS.
1. To reduce fractions to a common denominator.
Rule. Multiply each numerator into all the denominators,
except its own, for a numerator ; and all the denominators, for
a common denominator. Or,
2. Multiply the common denominator by the several giren
numerators, separately, and divide their product by the several
denominators, the quotients will be the new numerators.
EXAMPLES.
1. Reduce f and f to a common denominator.
Facit, ^ and -Jf .
1st num. 2d num.
2x7=14 4x4=16, then 4x7=28 den.=Jf and f|.
2. Reduce ^, f , and -f, to a common denominator,
3. Reduce f , f, -^, and f , to a common denominator.
4. Reduce -f^t f ,
'Pacit. 88*fl 824(1 tnifl aBSft
fauil, 386 0* M6ff> 8860* 8969'
7>
and f, to a common denominator.
Facit,
1 n n a
1«80>
8,4 0. ,a.4.o.
1680)1680'
5. Reduce f , f , f-, and -^i to a common denominator,
Facit, fH
1686'
6.
» 8To» 8«o»
Reduce f , f , f, and f , to a common danominator.
ttt*
Facit,
Tan
8 160»
iH
0*
K A ft
jtaaa
2I«0'
2. To reduce a vulgar fraction to its lowest terms.
Rule. Find a common measure by dividing the lower term
by the upper, and that divisor by the remainder followingr till
nothing remain : the last divisor is the common measure ; then
divide both parts of the fraction by the common measure, and
the quotient will give the fraction required.
Note. If the common measure happens to be one, the fraction
is already in its lowest term : and when a fraction hath ciphers at
the right hand, it may be abbreviated by cutting them off, as W%.
EXAMPLES.
7. Reduce |-f- to its lowest terms.
24)32(1
24
Com. measure, 8)24(3 Faciv.
RXVUOTlOIf OF VITLOAR FRACTIONS.
107
8. Rednce -^ ta its lowest termv. Facit, ^5-.
9. Reduce -f^ to its lowest ter ^8. Facit, -jVi-.
la Reduce ^ to its lowest i; s. Facit, i.
1 1. Reduce fff- to its lowest terms. Facit, f^.
12. Reduce f^^ to its lowest terms. Facit, f .
3. To reduce a mixed number to an improper fraction.
Rule. Multiply the whole number by the denominator of
(he fraction, and to the product add the numerator for a new
numerator, which place over the dienominator.
Note. To express a whole number fraction-ways set 1 for
the denominator given.
EXAMPLES.
13. Reduce 18f to an improper fraction..
18X7+3=129 new numerator=»f •.
14. Reduce 56^ to an improper fraction.
15. Reduce 183^ to an improper fractioa
16. Reduce 131- to an improper fraction.
17. Reduce 27^ to an improper fraction.
18. Reduce &14|^ to an improper fraction.
4. To reduce an improper fraction to its proper terms.
Rule. Divide the upper term by the lower.
Facit,
Facit, -Lfft.
Facit, »|t».
Facit, Y-
Facit, «f ».
Facit, «ff •.
EXAMPLES^
19. Reduce >f » to its proper terms*
129+7=18f,
20. Reduce »ff-» to its proper terms,
21. Reduce 'ff^ ^q j^g proper terms*
22. Reduce ^ to its proper terms.
23. Reduce «f » to its proper terms.
24. Reduce ^ff » to its proper terms.
Facit, 18f.
Facit, 56ff .
Facit, 183^.
Facit, 131^.
Facit, 27f .
Facit, 614tV.
5. To reduce a compound fraction to a single one.
-J'^i^^l Multiply all the numerators for a new numerator,
and all the denominators for a new denominator.
Reduce the new fraction to its lowest terms by Rule 2.
106
REDUCTION OF VULGAR FRACTIONS.
il
II
EXAMPLES.
35. Reduce ^ of f of | to a sixigle fraction.
2X3X5= 30
Facit, — reduced to the lowest term=sf .
3X5X8=120
26. Reduce ^ of 4^ of -J^ to a single fraction.
Facit, fif =iVV-
27. Reduce -{i of fj of |i to a single fraction.
Facit, iiff =^.
28. Reduce | of f of ^^ to a single fraction.
29. Reduce f of f of f to a single fraction.
Pacit •^-^-^=A
30. Reduce f of f of i\ to a single fraction.
Facit. »ft — -g-
6 To reauce fractions of one denomination to the fraction of
another, but greater, retaining the same value.
Rule. Reduce the given fraction to a compound one, by com-
paring it with all the denominations between it and that denomi-
nation which you would reduce it to ; then reduce that compound
fraction to a a single one.
EXAMPLES.
3L Reduce f of a penny to the fraction of a pound.
00 T, A . c r, Facit,fof J5 0f,J-,=T^. .
Jx, Reduce t of a penny to the fraction of a pound.
Facit, j^.
33. Reduce f of a dwt. to the fraction of a lb. troy.
Facit, TsVo"'
34. Reduce f of a lb. avoirdupois to the fraction of a cwt.
Facit, -yfj,
7. To reduce fractions of one denomination to the fraction of
another, but less, retaining the same value.
Rule. Multiply the numerator by the parts contained in the
several denorainatioiia between it, and that you would rec je it
to, for a new numerator, and place it over the given denominator.
REDUCTION OF TULOAR FRACTIONS.
EXAMPLES.
10»
— 148
fe*
Ji—2.
— Ifi'
68*
miction of
by com-
denomi-
•mpound
TTsTT*
'» •«0'
1200*
Wt.
» 7 84»
iction of
d ia the
et. ze it
ninator.
35. Reduce j^ of a pound to the fraction of a penny.
Faci^ 2.
7X aOX 12=1680 -iiii reduced to its lowest term=f .'
36. Reduce y^. of ^ pound to the fraction of a penny.
37. Reduce -oVo of a pound troy, to the fraction of a pennv-
^«ignt- Facit, *.
38. Reduce ^h of a cwt. to the fraction of a lb.
Facit, f .
8. To reduce fractions of one denomination to another of the
same value, having a numerator given of the required fraction
Rule. As the numerator of the given fraction : is to its deno-
mmator : : so is the numerator of the intended fraction : to its
uenommator.
EXAMPLES.
39. Reduce f to a fraction of the same value, whose numera-
VIA U ^ ^^' As 2 : 3 : : 12 : 18. Facit, 44.
40. Reduce f to a fraction of the same value, whose numera-
tor shall be 25. p^cit, ^.
41. Reduce f to a fraction of the same value, whose numera-
tor shall be 47. ^^
Facit,
65^.
9. To reduce fractions of one denomination to another of the
same value, having the denominator given of the fractions re-
quired.
Rule. As the denominator of the given fraction : is to its
numerator : : so is the denominator of the intended fraction : to
Its numerator.
EXAMPLES.
42. Reduce f to a fraction of the same value, whose denomi-
■ator shall be 18. As 3 : 2 : : 18 : 12. Facit, -ff.
43. Reduce ^ to a fraction of the same value, whose denomi-
nator shall be 35. Facit, ^^.
44. Reduce f to a fraction of the same value, whose denomi-
nator shall be 65f . 47
Facit,
65f.
no
REDVCTION OF VULCtAK VRACTIONS*
10, To reduce a mixed firaetion to a single one.
RuLK. When the numerator lis the integral part, multiply it
by the denominator of the fractional part^ addinginthe numerator
Of tfte fractional part for a new numerator ; then multiply the de-
nominator of the fraction by the denominator of the fractional
part foi anew denominator.
EXAMPLESi
Facit, m=n-
36f
46. Reduce — to a simple fraction..
48
36 X 3 -f 2=1 10 numerator.
48 X 3 =144 denominator.
23f
46i Reduce— to a simple fraction* Facit,^=f^.
When the denominator is the integral part, multiply it by the
denominator of the fractional part^ adding in the numerator of
the fractional part for a new denominator ; then multiply the
numerator of the fraction by the denominator of the fractional
part for a new numerator.
EXAMPLES.
^ 47. Reduce^to a simple fraction. Facit. 4M-»^
; 19°
48. Reduce— to a simple fraction. Facit. -A?-- ^
11. To find the proper quantity of a fraction in the known
parts of an integer.
Rule. Multiply the numerator by the common parts of the
integer, and divide hy the denominator.
EXAMPLES.
Q V 2ii5S?"5® t^^ * pound sterling to its proper quantity.
J X 20=60-4-4=168. ^ Facit, 168
50. Reduce fofa shilling to its proper quantity.
Ki u J ^ ^ , ^*ciC 4d. 34- qrs.
&1. Keducef of a pound avoirdupois to its proper quantity
Ro D J , i. Facit,9oz.2f dr.
04. KedUCe ■*• of a CXVL tn its nrnner /inantU^r
Facit, 3 qrs. 3 lb. 1 oz. ISf dr.
i
KKOOOTIOK Of TVLOAA VRAOTIOITS.
Ill
nultiply it
mmcrator
>ly the de-
fractional
i?=H.
HtW.
it by the
erator of
Itiply the
fractional
e known
t8 of the
t, 15s.
li qrs.
}uantity
2f dr.
2idr.
I
153. Reduce f of a pound troy to its proper quantity.
Facit, 7 oz. 4 dwts.
54. Reduce ^ of an ell English to its proper quantity.
Facit, 2 qrs. 3^ nails.
oo. Reduce f of a mile to its proper quantity.
_ _ , Facit, 6 fur. 16 poles.
66. Reduce f of an acre to its proper quantity.
Facit, 2 roods, ao poles.
57. Reduce f of a hogshead of wine to its proper quantity.
Facit, 64 gallons.
88. Reduce ^ of a barrel of beer to its proper quantity.
Facit, 12 gallons.
59. Reduce i^ of a chaldron of coals to its proper quantity.
Facit, 15 Bushels.
60. Reduce f of a month to its proper time.
Facit, 2 weeks, 2 days, 19 hours, 12 minutes.
12. To reduce any given quantity to the fraction of any greater
denomination, retaining the same value.
Rule. Reduce the given quantity to the lowest term men-
tioned for a numeratOi , under which set the integral part reduced
to the same term, for a denominator, and it will give the fraction
required.
EXAMPLES.
61. Reduce t5s. to the fraction of a pound sterling.
Facit, ii=i£.
62. Reduce 4. 3^ qrs. to the fraction of a shilling.
Facit, f .
63. Reduce 9 oz. 2f dr. to the fraction of a pound avoirdupois.
Facit, f .
64. Reduce 3 qrs. 3 lb. 1 oz. 12t dr. to the fraction of a cwt.
Facit, ^.
66. Reduce 7 oz. 4 dwts. to the fraction of a pound troy.
Facit, f.
66. Reduce 2 qrs. 3^ nails to the fraction of an English ell.
Facit, f .
67. Reduce 6 fur. 16 poles to the fraction of a mile.
V Facit, f .
68. Reduce 2 roods 20 poles to the fraction of an acre.
_ _ Facit, -f.
09. Reduce &4 gallons to the fraction of a hogshead of wine.
Facit, f .
112
SUBTRACTION OV TULOAR FRACTIONS.
70 Reduce 12 gallons to the fraction of a barrel of beer.
71 . Reduce fifteen bushels to the fraction of a chaldron of coals.
Facit A
72. Reduce 2 weeks, 2 days, 19 hours, 12 minutes,\o the
fraction of a month. Facit, f .
ADDITION OF VULGAR FRACTIONS.
.u ^"^j J i?l^"^® *^® ^^^®" fractions to a common denominator,
then add all the numerators together, under which place the com-
mon denominator.
EXAMPLES.
1. Add f and I together. Facit, J4+if=^f=l^.
2. Add i, f and f together. Facit, Ifjf .
3. Add i-, 4i and f together. Facit, 4f •.
4. Add 7f and f together. Facit, S^.
5. Add f and f of f> together. Facit, if.
6. Add 5f, 6f and 4^ together. Facit, 17^^.
2. When the fractions are of several denominations, reduce
them to their proper quantity, and add as before.
7. Add f of a pound to |- of a shilling. Facit, 15s. lOd.
a Add ^ of a penny to f of a pound. Facit, 13s. 4id.
9. Add 1^ of a pound troy to i of an ounce.
Facit, 9 oz. 3 dwts. 8 grs.
10. Add f of a ton to f of a lb.
Facit, 16 cwt. qrs. lb. 13 oz. 5J- dr.
11. Add f of a chaldron to f of a bushel.
,„ . ,^ Facit, 24 bushels 3 pecks.
14. Add J- of a yard to f of an inch.
Facit, 6 inch. 2 bar. c.
SUBTRACTION OF VULGAR FRACTIONS.
the^^subtraJI'thpT ^^' ^''^'" fraction to a common denominator,
Mien subtract the less numfirator fmm th- "-Psf J -» -^
remainder over the common"dcnomi„Vto;.* ' """ *'""^' ""
HULTIPLI0ATI05.
113
2. When the lower L;ii;tion is greater than the upper, sub-
tract the numerator of the lower fraction from the denominator,
and to that difference add the upper numerator, carrying one to
the unit's place of the lower whole number.
EXAMPLES.
1. From ^ take i 3X7=21. 5X4=20. 21— 20=1 num.
4 X 7=28 den. Facit, -»-.
2. From -g- take f of |. Pacit, ||!
3. From &| take W- Facit, d%.
4. From ff- take f Facit, ^^.
6. From ^ take | of f . Facit ^-^
6. From 64| take f of f . Facit, 63|'
3. When the fractions are of several denominations, reduce
them to their proper quantities, and subtract as before.
7. From i of a pound take f of a shilling. Facit, 14s. 3d.
8. From -f of a shilling take ^ of a penny. Facit, 7^.
9. From f of a lb. troy take f of an ounce.
Facit, 8 oz. 16 dwts. 16 grs.
16. From f of a ton take f of a lb.
Facit, 15 cwt. 3 qrs. 27 lb. 2oz. lOf drs.
11. Fromf of a chaldron, fake ^ of a bushel.
Facit, 23 bushels, 1 peck
12. From f of a yard, take f of an inch.
F&cit, 5 in. 1 b. c.
MULTIPLICATION OF VULGAR FRACTIONS.
Rule. Prepare the given numbers (if they require it)by the
rules of Reduction ; then multiply all the numerators together for
a new numerator, and all the denominators for a new denomin-
ator.
EXAMPLES.
1. Multiply f by f .
Facit, 3X3=9 num.
2. Multiply f by f.
3. Multiply 48^3- by 13f .
4. Multiply 430-1%- by 18|-.
5. Multiply fi by f of f of f.
6. Multiply -^,- by f of f of ^.
K3
4X5=20 den.—„a
2 0'
2 7*
6723^.
Facit,
Facit,
Facit, 7935f4.
fdCll, 2 4
Facit,
4 9'
a.
8*
114
SINOLB RVLB Of THRBB PIRBOT.
?. Multiplyfoff byf off
8. Multiply i off by f.
9. Multiply 5^ by f.
10. Multiply 24 by f .
11. Multiply f of 9 by f.
13. Multiply 9^ by f .
Facit, f
Fmcit, j^.
Facit,4t2.
Facit, 10.
Facit, 5ff .
Facit, hi.
DIVISION OF VULGAR PRACT0N8.
^'^'f* Prepare the given numbero (if they require it) by the
rules of Reduction, and invert the divwofr then proceed a»lo
Multiplication.
EXAMPLES.
1. Divide^ by f.
Facit, &X9=±4&mdm^ZXSO'=60
2. Divide if by f
3. Divide 672A by ISf.
4. Divide 7935af by 18f
5. Divide f by f of f of f
6. Divide f of 16 by f of f
7. Divideioff byf off
8. Divide9f«, by^ofr
9. Divide ^V by 4f
10. Divide 16 by 24.
U. Divide 5206jV by f of 9K
12, Divide 3i by 9f
den.-4f=f
Facit, f
Fa<!i4,46f
Facit, 430f .
Facit, -j^
Facit, 19ti.
Facit, if =|.
Facit, 2H.
Facit, f .
Facit, f
Facit, 71f
Facit, f .
THE SINGLE RULE OF THREE DIRECT, IN VULGAR
FRACTIONS.
Rule. Reduce the numbers as before directed in Reduction.
State the question as in the Rule of Three in whole numbers, and
invert the first term in the proportion, tlien multiply the three
terms continually together, and the product will be the answer.
fINOLB ftVLB Of TBRSB INVBRM.
lt&
EXAMPLES.
1. If I of a yard cost | of £1, - hat will -ft of a yard come to
at that rate ? Ans, ^*=:158.
yd. £ yd. £
As f : f : : -ft : ^=158.
and 3X8X10=340 den. °'t^»o-n iJKUo*"
2. If I of a yard cost f of £1, what will ii- of a yard cost!
^715. 14s. 8d.
3. If f of a yard of lawn cost 7s. 3d., what will \0\ yardtr
cost ! . Ans, £4 : 19 : 10|f .
4. Iff lb. cost ^3. how many pounds will f of Is. buy?
Ans. 1 lb.-5-f-j-=iV»
6. Iff ell of Holland cost \ of £1, what will 13f ells covt at
the same rate ? AnsiCH : : 8J ^.
6. If 12^ yards of cloth cost 15s. 9d., m^at wfll 4Bk cost at the
same rate ? Ans. £3:0:9^ -^.
7. If tV o^ ft cwt, cost 284s. what will 7^ cwt. cost at the same
rate.? il«s. £118:6 fa
8. If 3 yards of broad cloth cost £2^, what will lOf yard*
eost ? Ans. £9 : 1%
9. If i of a yard cost i of £1, what will f of an ell English
come to at the same rate? Ans, £2.
10. If 1 lb. of cochineal cost £1 : 6, what will 36 f. lb. come
tot ilii5. £45 : 17 : 6.
11. If 1 yard of broad cloth cost 15|8., what will 4 pieces coat,
6ach containing 27f yards ? Ans. £85 : 14 : 3| f§^ or f .
12. Bought 3^ pieces of silk, each containing 24f ells, at 68.
dfd. per ell. I desire to know what the whole quantity cost ?
Ans. £25 : 17 : t^ ^.
THE SINGLE RULE OF THREE INVERSE, IN VULGAR
FRACTONS.
EXAMPLES.
1. If 48 men can build a wall in 24^ days, how many men
can do the same in 192 days ? Ans. 6^*^. men.
2e If 25?-s= will nay for the carriace of 1 cwt= 145-i miles, how
far may 6^ cwt. be carried for the same money ?
Ans, 22g^ miles.
no
THE DOUBLE RULE OF THREE.
3. If 3| yards of cloth, t^^ « ^ y»fd wide, be sufficient to
make a cloak, how utuch mu t >^ ve of that tiurt which is f yard
wide, to make another of Vht ajm* bigness?
Ans. 4| yards.
4. If three men ctn do a piece of work in 4^ hours, in how
many hours will tiill ^«en du the same work ?
Ans. r§^o hour.
5. If a penny white lual w< i^hs 7 oz. when a buslu ' of wheat
cost 6s. 6d., what is a bushel worth when a penny white loal
weighs but 2^ oz. ? . Ans. 16. 4fd.
6. What quantity of shalloon, that is f- yard wide, will lineT^
yards of cloth, that is 1^ yard wide? Ans. 15 yards.
THE DOUBLE RULE OF THREE, IN VULGAR
FRACTIONS.
EXAMPLES.
K
1. If a carrier receives £2-^ for the carriage of 3 cwt. 160
miles, h* , mu^^ ought he to receive for the carriage of 7 cwt.
3i qrs. 5U mikt Ans. £1 : 16 : 9.
2. If £100 i 12 months gain £6 interest, what principal will
gain £3f in 9 months ? Ans. £76.
3. If 9 students spend £10|-in 18 days, how much will 20
students spend in 30 days ? Ans. £39 : 18 : 4^^^^
4. A man and his wife having laboured one day, earned 4fs.
how much rjust they have for 10^ days, when their two sons
helped them ? Ans. £4 : 17 : 1^.
6. If £50, in 5 months, fjain £2iVT» what time will £13f re-
quire to gain £1 iV ' ^'"'S' 9 months.
6. If the carriage of 60 cwt. 20 miles cost £14|-, what weight
can I have carried 30 miles for £5-jV ? -^ns. 15 cwt.
117
fficient to
I is f yard
r f ards.
8, in how
^Q hour.
' of wheat
vhite loat
[5. 4td.
all line 7^
> yards.
LGAR
\ cwt. 1 5a
of 7 cwt.
: 16 : 9.
icipal will
IS. £75.
h will 20
irned 4fs.
two sons
17 :1^
1 £13i re-
months.
lat weight
15 cwt
THE
TUTOR'S ASSISTANT.
PART III.
DECIMAL FRACTIONS.
In Decimal Fractions the integer or whole thing, as one pound,
one yard, one gallon, dec. is supposed to be divided into 10 equal
parts, and those parts into tenths, and so on without end.
So that the denominator of a decimal being always known to
consist of an unit, with as many ciphers as the numerator has
places, therefore is never set down ; the parts being only distin-
guished from the whole members by a comma prefixed : thus ,&
which stands for -^5, ,26 for VW, ,123 for -iVW-
But the different value of figures appears plainer by the fol-
lowing table.
Whole numbers. Decimal part*.
7654321, 3 34567
•^ ■-•> "^ IHJ MJ >-H
5 3"^
■ S Q
n
2 6'='
5 p
B a
From which it piainly appears, that as whole numbers increaie
bt a ten-fold proportion to the left hand, so decimal parts decrease
in a ten-fold proportion to the right hand ; so that ciphers placed
118
ADDITION OF DECIMALS.
befors decimal parts decrease their value by removing them far
ther from the comma, or unit's place ; thus, ,5 is 5 parts of 10, or
A ; ,05 is 5 parts of 100, or ^h ; ,005 is 5 parts of 1000, or
tAo ; »0005 is 6 parts of 10000, or -foioi- B"t ciphers after
decimal parts do not alter their value. For ,5, ,50, ,500, &c.
are each but -^ of the unit.
A FINITE DECIMAL is that which ends at a certain number of
places, but an infinite is that which no where ends.
A recurring decimal is that wherein one or more figurct
are continually repeated, as 2,75222.
And 52,275275275 is called a compound recurring deci
NAL.
Note. A finite decimal may be considered as infinite, by ma-
king ciphers to recur ; for they do not alter the value of the deci-
mal.
In all operations, if the result consists of several nines, reject
them, and make the next superior place aa unit more ; thus, for
26,25999, write 26, 26.
In all circulating numbers, dash the last fignre.
ADDITION OF DECIMALS.
RiTL5. In setting down the proposed numbers to be added,
great care must be taken in placing every figure directly under-
neath those of the same value, whether they be mixed numbers,
or pure decimal parts ; and to perform which there must be a due
regard had to the commas, or separatikig points, which ought
always to stand in a direct line, one under another, and to the
right hand of them carefully place the decimal parts according
to their respective values ; then add them as in whole numbers.
EXAMPLES.
I. Add 72,5+32,071 + 2,1574 + 371,44-2,75.
Facit, 480,8784.
f. Add 30,07 + 2,0071 + 59,432 + 7,1 .
». Add 3,6 + 47,25 + 927,01 + 2,0073 + 1 ,5.
4. Add52,75 + 47,2l + 724+31,452+,3076.
$. Add 3275 + 27,514 + 1,005 -f- 725 + 7,32.
«. Add 27,5 + 52 + 3,2675+,5741 + 2720,
V them far
ts of 10, or
»f 1000, or
phers after
1 1500, 6cc»
number of
»
ore figurefl
UNO DECI
itc, by TTia-
)f the deci-
nes, reject
; thuSffor
be added,
;tly under-
I numbers,
st be a due
iich ought
and to the
according
! numbers.
»,8784.
MVLTIPtSCATION OF DE0IHAL9, II
SUBTRACTION OF DECIMALS,
ftuLB. Subtraction of decimals differs but little front whole
numbers, only in placing the n«mbers, which mutt be carefully
observed, as in addition.
EXAMPLES.
1. Prom ,5754 takft ,2371.
3. From ,237 take 1,76.
3. From 271 take 215,7.
4. Prom 270,2 take 75,4075.
5. Prom 571 take 94,72.
6. From 625 take 76,91.
7. From 23,415 take ,3742.
8. From ,107 take ,0007.
MULTIPLICATION OF DECIMALS.
Rule. Place the factors, and multiply them, as in whole num-
bers, and from the product towards the right hand, cut off as
many places for decimals as there are in both factors together ;
but if there should not be so many places in the product, sup^
ply the defect with ciphers to the left hand.
EXAMPLES.
Facft, ,05758775.
7. Multiply27,35 by 7,70071.
8. Multiply 57,21 by ,0075.
9. Multiply ,007 by ,007.
10. Multiply 20,15 by ,2705.
11. Multiply ,907 by ,0025.
1. Multiply ,2365 by ,3435.
3. Multiply 2071 by 2,27.
3. MulUpIy 37,15 by 25,3.
4. Multiply 72347 by 23,15.
5. Multiply 17105 by ,3257.
6. Multiply 17105 by ,0237.
•iwSf^f " *"^ number of decimals is to be multiplied by 10, 100^
1000, &c, it is only removing the separating point in the multl-
plicand so many places towards the right hand as there are ciphers
cJ^.!S2!^'P?fI- tJ^"s, ,578X10 = 5,78. ,578X100 = 5,78.
,578X1000 = 578; and ,678X10000 = 5780.
CONTRACTED MULTIPLICATION OP DECIMALS.
Rule. Put the unit's place of the multiplier under that nlare
of the multiplicand that is intended to be kep't in the product,' then
invert the order of all the other fiaures. i. e. write them all the
1^
CONTRACTED MULTIPLICATION.
contrary way ; and in multiplying, begin at the figure in the mul-
tiplicand, which stands over the figure you are then multiplying
with, and set down the first figure of each particular product di-
rectly one under the other, and have a due regard to the increase
arising from the figures on the right hand of that figure you begin
to multiply at in the multiplicand.
Note. That in multiplying the figure left out every time next
the right hand in the multiplicand, and if the product be 5, or
upwards, to 15, carry 1 ; if 15, or upwards, to 25, carry 2; and
if 25, or upwards, to 35, carry 3, &c.
EXAMPLES.
12. Multiply 384,672158 by 36,8345, and let there be only
four places of decimals in the product.
Contracted way.
384,672158
5438,63
115401647
33080329
3077377
115402
15387
1923
14169,2065
Common way.
384,672158
36,8345
1923
15386
115401
3077377
23080329
115401647
360790
88632
6474
264
48
4
14169,2066
038510
Facit, 14169,2065.
13. Multiply 3,141592 by 52,7438, and leave only four places
of decimals. Facit, 165,6994.
14. Multiply 2,38645 by 8,2175, and leave only four places
of decimals. * Facit, 19,6107.
15. Multiply :^75,13758 by 167324, and let there be only one
place of decimals. Facit, 6276,9.
16. Multiply 375,13758 by 16,7324, and leave only four placef
of decimals. Facit, 6276,9520.
17. Multiply 395,3766 by ,75642, and let there be only foui
place« of decimals. Facit, 299,0699.
DIVISION OF DECIMALS.
121
he mul-
tiplying
duct (li-
ncrease
lu begin
me next
be 5, or
' 2 ; and
be only
DIVISION OF DECIMALS
This Rule is also worked as in whole numbers ; the only dif-
ficulty is in valuing the quotient, which is done by any of the fol-
lowing rules :
Rule 1. The first figure in the quotient is always of the same
value with that figure of the dividend, which answers or stands
over the place of units in the divisor.
2. The quotient must always have so many decimal places,
as the dividend has more than the divisor.
Note 1. If the divisor and dividend have both the same num-
ber of decimal parts, the quotient will be a whole number.
2. If the dividend hath not so many places of decimals as are
in the divisor, then so many ciphers must be annexed to the divi-
dend as will make them equal, and the quotient will then be a
whole number.
3. But if, when the division is done, the quotient has not so
many figures as it should have places of decimals, then so many
ciphers must be prefixed as there are places wanting.
EXAMPLES.
,2066.
ir places
,6994.
r places
,6107.
only one
.276,9.
ar placef
l,9520«
»nly foul
l,0699«
1. Divide 85643,825 by 6,321.
2 Divide 48 by 144.
3. Divide 2lt,75 by 65.
4. Divide 125 by ,1045.
5. Divide 709 by 2,574.
6. Divide 5,714 by 8275.
Facit 13549.
7. Divide 7382,54 by 6,4252.
8. Divide ,0851648 by 423.
9. Divide 267,15975 by 13,25.
10. Divide 72,1564 by ,1347.
11. Divide 715 by ,3075.
When numbers are to be divided by 10, 100, 1000, 10,000,
&c. it is performed by placing the separating point in the dividend
so many places towards the left hand, as there are ciphers in the
divisor.
Thus, 5784- 10=578,4.
5784-^100=57,84.
5784-i- 1000=:55784.
6784-10.66o=,5Ti4.
122
CONtttACtfii) DITISIOH.
CONTRACTED DIVISION OF DECIMALS.
Rule. By the first rule find what is the value of the first figure
in the quotient : then by knowing the first figure's denomination,
the decimal ]places may be reduced to any number, by taking as
many of the left hand figures of the dividend as will answer them ;
and in dividing, omit one figure of the divisor at each following
operation.
Note. That in multiplying every figure left out in the divisor,
you must carry 1, if it be 5 or upwards, to 15 ; if 15, or upwards,
to 25, carry 2 ; if 25, or upwards, to 35, carry 3, &€.
EXAMPLES.
12. Divide 721,17562 by 2,257432i and let there be only thr««
places of decimals in the quotient.
Contracted.
2,257433)721 , 17562(319,467
6772296
Common way-
3,357432)721,17562(319,467
6772296
439460.
225743 .
213717..
203169..
10548..
9030..
1518.
1354.
164
158
13. Divide
14. Divide
15. Divide
16. Divide
18. Divide 27,104 by 3,712.
8,758615 by 5,2714167.
51717591 by 8,7586.
25,1367 by 217,35.
51.47512 by ,133415.
■yn no i... "^ r^opo
439460
225743
21371700
303168 88
120
738
392S
135414592
10548
9029
1518
163
158
93280
02024
91256
RfiOUCTION OF DSCIMAL8.
183
S.
irst figure
mination,
taking as
rer them ;
following
;e divisor,
upwards,
miy thrtse
19,467
3
i
280
REDUCTION OF DECIMALS.
To reduce a Vulgar Fraction to a Decimal.
Rule. Add ciphers to the numerator, and divide by the de-
nommator, the quotient i« the decimal fraction required.
EXAMPLES.
1. Reduce \ to a decimal. 4)1,00(,25 Facit.
2. Reduce i ....v to a decimal. Facit, ,5.
3. Reduce I k to a decimal Facit, ,76.
4. Reduce f to a decimal. Facit, ,375.
5. Reduce ^ to a decimal. Facit, ,1923076-f-.
6. Reduce W oi\^, to a decimal. Facit, ,6043956+.
Note. If the given parts are of several denominations, they
n.^y be reduced either by so many distinct operations as there
are different parts, or by first reducing them into their lowest
denomination, and then divide as before ; ofj
2ndly. Bring the lowest into decimals of the next superior de-
nomination, and on the right hand of the decimal found, place the
parts given of the next superior denorhination ; so proceeding till
you bring out the decimal parts of the highest integer required, by
•till dividing the product by the next superior denominator ; of.
3dly. To reduce shillings, pence, and farthiiigs. If the num-
ber of shillings be even, take half for the first place of decimals,
and let the second and third places be filled with the farthings
contained in the remaining pence and farthings, always remem-
bering to add 1, when the number is, or exceeds 25. But if the
nuTTiber of shillings be odd, the second place of decimals mu»t
be increased by 5.
7. Reduce 5s. to the decimal of a £. Facit, ,25.
!^. -vr^!.!.,,^. i,c. i„ liic uv;v,iniai Ul ;t 3t. 1' ECU, ,'*0.
9. Reduce UJs. to tlie decimal of a £. Facit, ,a
L2
i j
\!
\%i REDUCTION OF DECIMALS.
10. Reduce 8s. 4d. to the decimal of a £.
Facit, ,4166.
11. Reduce 16s. 7|d. to the decimal of a £.
Facit, ,8322916,
last.
16s. 7|d.
12
199
4
960)799(8322916
second. third.
4)3,00 2)16
12)7,75 ,832
2)0)16,64583
,8322916
7|d.
4
ii
12. Reduce 19s. 5^d. to the decimal of a £.
Facit, 972916.
13. Reduce 12 grains to the decimal of a lb. troy.
Facit, ,002083.
14. Reduce 12 drams to the decimal of a lb. avoirdupois.
Facit, ,046875.
15. Reduce 2 qrs. 14 lb. to the decimal of a cwt.
Facit, ,625
16. Reduce two furlongs to the decimal of a league.
Facit, ,0833.
17. Reduce 2 quarts, 1 pint, to the decimal of a gallon.
Facit, ,625.
18. Reduce 4 gallons, 2 quarts of wine, to the decimal of a
hogshead. Facit, ,0714284-.
19. Reduce 2 gallons, 1 quart of beer, to the decimal of a bar-
rel. Facit, ,0625.
20. Reduce 62 days to the decimal of a year.
Facit, 1424654-.
To find the value of any Decimal Fraction in the known parts
of an Integer.
Rule. Multiply the decimal given, by the number of parts of
the next inferior denomination, cutting off the decimals from the
product; then multiply the remainder by the next inferior deno-
mination ; thus proceeding till you have brought in the least
ku&'wn parts of an integer.
REDUCTION OF DECIMALS.
125
EXAMPLES.
21. What is the value of ,8322916 of a lb.?
Ans. 16s. 7id.+.
ao
16,6458320
12
7,7499840
4
2,9999360
22. What is the value of ,002084 of a lb. troy?
oo «ru . , ^^«- 12,00384 gr.
43. What is the value of ,046875 of a lb. avoirdupois ?
24. What IS the value of ,625 of a cwt. ?
oc ^uri . , -^"*- 2 qrs. 14 lb.
25. What IS the value of ,626 of a gallon?
tui XT^^. . , -^^** 2 quarts 1 pint
26. What IS the value of ,071428 of a hogshead of wine ?
o» wu . . ^ •^^*- * gallons 1 quart, ,999866.
»7. What IS the value of ,0625 of a barrel of beer ?
oo «ri. . , ^^^* 2 gallons 1 quart
28. What IS the value of ,142465 of a year ?
il»5. 51,999726 days.
126
; f
DEOIMAL TABLES OF COIN, WBlOfST, AND MEASURE.
TABLE I.
English Coin.
£ 1 the Integer.
^h.
Dec.
Sh.
19
,95
9
18
,i>
8
17
,85
7
16
,8
6
15
,75
5
14
.7
4
13
65
3
13
,6
2
11
,55
1
10
,5
Dec.
,45
I
K
,15
|05
Pence.
6
5
4
3
2
1
Decimals.
,025
,020833
,016666
,0135
,008333
,004166
Farth.
3
2
1
Decimals.
,003125
,(0020833
,0010416
Farth.
3
2
I
Decimals.
,06i?5
,041666
,020833
TABLE III.
Troy Wbioht.
1 lb. the Integer.
Ounces the same as
Pence in the last
Table.
TABLE II.
Enolish Coin. 1 Sh.
Long Measure. 1 Foot,
the Integer.
Penoe &i
Inches.
6
5
4
3
3
1
u,
Decimals.
,5
,416666
.333333
,25
,166666
,083333
Dwts.
10
9
8
7
6
5
4
3
2
1
Decimals.
,041666
,0375
,033333
,029166
,025
,020833
,016666
,0125
,008333
,004166
Grains.
12
11
10
9
8
7
6
5
4
3
2
1
Decimals.
,002083
,001910
,001736
,001562
,001389
,001215
,001042
,000868
,000694
,000521
,000347
,000173
Grains
12
11
10
9
8
7
6
5
4
3
2
1
DecimaU.
,058
,022916
,020833
,01875
,016()6tf
,•14583
,0125
,010416
,008333
,00625
,0ft4166
,002083
TABLE IV.
Ayoir. WncHT.
113 Ibe. tlM Integot.
an.
3
3
1
Decimals*
.5
,25
1 oz. the Integer.
Pennyweights the same
as Shillings in the first
Table. '
Pounds.
14
13
12
11
10
9
8
w
4
Q.
5
4
3
3
1
Decimals.
,125
,116071
,107143
,098214
,089286
,080857
,071438
,0625
,053571
,044643
,035714
,026786
,017857
,008928
Cuiicca.
8
7
TA — : — I-
,004464
,003906
! \':'
m
SURE.
DecimaU.
,058
,022916
,020833
,01875
,016(J6«
,•14583
,0125
,010416
,008333
,00625
,0^4166
,002083
-EIV.
WacBT.
M Integer.
Decimala.
f
_,25
Decimals.
,125
,116071
,107143
,098214
,089286
,080357
,071428
,0625
,053571
,044643
,035714
,026786
,017857
,008928
r\ : — 1_
,004464
,003906
DBCIMAl, TABLES OF COIN, WEIGHT, AND MEASURE.
6
5
4
8
e
I
,003348
002790
K)2232
,i, '*^74
,001116
,000558
\ Oz.
3
3
1
Decimals.
,000418
,000279
,000139
TABLE V.
Atoudopou weight.
1 lb. the lateger.
OunccB.
8
7
6
5
4
3
2
1
Dnms.
8
7
6
5
4
3
2
1
Decimals.
,5
,4375
,375
»3185
,25
,1875
»125
,0625
Dewnals.
,03125
,027343
,023437
,019531
,015625
,011718
,007812
,003906
TABLE VL
LlQ,DID MEASURE.
1 tun the lateger.
CUllons.
100
90
Decimals.
,396825
,357142
60
70
60
50
40
30
20
10
9
8
7
6
5
4
3
1
,317460
,27
,238095
,198412
,158730
,119047
,079365
,039682
,035714
,031746
,027
,023809
,019841
,015873
,011904
,007936
,003968
Pints.
4
3
fi
1
Decimals.
,001984
,001488
,000992
,000496
A
Hogshead the
Integer.
Gallons.
Decimals.
30
,476190
90
,3m60
10
,158730
9
,142857
8
,126984
7
,111111
6
,095238
5
,079365
4
,063493
3
.047619
2
,031746
1
,015873
Pints.
3
2
1
Decimals.
,005952
,003968
,001984
TABLE Vn.
Mbasures.
Liquid. Dry.
1 GaL
1 Or.
Integer.
Tti:
4
3
2
1
Decimals.
,5
,375
,25
,125
Ctpt.
3
3
1
Decimals.
,09375
,0625
,03125
Bosh.
4
3
2
1
TSET
3
%
1
Decimals.
,0234375
,015625
,0078125
^Pks.
3
3
1
Decimals.
,005859
,003906
,001953
Pints.
3
9
1
TABLE VIIL
Long Measure.
1 Mile the Integer.
Yards.
Decimals.
1000
,568182
900
,511364
800
JLfJLfAf^
700
,397727
600
,340909
■HH
128
DECIMAL TABLES OF COIN, WEIGHT, AND MEASURE. ^
500
400
300
200
100
90
80
70
60
50
40
30
20
10
9
8
7
6
5
4
3
2
1
,284091
,227272
,170454
,113636
,056818
,051136
,045454
,039773
,034091
,028409
,022727
,017045
,011364
,005682
,005114
,004545
,003977
,003409
,002841
,002273
,001704
,001136
,000568
Feet.
2
1
Decimals.
,0003787
,0001894
Inches.
6
3
1
Decimals.
,0000947
,0000474
,0000158
TABLE IX.
Time.
1 year the Integer.
Months the same as
Pence in the second
Table.
80
70
60
50
40
30
20
10
9
8
7
6
5
4
3
2
1
,219178
,191781
,164383
,136986
,109589
,082192
,054794
,027397
,024657
,021918
,019178
,016438
,013698
,010959
,008219
,005479
,002739
1 day the Integer.
Decimals.
1,000000
,821918
,547945
.273973
,246575
Hours.
12
11
10
9
8
7
6
5
4
3
2
1
Decimals.
,5
,458333
,416666
,375
,333333
,291666
,25
,208333
,166666
,125
,083333
,041666
Minutes.
Decimals.
30
,020833
20
,013888
10
,006944
3
,00625
8
,005555
7
,004861
6
,004166
5
,003472
4
,002777
3
,002083
2
,001389
1
,000664
TABLE X.
Cloth measure.
1 Yard the Integer.
(sluarters the same as
Table 4.
Nails.
2
1
Decimals.
,125
,0625
TABLE XI.
Lead Weight.
A Foth. the Integer.
Hund.
10
9
8
7
6
5
4
3
2
1
Decimals.
,512820
,461538
,410256
,358974
,307692
,256410
,205128
,153846
,102564
,051282
ars.
2
1
Pounds.
14
13
12
11
10
9
8
7
6
5
4
3
2
1
Decimals.
,025641
,012820 I
Decimals. I
,0064102
,0059523
,0054945
,0050366
,0045787
,0041208
,0036630
,0032051
,0027472
,0022893
,0018315
,0013736
,0(J05/i37
,0004578
lilt RULl or THRBl IN DlOIMAtS. l^Q
THE RULE OP THREE IN DECIMALS.
EXAMPLES.
If 26i yards co8t £3 : 16 : 3, what will 32i yards come to?
Ans. £4 : 13 : 9|.
yds. £ y(}g
26,6 : 3,8125 :: 32,25 ;
32^25
26,6)122,ft53126{4,63974==£4 : 12 : 9f
^2. What will the pay of 540 me« come to. at £1 : 5 : 6 per
n a 1- «* ^^*' ^11 : 14 : 2 3,6 ars
CO for i^78"fi%'^,.'? '.?,7'- *•>"• " •'»' 18 oz. of ^teo
J «fr^'° 6:4, what will 1 oz. come to J An, 1A
fo 's^e/'^"'" *^ "*• °' '«'""^° <="»« '»• ''''«» ijlru .* Id
r VV^ti, the worth of 19 oz. 3 dwt, 6 glrif'J^li V. Is :
a wi ;• .u . -^ns- £56 : 10 : 6 2,99 ors
yard ' " "" ""'* °^*"* ''''"'» °f P-^W. aflftj^rper
.0 Ld 11''^^'^^ ^" t of « y-.^wluV;urhe
10. If J of a yard of cloth, that a 8i yards broad makpT™,
rnent, how much that ia * of. yard wVde wmmaK sam^t"
ars 14 Ih Z,» f .r™"'' "°". *a = » • 6. V hat will 45 cwt. 3
qrs. 14 10. cost at the samA rate ? a-~ *»i^" ..« #^,
^»,9 £113: a
19Q
SXTRXCTION Of THE, fQUARI ROOT.
15. Bought a tankard for £10 \l% at the rate of St. 4d. per
uuac«, what was the weight ?
._ijq • Ana. 39 oz. 16 dwti.
10. Gave £18') : 3 : 3, for 25 cwt. 3 qrs. 14 lb. of tobacco,
a: Arhat rate did I buy it per lb. T
Ans, U 3id.
17. Bought 20 lb. 4 oz. of coffee, for £10 : 11 : 3, what is the
rhlueof31b.? ^n^. £1 : 1 : 8.
18. If I give Is. Id. for 3} lb. cheese, wha* will be the value
of 1 cwt. ? Ans. £1 : H : 8.
EXTRACTION OF THE SQUARE ROOT.
Extracting the Square Root is to find out such a number as, being
multiplied into itself, the product will be equal to the given num-
ber.
Rule. First, Point the dven number, beginning at the unit's
place, then proceed to the hundreds, and so upon every second
figure throughout
Secondly. Seek the greatest square number in the first point
towards the left hand, placing the square number under the first
point, and the root thereof in the quotient ; subtract the square
number from the first point, and to the remainder bring down
the next point and call that the resolvend.
Thirdly. Double the quotient, and place it for a dirisor on the
left hand of the resolvend ; seek how often the divisor is contain-
ed in the resolvend j (preserving always the unit's place) and pu»
the answer in tlie quotient, and also on the right-hand side of the
divisor ; then multiply by the figure last put in the quotient, and
subtract the product from the resolvend ; bring down the next
point to the remainder if there be any more) and proceed as be-
fore, , . ^ G1
hiRoOTS,
Squares.
1. 2. 3. 4. 6. 6. 7. 8. 9.
4. 9. 16. 26. 36. 49. 64. 81.
. 4d. per
dwti.
tobaceo.
sSid.
lat is thtf
I :».
he value
W:8.
IS, being
'en num-
he unU*s
Y second
rst point
' the first
le square
ngdown
or on the
I contain-
i) and pa«
ide of the
tient, and
the next
ed as be-
9.
n.
■XTR40TI01f or THB SQUARI ROOT. 131
EXAMPLES.
1. What i» the square root of 119035 1 Ans. 346.
119090(846
9
64)390
266
685)3425
3425
2. What is the square root of 106929 ? Ans. 327-I-.
3. What is the square root of 2268741 ? Ans. 1606,2if.
4. What is the square root of 7696796 T Ans. 2756,228+.
5. What is the square root of 36372961 ? Ans. 6031.
6. What is the square root of 22071204 ? Ans. 4698.
When the given num1>er consists of a whole number and deci-
mals together, make the number of decimals even, by adding ci-
phers to them; so that there may be a point fall on the unit's
place of the whole number.
7.
a
9.
10.
11.
12.
What is the square root of 3271,4007?
What is the square root of 4795,25731 ?
What is the square root of 4,372594?
What is the square root of 2,2710967?
What is the square root of ,00032754?
What is the square root of 1,270059?
Ans. 57,19-f-.
Ans. 69,247+.
Ans. 2,0914-.
Ans. 1,60701-1-.
Ans, ,018094-.
Ans. 1,12694-
To extract the Square Root of a Vulgar Fraction.
Rule. Reduce the fraction to its lowest terms, then extract
the square root of the numerator, for a new numerator, and the
square root of the denominator, for a new denominator.
If the fraction be a surd («. e.) a number where a root can ne-
ver be exactly found, reduce it to a decimal, and extract the root
from it.
EXAMPLES.
13. WTinf Im iKa onvittvA ^^^^^ r^C 2 3 4 ^
14. What is the square root of ^flf?
1 5. What is the squaw rcu^t o» -^^auLflj. f
Ans. 4.
Ans. f.
I iii
Ml
192
EXTRACTION OF THE SRUARE ROOT.
SURDS.
16. What is the square root of ff^?
17. What is the square root of ^^f?
IS. What is the square root of fff ?
Ans. ,89902^
Ans. ,86602+,
Ans. ,93309+.
To extract the Square Root of a mixed number*
Rule. Reduce the fractional part of a mixed number to its
lowest term, and then the mixed number to an improper fraction.
3. Extract the root of the numerator and denominator for a
new numerator and denominator.
If the mixed number given be u surd, reduce the fractional
part to a decimal, annex it to the whole number, and extract the
square root therefrom.
EXAMPLES.
19. What is the square root of 51|^ ?
30. What is the square root of 21-f^ ?
21. What is the square root of 9ff ?
SURDS.
22. What is the square root of 8&^?
23. What is the square root of 8f- ?
24. What is the square oot of 6f ?
Ans» 7|.
Ans. 5}.
Ans. 3|?
Ans. 9,27+
Ans. 2,9519+.
Ans. 2,5819+.
To find a mean proportional between any two given numbers.
Rule. The square root of the product of the given number
is the mean proportional sought.
EXAMPLES.
5. What is the mean proportional between 3 and 12 ?
Ans. 3 X 12=36. then V 36=6 the mean proportional.
6. What is the mean proportional between 4276 and 842 ?
Ans. 1897,4+.
To find the side of a square equal in a'^^'.a to any given
superficies.
Rule. The
18 the side of the
square root of the content of any given superficies
square equal sought. ? 1*
EXTRACTION OF THE SQUARE ROOT.
13a
EXAMPLES.
87. If the content of a given circle be 160, what is the side of
the square equal? Ans, 12,64911.
28. If the area of a circle is 750, what is the side of the square
®q"*l* iins. 27,38612.
7%c Area of a circle given to find the Diameter,
Rule. As 355 : 452, or, as 1 : 1,273239 : : so is the area : to
the square of the diameter ;— or, multiply the square root of the
area by 1,12837, and the product will be the diameter.
EXAMPLES.
29. What length of cord will be fit to tie to a cow's tail, the
other end fixed in the ground, to let her have liberty of eating
an acre of grass, and no more, supposing the cow and tail to
measure 5 J yards ? ^n*. 6,136 perches.
TJui area of a circle given, to find the periphery, or
circumference.
Rule. As 113 : 1420, or, as 1 : 12,56637 : : the area to the
square of the periphery ; — or, multiply the square root of the
area by 3,5449, and the product is the circumference.
EXAMPLES.
30. When the area is 12, what is the circumference ?
Ans. 12,279.
31. When the area is 160, what is the periphery ?
Ans, 44,839
Any two sides of a right-angled triangle given, to find the third
<ide.
1. The base and perpendicular given to find the hypothenuse.
Rule. The square root of the sum of the squares of the base
md perpendicular, is the length of the hypothenuse.
M
OiM—
m
EXTRACTtON Of THE Bt^VM^M EOOt.
EXAMPLES.
32. The top of a castle from the ground is 45 yards high, and
*ui.-oimaed with a diwh tJO yards broad ; what leagth mmimbA.
Cer be to. reach from the outside af the ditch tc^ the top of lb*
^^^•^ -Afw. 76 yards.
f.
"5
"•J
s
Diteh
Baae60yaniB.
33. The wall of a town is 25 feet high, which is surrounded
by a moat of 30 feet in breadth : I desire to know th" length of
a ladder that will reach ^rom the outside of the moat to the top
of the wall? An*. 39,06 feet.
The hypothenuse and perpendicular given., to find the haae,
RuLR. The square root of the difference of the squares of the
hypothenuse and perpendicular, is the length of the base.
The base and hypothenuse given, to find the perpendicular.
Rule. The square root of the difference of the squares of th<
hypothenuse and base, is the height of the perpendicular.
N. B. The two last questions may be raried (or examples to
the two last propositions.
Any number of men being given, to form them into a square
battle, or to find the number of rank imdfile*
Rule. The square ropt of the number of men giren, is the
number of men either in rank or file.
34. An army consistino^ of 331776 men, I desire to know how
voMaj rank and file ? Ans, 676.
35. A certain square pavement contains 48841 square stones.
of the sides?
Ans. 221
I
t
n
i
fa
tj
3
U
U
a
IXTRACTION or THE CUBB <^00T.
IS^
high, and
top of t^
S yards.
nrroundcd
length of
to the top
06 feet.
the base.
ires of the
Me.
iiculan.
res of th€
ular.
amples to
a square
'en, is the
:now how
is, 576.
re stones,
^j :
'wU Hi wii9
I*. 221.
BXTRACTION OF THE CUBE ROOT
To extract the Cohe Root is to find out one number, which be-
ing multiplied into itself, and then into that product, producettf
Ue giren number.
R^LE 1. Point ercry third figure of the cnbe given, beginnin?^
at the unit's place ; seek the greatest cube to the first pMnt, an3
^lab^ct it therefrom ; put the root in the quotient, and bring dowi>
the figures in the next point to the remainder, for a Resolve ivi>.
^ Find a Divisor by multiplyinff the square of the quotient
/ ^^* ^^^ ^^^ *' " contained in the resolvend, rej«ctin«f
the units and tens, and put the answer in the quotient. '
3. To find the Subtrahend. ! Cube the last figure In the
Quotient. 2. Multiply all the figures in the quotient by 3, except
the last, and that product by the square of the last. 3. Multiply
the divisor by the last figure. Add these products together, for
the subtrahend, which subtract from the resolvend; to the re-
mainder bring down the next point, and proceed as before.
Roots. 1.2. 3. 4. 5. 6. 7. a 9.
Cubes. 1. 8. 27. 64. 125. 216. 348, 512. 729.
EXAMPLES.
1. What is the pube root of 99252847 ?
Divisor-
99252847(463
64 sscube of 4
Square of 4 X 3=48)35252 resolvend.
216=.cube of 6.
432 «4X3Xby square of 6.
298 «divisor X by 6.
Divisor-
33o36 subtrahend.
Square of 46 x 3=6348)1916847 resolvend.
27=cube of 3.
1242 =46X3xbysquareof3.
19044 =rHvianr V K,r •)
1916847 subtrahend.
M3
sa^^M
136
BXTRACTION OF THE CUBE ROOT.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
What
What
What
What
What
What
What
What
What
What
Wh^t
8 the cube root of 389017?
s the cube root of 5735339 ?
s the cube root of 32461750?
s the cube root of 84604519?
s the cube root of 259694072 ?
8 the cube root of 48228544 ?
s the cube root of 27054036008 ?
8 the cube root of 22069810125?
8 the cube root of 122615327232?
s the cube root of 219365327791 ?
8 the cube root of 673373097125?
Aii^.
73.
Ans.
179.
Ans.
319.
Ans,
439.
Ans,
638.
Ans.
364.
Ans,
3002.
Ans,
2805.
Ans.
4968.
Ans.
6031.
Ans.
8766.
When the given number consists of a whole number and deci-
mals together, make the number of decimals to consist of 3, 6, 9,
&c. places, by adding ciphers thereto, so that there may be a
point fall on the unit's place of the whole number.
13. What is the cube root of 12,077875 ? Ans. 2,35.
14. Wh«t is the cube root of 36155,02756 ? Ans. 33,06+.
15. What is the cube root of ,001906624 ? Ana. ,124.
16. What is the cube root of 33,230979937 ? Ans. 3,215+.
17. What is tie cube root of 15926,972504? Ans. 25,16+.
18. What is the cube root of ,053157376 ? Ans. ,376.
To extract the cube root of a vulgar fraction.
Rule. Reduce the fraction to its lowest terms, then extract
the cube root of its numerator and denominator, for a new nu-
merator and denominator ; but if the fraction be a surd, reduce
it to a decimal, and then extract the root from it.
EXAMPLES
19. What is the cube root of ffi ? Ans. |.
20 What is the cube root of ^^Vo" ? Ans. f .
21. What is the cube root of i^^f. Ans. |.
SURDS.
Ans. ,829+.
Ans. ,822+,
Ans. ,873+.
To extract the cube root of a mixed number.
Rule. Reduce the fractional part to its lowest terms, and then
tue lui&cu number to an improper fraction, extract the cube rooi
of the numerator and denominator for a new numerator and deno-
22. W-at is the cube root of f ?
23. What is the cube root of |- ?
24. What is the cube root of f ?
EXTRACTION OF THE CUBE ROOT.
137
73:
179.
319.
439.
638.
384.
3002.
2805.
4968.
6031.
8766.
and deci-
3f3,6,9,
nay be a
2,35.
},06+.
,124.
2154-.
>,16+.
,376.
[1 extract
new nu-
t, reduce
ns. \.
ns. -f-.
ns. f.
829+.
822+,
873+.
and then
ube root
nd deno-
minator ; but if the mixed number given be a surd, reduce the
fractional part to a decimal, annex it to the whole number, and
extract the root therefrom.
EXAMPLES.
25. What is the cube root of 12^ ?
26. What is the cube root of 31 gVg- ?
27. What is the cube root of 405 ^hr ?
SURDS.
28. What is the cube root of 7^ ?
29. What is the cube root of 95- ?
30. What is the cube root of 8f ?
Ans, ^.
Ans. 3f.
Ans. 7f .
Ans. 1,93+.
Ans. 2,092+.
Ans. 2,057+.
THE APPLICATION.
1. If a cubical piece of timber be 47 inches long, 47 inches
broad, and 47 mches deep, how many cubical inches doth it con-
Ans. 103823
u ^' jI^®^®,^! ^ °,®"f ^"^' *^^* ^^ *2 ^«e* every way, in length,
breadth, and depth ; how many solid feet of earth were taken out
*^ Ans. 1728.
3. There is a stone of a cubic form, which contains 389017
olid feet, what is the superficial content of one of its sides?
Ans. 5329.
Between two numbers given, to find two mean proportionals.
Rule. Divide the greater extreme by the less, and the cube
root of the quotient multiplied by the less extreme, gives the less
mean ; multiply the said cube root by the less mean, and the pro-
duct will be the greater mean proportional.
EXAMPLES.
4. What are the two mean proportionals between 6 and 162 ?
e yur, ^ , Ans. 18 and 54.
o. Wiiat are the two mean proportionals between 4 and 108?
Ans. 12 and 36.
To find the side of a cube that shall be equal in solidity to any
given sohd, as a globe, cylinder, prism, cone, 4'C.
\ Rule. The cube root of the solid content of any solid bodi
given, IS the side of the cube of equal solidity.
M3
m
EXTRACTING llOOtS Ot ALL POWBRS.
EXAMPLES.
6. If the solid content of a globe is 10618» what is the side 9t
fa cube of equal solidity ? j^ji^^ 22,
*rhe side o/ a cube being eivtn^ to find the side of a cube that
shall be double^ treble^ ^t?* in quantity to the cube given.
UuLE» Cube the side given, and multiply it by S, 3, &c., Um
cube root of the product is the side sought.
EXAMPLES,
% There is a cubical vessel, whose side is 12 inches, and it i«
required to find the side of another vessel, that is to contain three
times as much ? Ans. 17,306.
EXTRACTING OF THE BIQUADRATE ROOT.
To extract the Biquadrate Root, is to find out a number, which
being involved four times into itself, will produce the given num*
bcr.
Rule. First extract the square root of the given number, and
then extract the square root of that square root, and it will ^t»
the biquadrate root required.
EXAMPLES.
1. What is the biquadrate of 27? ^n^. 53144 K
2. What is the biquadrate of 76 ? Ans. 33362176.
3. What is the biquadrate of 275? ^«*. 5719140625.
4. What is the biquadrate root of 531441 ? Ans. 27.
5. What is the biquadrate root of 33362176? Ans. 76.
6. What is the biquadrate root of 5719140625? Ans. 275.
A GENERAL RULE FOR EXTRACTING THE ROOTS
OF ALL POWERS.
1. Prepare the number given for extraction, by pointing off
from the unit's place as the root required directs.
2. Find the first figure in the root, which subtract from the
giten number.
3. B>fing down the first figure in the next point to Ihf resosia
4er, and call it the dividend.
the Bide St
ins. 22,
I cube that
given*
B, and it i«
itain three
17,306.
OOT.
ler, which
iven num«
mber, and
t will giT9
S3144K
368176.
140625.
ns» 2t.
ns. 76.
s, 276.
ROOTS
tinting off
from the
efeslsia
fiXTRACTING ROOTS OF ALL POWERS*
m
4. Involre the root into the next inferior power to that which
IS given, multiply it by the dven power, and call it the divisor
6. Find a quotient figure by common division, and annex it to
the root ; then involve the whole root into the given power, and
call that the subtrahend. * ^
6. Subtract that number from as many points of the given
power as are brought down, beginning at the lower place, and
to the remainder bring down the first figure of the next point for
a new dividend. *
7. Find a new divisor, and proceed in all respects as before*
EXAMPLElS.
I. What is the square root of 141376 ?
141376(376
6)51 dividend.
1369 subtrahend.
3X 5^6 divisor.
37 X 37=i=1369 subtrahend.
37 X 2=74 divisor.
376 X 376=141376 subtrahend,
74)447 dividend.
141376 subtrahend,
8. What is the cube root of 63157376?
63157376(376
27
27)261 dividend.
50653 subtrahend.
4107)25043 dividend.
53157376 subtrahend,
3X 3X 3=27 divisor.
w« /\ o« A a7=ovn30u suoiranend.
37 X 37 X 3=4107 divisor.
376 X 376 X 376=53157376 attbtrahend.
''*^ SIMPLE INTEREST.
3. What is the biquadrate of 19987173376?
19987173376(376
108)1188 dividend.
1874161 subtrahend.
202612)1245563 dividend.
19987173376 subtrahend.
3x 3X 3X 4=108 divisor.
37 X 37 X 37 X 37=1874161 subtrahend.
37X 37X 37X 4=202612 divisor.
376 X 376 X 376 X 376=19987173376 subtrahend.
SIMPLE INTEREST.
There are five letters to be observed in Simple Interest, viz,
P. the Principal.
T. the Time.
R. the Ratio, or rate per crnU
I. the Interest.
A. the Amount.
A TABLE OP RATIOS.
3
,03
H
,055
8
,08
5^
,035
6
,06
8*
,085
4
,04
H
,065
9
,09
^
,045
7
,07
9^
,095
5
,05
n
,075
10
,1
Note. The Ratio is the simple interest of £1 for one year, at
the rate per cent, proposed, and is found thus :
£ £ £
As 200 : 3 : : 1 : ,03 As 100 : 3,5 : : 1 : ,035.
SIMPLE INTEREST.
HI
When the principal, time, and rate per cent, are given, to find
the interest.
Rule. Multiply the pri icipal, time, and rate together, and it
will give the interest required.
Note. The proposition and rule are better expressed thus :-v
I. When P R T are given to find I.
Rule. prt=I.
Note. When two or more letters are put together like a word,
they are to be multiplied one into another.
EXAMPLES.
1. What is the interest of £945 : 10, for 3 years, at 6 per cent,
per annum. Ans. 945,6 X,05 X 3=141,825, or £141 : 16 : 6.
2. What IS the interest of £547 : 14, at 4 per cent, per annum,
lor 6 years ? Ans. £131 : 8 : 11, 2 qrs. ,08.
3. What 18 the interest of £796 : 15, at 4^ per cent, per an-
"T wl^J^^t" ^ . ^^«- £179 : 5 : 4 2 qrs.
4. What IS the interest of £397 : 9 : 5, for 2A years, at 34 oer
cent, per annum ? Ans. £34 : 15 : 6 3,5499 qrs.
5. What 18 the interest of £554 : 17 : 6, for 3 years, 8 months,
i*li?u *^''"** l^^ annum? Ans. £91 : 11 : 1 ,2.
6. What 18 the interest of £236: 18 : 8, for three years, 9
months, at 5^ per cent, per annum ? Ans. £47 : 15 : 7^,293.
When the interest is for any number of days only.
Rule. Multiply the interest of £1 for a day, at the given rate
by the principal and number of days, it will give the answer. '
INTEREST OP £1 FOR ONE DAY.
per cent.
3
3i
4
4^
5
6
Decimals.
,00008219178
,00009589041
,00010958904
,00012328767
,00013698630
,00015068493
,00016438356
percenl.
6i
7
8
8^
9
9^
Decimals.
,00017808219
,00019178082
,00020547945
,00021917808
,00023287671
,00024657534
,00026027397
Note. The above table is thus found :—
As 3G5 : ,03 : : i : ,00008219178. And as 365 : ,035 : : 1 :
,00009589041, &c.
14ft
SIH^LB iKTKRKa'f.
EXAMPLES.
7. What is the interest of £240, tot 120 days, at 4 per cent,
per annum ? Ans. ,00010968904 X 240 X 120=£3 : 3 : U-
8. What is the interest of £364 : 18, for 164 day», at 6 pet
cent, per annum? Ans. £7 : 13 : 11|.
9. What is the interest of £726 : 15, for 74 days, at 4 per cent
per annum ? Ans. £5 : 17 : 8^.
10. What is the interest of £100, from the 1st of June, 1776,
to the 9th of March following, at 5 per cent, per annum ?
Ans. £3 : 16 : llf.
11. When P R T are given to find A.
RuLK. prt + ps=A.
EXAMPLES.
11. What will £279 : 12, amount to in 7 years^ at 4^ per cent,
per annum ? Ans. £367 : 13 : 6 3,04 qri.
279,6 X ,045 X 7 + 279,6=367,074.
12. What will £320 i 17, amount to in 5 yeats, at 3^ per cent,
per annum ? Ans» £376 : 19 : 11 2,8 qre.
When there is any odd time given with the whole years, reduce
the odd time into days, and work with the decimal parts of a
year which are equal to those days.
13. What will £926 : 12, amount to in 5^ years, at 4 per cent,
per annum ? Ans. £1130 : 9 : 0;^ ,92 qrs.
14. What will £273 : 18, amount to in 4 years, 175 days, at^
per cent, per annum ? Ans. £310 : 14 : 1 3,35080064 qra.
III. When A R T are given to find P.
a
RVLB. >=P.
rt+l
EXAMPLES.
15. What principal, being put to interest, will amount to £367
: 13 : 5 3,04 qrs. in 7 vears, at 4^ per cent, per annum?
Ans. ,045 X 7+ 1:^=1,315 then 367,674+1, 31 5=£379 : 12.
16. What principal, being put to interest, will amount to £376
: 19 : 11 2,8, in 5 years, at 3.] per cent, per annum?
Ans. £320 : 17.
SIMPLE INTBRB8T.
143
per cent.
: 3 : U.
at 5 per
I: lU.
per cent.
17 : 8^.
ne, 1776,
m?
\ : llf.
per cent.
04 qrs.
per cent.
1,8 qrs.
rs, recluce
»art8 of a
per cent^
[)2qni.
lays, at^
64 qrs.
It to £367
?9:12.
itto£31G
50: 17.
riiln^n**^ principal, being put to interest, will amount lo
£1 130 : 9 : 0^ ,92 qrs. in 6^ years, at 4 per cent, per annum ?
A.nt, iC926 * 1*^
18. What principal will amount to £310 : 14 : 1 3,36080064
qrg. m 4 years, 176 days, at 3 per cent, per annum ?
IV. When A P T are giyen to find R.
RVLE.-
a-
=R.
pt.
EXAMPLES.
19. At what rate per cent, will £27tl : 12, amount to £367 i
13:5 3,04 qrs. in 7 years ?
Ans. 367,674—279,6=88,074, 275,6 x 7=1957,2.
then 88,074+1957,2=,046 or 4^ per cent
20. At what rate per cent, will £320 : 17, amount to £376 :
19:11 2,8 qrs. in 5 years ? ^ Ans. 3^ per cent.
21. At what rate per cent, will £926 : 12, amount to £1130 :
9 : Oi ,92 qrs. in 5| years ? Ans. 4 per cent
22. At what rate per cent, will £273 : 18, amount to £3ia
14 : 1 3,35080064 qrs. in 4 years, 176 days ?
xr ^»r. . ^ ^ ^"^' 3 per cent
V. When A P R are given to find T.
a— p
Rule. =T.
pr.
EXAMPLES.
23. In what time will £279 : 12, amount to £367 : 13 : 6 3,04
qrs. at 4^ per cent. ?
Ans. 367,674—279,6:^88,074. 279,6 X ,045=: 12,5820, then
' 88,074+12,5820=7 years.
24. In what time will £320 : 17, amount to £376 : 19 : 1 1 2,&
qrs. at 3^ per cent. ? Ans. 5 years.
25. In what time will £926 : 12, amount to £1130 : 9 : 0^
,92 qrs. at 4 per cent. ? Ans. 5^ years.
28. In what time will £273 : 18, amount to £310 : 14 : I
3,35080064 qrs. at 3 per cent. ? Ans. 4 years, 175 days.
ANNUITIES OR PENSIONS, &c. IN ARREARS.
Annuities or pensions, <fcc. are said to be in arrears, when they
fire navable or dnp.. o\thpr vonrlv hnU.vn^r^tr n* ri»f>f<o>.K' ~.>Ii
ire unpaid for any number of payments.
quarterly, antf;
^PflJ^.i^Ki-riini.ii'aL"
144
SIMPLE INTEREST.
Note. U repreaents the annuity, pension, or yearly rent, T
H A. as before. n
I U R T are given to find A.
ttu — tu
Rule. X r : + tu=A.
EXAMPLES.
27. If a salary of £150 be forborne 6 years at 6 per cent, what
will it amount to ? Ans. £826.
3000
6 X 5X 150—5 X 150=3000 then X ,05 + 5 X 150=£825.
2
28. If £250 yearly pension be forborne 7 year«, what will it
amount to in that time at 6 per cent. ? Ans. £2065.
29. There is a house let upon lease for 5^ years, at £60 per
annum, what will be the amount of the whole time at ^ per
cent. ? Ans. £363 : 8 : 3.
30. Suppose an annual pension of £28 remain uppaid for 8
years, what would it amount to at 5 per cent. ?
Ans. £263 : 4.
Note. When the annuities, &c. are to be paid half-yearly or
quarterly, then
For half-yearly payments, take half of the ratio, half of the
annuity, &c., and twice the number of years — and
For quarterly payments, take a fourth part of the ratio, a fourth
part of the annuity, &c., and four times the number of years,
and work as before.
EXAMPLES.
31. If a salary of £150, payable every half-year, remains un-
paid for 5 years what will it amount to in that time at 5 per
cent.? Ans. £834: : 7 : 6.
32. If a salary of £150, payable every quarter, was left unpai('
for 5 years, what would it amount to in that time at 5 per cent, t
' Ans. £839 : 1 : 3.
Note. It may be observed by comparing these last examples,
the amount of the half-yearly payments are more advantageous
than the yearly, and the quarterly more than the half-yearly.
11. When A R T are given to find U.
RULE."
2a
ttr — tr4-2t
=U.
ly rent, T
StMPLI INTBSB8T«
146
rent, what
f. £825.
30=£825.
hat will it
£2065.
t £60 per
at 4^ per
: 8 : 3.
3aid for 8
263 : 4.
yearly or
all of the
D, a fourth
of years,
mains un-
! at 5 per
: 7 : 6.
;ft unpaid
ler cent ?
: 1 :3.
ixamples,
ntageous
y^early.
38. If a salary amounted to £825 in 5 years, at 5 per cent,
what was the salary ? Ana £lMi
826 X2»1660 6 X 6 X ,06-6 X ,06+ 6 X 2-1 1 th ^1650^
ll=£16a
34. if a house is to be let upon a lease for 5* years, and the
vrrUntt***' ''""' is ^£363 : 8 : 3, at 4i percent, what ii the
yearly rent t ^^^ ^^^
«w '^ * r""*"" '^T"^'*^ t<> ^«065, in 7 years, at 6 ^r cent,
what was the pension ? ^ \^^^ £25i)
38. Suppose the amount of a pension be £263 : 4 in 8 years,
at 6 per cent, what was the pensioa ? Am, £28.
h^fVni ^®" ^\ payments are half-yearly, then take 4a, and
?K ^/?®o*'**'' *".^ ^'^'''^ ^^^ ""™^'' «f years ; and if quart^rlv:
of years, and proceed as before.
.♦ V' ^^ *^! wnownt of a salary, payable half-yearly, for 5 veart.
at 6per cent, be i^ : 7 : 6, wLt was the salary ? 5«1 l/S ^
I .^ <J R *°*°"'l' ^^ *" """"^'J^' P*y*^J« quarterly, be £839 :
I : 3, for 6 years, at 6 per cent, what was the annuity T
^, .4n«.£160.
III. When U A T are given to find R.
2a— -2ut
RlLB.-
-=R.
utt—ut
EXAMPLES
-A^- ^ *u '*'*'^ of £150 per annum, amount to £825. in 5 rear,
what 18 the rate per cent, t "j«5^, m o years,
»» + »-160 +6 +2=160 thei, ^^ ^ p^-
150 X 5 X &-160X6
rate per cent ? ^^1 ^ * J ^'*** J*' *"«
re^ IteZr^l p^^eS:?"""'^ -^i|S^t ,
. 4a Suppose thcamoCt of . vea,l.„,„.,„f!!?-^L'='»»-
«. in » years, what is the rate per centY """Ji^.lr' """^
per cent.
146
StMPLB INT1RE8T*
Note. When the payments are half-yearly, take 4 a — 4 a| for
a dividend, and work with half the annuity, and double the num-
ber of years for a dirisor ; if quarterly, take 8 a — 8 ut, and work
with a fourth of the annuity, and four times the number of years*
43. If a salary of £160 per annum, payable half-yea|>]y,
amounts to £834 : 7 : 6, in 5 years, what is the rate per cent ?
Ans, 5 percent.
44. If an annuity of £150 per annum, payable quarterly*
amounts to £839 : 1 : 3, in 5 years, what is the rate per cent ?
Ans, 6 per cent.
IV. When U A R are giren to find T.
2 $^ zx z
RutE. First,- l=z then : V— -{ =T,
V wr 4. 2
fiXAMPLES.
45. In what time will a salary of £150 per annum, amount id
£825, at 5 per cent.! Ans» 5 years.
2 896X2 39X39
1^39 =^aO =.380,26
>06
150X^5
4
39
V220-f380 ,25=24 ,5 =5 years.
2
46. If a house is let upon a lease for a certain time, for £60
per annum, and amounts to £363 : 8 : 3, at 4| per cent, what
time was it let for? Ans, ^^ yeart.
47. If a pension of £250 per^nnum, being forborne a oertafai
time, amounts to £2066, at 6 per cent., what was the time of
forbearance? Am, 7 years.
48. In what iime will a yearly pension of £28, amount to
£263 : 4, at ^ per cent t Atis, 8 years.
Note. If the payments are half-yearly, take half the ratio, and
half the annuity; if quarterly, one fourth of the ratio, and on«
fourvh of the annuity ; and T will be «qual to those half-yearly
or quarterly payments.
49. If an annuity of £150 per annum, payable haff-yearly,
amounts to £834 : 7 : 6, at 5 per cent,, whwt time was the pay-
ment forborne I Ans, % years.
BIXPtE INTERStT.
i the num-
, and work
r of years.
ilf-yearly,
er cent?
ercent.
quarterly,
er cent ?
er cent.
147
imonnt td
9 years.
I, for £6d
int, what
^yeart.
I a oertaia
e time of
r years,
motuit to
) yeari.
ratio, and
, and on«
Bilf-yearly
If-ycarly,
I the pay-
years.
«WW . 1 . J, at b per cent, what was the time of forbearance ?
Ans, 5 years.
PRESENT WORTH OP ANNUITIES.
Note. P represents the present worth ; U T R as before.
I. When U T R are given to find P.
ttr— tr + 2t
RutE -; X U=P.
2tr-f 2
EXAMPLES.
. . ^TiSt £660*
Ans. £071 : 6.
thf^^^enfroXS^^^^^^^ '' -^« »>,« ^-nd that
thanVly, and qlterW
II. When P T R are given to find U.
tr-fl
ttr— tr-f2t
Miiiii
i^
SIIC^IB UfTEREST.
EXAMPLES.
56. If the present worth of a salary be £660, to continue 5
years, at B per cent., what is the salary ? Ans. £160.
5X,05H-l=«l^a5 5X5X,05— 5X,064-10=11.
1,25
-— X660x3=£160.
11
67. There is a house let upon lease for 6^ years to come, I de-
sire to know the yearly rent, when the present worth, at 4* pei
^^f',}^m:6:31 Ans,mV
68. What annuity is that which, for 7 years' continuance, at 6
per cent., produces £1464 : 4 : 6 present worth? Ans. £260.
69. What annuity is that which, for 8 years' continuance, pro-
duces £188 for the presen* worth, at 5 per cent. ? 4ns* £28.
NpTB. When the payments are half-yearly, take half the ratio,
twice the number of years, and multiply by 4 p ; and when quw-
terly, take one fourth of the ratio, and four times the number Of
years, and multiply by & p.
60. There is an annuity payable half-yearly, for 6 years to
come, what is the yearly rent, when the present worth, at 6 toer
cent., is £667 : 10 ? ^ns. £160;
?^*. "^^^'^ ** *n annuity payable quarterly, for 5 years to coxpe,
I desire to know the yearly income, when the present worth, at
^ per cent., is £671 : 6^ ^n*. £160.
- III. When U P T are given to find R.
ut— pX2
=1^.
2pt+ut— ttu.
EXAMPLES,
62. At what rate per cent, will an annuity of £160 per annum,
to continue 6 years, produce the present worth of £660?
Ans. 6 per cent.
150 X 5-660 X 2=180,2 X 660 X 6+6 X 160—6 X 6 X 160=3600
then 180-f-3600=,06-5 per cent.
63. If a yearly rent of £60 per annum, to continue 6^ years,
produces £291 : 6 : 3, for the present worth, what is the rate
Ans. 4^ per cent.
^ i. «
|;7i veil I. :
SIMPLB lirtEREST.
POT cent? • P""*"' ""'■*• '''«" *» *e "»
duces £188 for the present worth, whit i, the rate per c7nt "
Ans. 6 per cent
yo.^'.'r'J^^^I^/Z"^' --"^ *- - »<"- paid "..f-
S^t^pereKnT"* *" ''"""*"' '^ "« *« ~^ "^ ^^f
66. If an annuity of £180 per annum, payable half-rearlv h»
nag 5 yeare to come. is eolifor £667 :%! Xflft^Sj:;
61 If an annuity of £180 per annum, pay^btqi?/ h..
mg 6 years to come. i. z^ fyr £6T1 : 1, kat iTCSS Jr
WW nri ■^^** ^ per cent.
IV. When U P R aire given to find T
« 2 2p 2p xj. ^
KVLB. i=x then V— f —
r n ur 4 2
=T.
EXAMPLES.
6a If an annuity of £160 per annum, produces £tm fn* A-
present worth, a. 6 per ce„t..\h.. 1. 'tfe tirnHfircoSaJSi!
Ans, 6 years
2 660X2
*05 150
30,2 X 30,2
-1=30,2
660X2
^ITO
150X,06
=228,01 then V2a8,01 +176=90,1
20-1—
30,
ter
N3
150
SIMPLE INTEREST.
60. For what time may a salary of £60 be purchased for
£201 : 6 : 3, at 4^ per cent. ? Ana. 5^ years.
70. For what time may £250 per annum, be purchased for
£1454 : 4 : 6, at6 per cent 1 Ana. 7 years.
71. For what time may a pension of £28 per annum, be pur-
chased for £188, at 5 per cent. ? Ans, 8 years.
Note. "When the paymerts are half-yearly, then U will be
equal to half the annuity, dee. R half the ratio, and T the num-
ber of payments : and.
When the payments are quarterly, U will be equal to one
fourth part of the annul ty^ &c. R the fourth of the ratioy and T
the number of payments.
72. If an annuity of £150 per annum, payable half-yearly, is
sold for £667 : 10, at 5 per cent., I desire to know the number
of payments, and the time to come?
Ans. 10 payments, 5 years.
73. An annuity of £150 per annum, payable quarterly, is sold
for £671 : 5, at 5 per cent, what is the number of payments, and
time to come? Ans. 20 payments, 5 years.
ANNUITIES. &c. TAKEN IN REVERSION.
1. To find the present worth of an annuity, dee. taken in re-
version.
Rule. Find the present worth of the ttr — tr+2t
yearly sum at the given rate and for the ' ' : X u«P.
time of its continuance ; thus, 2tr+2
2. Change P into A, and find what prin-
cipal, being put to interest, will amount to a
A at the same rate, and for the time to — =F.
come before the annuity, dLC. commences ; tr f-1
thus, ^
EXAMPLES.
74. What is the present worth of an annuity of £160 per an-
num^ to continue 5 years, but not to commence till the end of 4
years, allowing 5 per cent, to the purchaser ? Ans. £550.
5 X 5 X ,06— 5 X ,06+2 X 6=4,4 X 150= 660
=660.
A N/ ARJL1
SIMPLE iNTSREST^
151
ased for
years,
ased for
years.
, be pur-
years.
I will be
the num-
1 to one
Of and^
rearly, is
I number
years.
f, is sold
ients,and
years.
:en in re-
75. What is the present worth of » foase of £50 per atinmn,
to continued years, but which is not to commence till th« end
of 5 years, allowing 4 per cent ta tliepur chaser ?
^919. £1521 1&^ 11 3qi!«.
76. A person having the promise of a pension o€ £20 per an*
num, for 8 years, but not to commence till the end of 4 years, is
willing to dispose of thie saim« ait 5 percenls.,. what will be the
present worth? Ans. £111 : 18 : 1 ,14+.
77. A legacy of £40 per annum being left for d^yeaxs,. Id a
person of 16 years of age, but whiich is not to commence till he
u 21 ; he, wanting money, is desirous of selling the same at 4
per eent^ what is the present worth ?
^n«.£l71:ia:. 11,0^^96.
%. To find the yearly income of an afimiity, &c. in rerersion.
RuLB li Find the amount of the present
worth at the givea rate, and for the time ptr+p=A.
before the reversion ; thus,
2. Change A into P, and find what an- . . -
nulty being sold, will produce F at the ^
same ratc> and for the time^of its continu- Z TTT.'
a«io« } tlkus, tti:--tri-2t
-:X2p=U.
t
:Xu»P.
per an-
1 end of 4
£550.
=550.
EXAMPLES.
78. A person hating an annuity left him for 5 years, which
docs not commence till the end of 4 years, disposed of it for £560,
allowing 6 percent., to the purchaser, what was the yearly in-
^ «^ Ans, £IS0,
• 6 X, 06 + 1,
650 X4X ,05+650=660 6 X 6 X ,05— 5 X ,05+6 X 2=
,113636 X 660 X 2«£160.
79. There is a lease of a house taken for 4 years, but not to
commence till the end of 5 years, the lessee would seU the same
for £162 : 6, present payment, allowing 4 per cent, to the pur-
chaser, what is the yearly rent ! An8, £50.
80. A person having the promise of a pension for 8 years,
which does not conunence till the end of 4 years, has disposed of
c«nW to the purchaser, what was the pension ? Ans, £20.
1
162
111
REBATE OR DISCOUNT*
81. There is a certain legacy left to a person of 15 years of age,
which is to be continued for 6 years, but not to eommenoe till he
arrives at the age of 21 ; he, wanting a sum of money, sells it for
£171 : 14, allowing 4 per cent, to the buyer, what was the an-
nuity left him » Ana. £40
REBATE OR DISCOUNT
Note. S represents the Smn to be discounted.
P the Present worth.
T the Time.
R the Ratio.
I. When S T R are given to find P.
Rule. =P.
tr+1
EXAMPLES.
1. What is the present worth of £357 : 10, to be paid9montli#
hence, at 5 per cent. ? Ans, £344 : 11 : 6i ,16a
2. What is the present worth of £275 : 10, due 7 monUw
hence, at 5 per cent, t Ans. £267 : 13 : 10^.
3. What is the present worth of £875 : 5 : 6, due at 5 months
hence, at 4^ per cent. ? Ans. £859 : 3 : 3| -rts .
4. How much ready money can I receive for a note of £75,
due 15 months hence, at 5 per cent. ?
^«i?.£70:il:9,1764d.
II. When P T R are given to find S.
Rule. ptr + p=S.
EXAMPLEa
5. If the present worth of a sum of money, due 9 months
hence, allowing 5 per cent, be £344 : 11 : 6 3,168 qw., what
was the sum first due t Ans, £367 : 10.
344,6783 X ,76 X ,06+ 344,6783=£357 : 10.
6# A person owing a certain sum, payable 7 months hence,
agrees with the creditor to pay him down £267 : 13 : lOg^, al
lowing 5 per cent, for present payment, what is the debt?
Ans. £275: 10.
% A person receives £b69 : 3 : S| jfj for a sum of m<mey
RBBATS OR OISCOVBrT.
188
due 6 months hence, allowing the debtor 4^ per cent, for present
payment, what was the sum due ? Ans, £876 : 6 : 6.
a A person paid £70 : 11 : 9,1764d. for a debt due 15
months hence, he being allowed 6 per cent, for the discount, how
much was the debt ? Ajis» £75.
III. When S P T are given to find R
s— p
RVLB. =R.
tp
EXAMPLES.
9. At what rate per cent, will £.357 : 10, payable 7 months
hence, produce £344 : 11 : 6 3,168 qrs. for present payment?
3675,-344,5783
— >=:,05=6 per cent
344,5783 X ,75
10. At what rate per cent, will £276 : 10, payable 7 months
hcnae, produce £367 : 13 : 10^ for the present payment!
A.n8. 6 per cent.
11. At what rate per cent, will £876 : 5 : 6, payable 6 months
hence, produce the present payment of £859 : 3 : 3| ^h ^
--. ., - ^7w. 4^ per cent.
la. At what rate per cent, will £75, payable 16 months hence,
produce the present payment of £70 : 11 : 9 ,1764d. ?
Ans, 5 per cent
IV. When S P R are given to find T.
s — p
Rule. -=T.
rp
EXAMPLES.
la The present worth of £357 : 10, dne at a certain time to
wme, is £344 : 11 : 6 3,168 qrs. at 5 per cent, in what time
should the sum have been paid without any rebate ?
Ans. 9 months,
357,5—344,5783
•*' ——=,76=9 montiis.
344,6783 X ,06
14. The present worth of £275 : 10, due at a certain time to.
imm»j ! ,T:';\,iH„-„ ...mi-f
~'««<MNMiH
i
154
EQUATION OF PA MBNT8.
come, 18 £267 : 13 : l(Wr, at 6 per cen , in w time should
the sum have been paid without any rebate ?
Ana, 7 months.
15. A person receives £659 : 3 : 3| ,0184, for £875 : 5 : 6,
due at a certain time to come, allowing 4^ per cent, discount, I
desire to know in what time the debt should have been discharg
ed without any rebate? Ans. 5 months.
16. I have received £70 : 11 : 9 ,1764d. for a debt of £75
allowing the person 5 per cent, for prompt payment, I desire to
know when the debt would have been payable without the rebate ?
Ans, 15 months.
EaUATION OF PAYMENTS.
To find the equated time for the payment of a sum of money
due at several times.
Rule. Find the present worth of each pay- s
ment for its respective time ; thus, =P.
Add all the present worths together, then.
EXAMPLES.
tr+l
»— p=D.
d
and— — =E
pr
1. D owes £ £200, whereof £40 is to be paid at three months,
£60 at six months, and £100 at nine months ; at what time may
the whole debt be paid together, rebate being made at 5 per cent ?
Ans. months, 26 days.
40 60 100
=39,5061 =ue,5365 =96,3866
1,0125 1,025 1,0375
then 200—39,5061+58,6365-1-96,3855=6,5719
5,5719
-=,57316=6 monifhs, 26 days.
194,4281 X ,06,
2. D owes E £800, whereof £200 is to be paid in 3 months,
£200 at 4 months, and £400 at 6 months ; but they, agreeing to
make but one payment of the whole, at the rate of 6 per cent,
rebate, the true equated time is demanded ?
Ans, 4 months, ^ days.
COMPOUND INTEREST.
165
i should
ontha.
5:6:6,
icount, I
lischarg
onths.
of £76-
iesire to
; rebate ?
Dnths.
f money
s
— =P.
f-1
p=D.
1
=E
T
months,
[me may
er cent ?
days.
5
719
months,
'eeing to
per cent.
3. E owes F £1200, which is to be paid as follows: £900
down, £600 at the end of 10 months, and the rest at the end of
SO months ; but they, agreeing to have one payment of the whole,
rebate at 3 per cent., the true equated time is demanded?
Ans, 1 year, U days.
COMPOUND INTEREST.
The letters made use of in Compound Inte^eat^ aie,
A the Amount.
P the Principal.
T the Time.
R the Amount of £1 for 1 year at any given rate i
which is thus found :
As 100 : 105 : : 1 : 1,06. As 100 : 106,5 : : 1 : 1,065.
A Table of the amount of£l for one year.
RATES
PER CENT.
T
H
4
4i
AMOUNTS
OP £1.
1,03
1,035
1,04
1,045
1,05
RATES
PER CENT.
54
6
64
7
74
AMOUNTS
OP £1.
1,055
1,06
1,065
1,07
1,075
RATES
PER CENT.
8
84
9
94
10
AMOUNTS
0P£1.
1,08
1,085
1,09
1,095
1,1
Table shming the amount of £1 for any number of years
under 31, at 5 and 6 per cent, per, annum.
TEARS.
days.
1
3
3
4
5
6
7
8
9
10
11
12
13
14
15
5 RATES. 6
1,05000
1,10250
1,15762
1,21550
1,27628
1,34009
1,40710
1,47745
1,55132
1,62889
1,71034
1,79585
1,88565
L,97993
2,07892
1,06000
16
1,12360
17
1,19101
18
1,26247
19
1,33822
20
1,41852
21
1,50363
22
1>59385
23
1,68948
24
1,79084
25
1,89829
26
2,01219
27
2,13292
28
2,26090
29
«,dybOO
30
YEARS, I 5 RATES. 6
2,18287
2,29201
2,40662
2^2695
2,65329
2,78596
2,92526
3,07152
3,22510
3,38635
3,55567
3,73345
3,92013
4,11613
4,32194
2,54035
2,69277
2,85434
3,02560
3,20713
3,39956*
3,60353
3,81975
4,04893
4,29187
4,54938
4,82234
5,11168
5.41838
5174349
H
I
mmmmm
156
COMPOUND INTEREST.
Note. The preceding table is thus made— As 100 : 106 : : 1 :
1,05, for the first year ; then, As 100 : 106 : : 1,06 : 1,1025, •©•
oond year, d&c.
I. When P T R are given to find A.
Rule, p X rt=A.
EXAMPLES.
1. "What will £325 amount to in 3 years* time, at 5 per cent
per annum?
Ans. 1,05 X 1,05 X 1,05=1,157625, then 1,157625 X 226«
£260:9:33qr8.
2. What will £200 amount to in 4 years, at 6 per cent, per
annum? -Atw. £>i43 2,0258.
3. What will £450 amount to in 5 years, at 4 per cent per
anmim? ^ws. £547 : 9 : 10 2,0538368 qrs.
4. What will £500 amount to in 4 years, tt 5^ per cent, per
annum? ilns. £619 : 8 : 2 3,8323 qrs.
II. When A R T are given to find P.
a
Rule. =P.
rt
EXAMPLES.
5. What principal, being put to interest, will amount to £960;
9:33 qrs. in 8 years, at 6 per cent, per annum ?
^ ^ 260,465625
1,05 X 1,05 X 1,05=1,167625— «£225.
6 What principal, being put to interest, will amount to^543
2,025s. in 4 years, at 5 per cent per annum ? ^1"^^'
7. What principal will amount to £547 : 9 : 10 2,05383^rs.
in 6 years, at 4 per cent, per annum ? J^ £450.
a What principal will amount to £619 : 8 : 2 3,8323 qi^n 4
years, at 6^ per cent, per annum t -47is. £500.
III. When P A T are given to find R-, ^ , r *-
a which being extracted by the rule of extrae-
RuLE.~~=rt tion, (the time given to the question showing
p the power) will give K.
)5: : 1;
025,
ter cent
.X22B«
Sqw.
«nt. per
,0258.
ent pef
8 qrs.
xnt. per
^qrs.
to £260;
Uo£243
£200.
8368 qrs.
£450.
qrs. in 4
£500.
f extrae-
showing
COMfO«KB IVTERE8T.
EXAMPLES.
167
9. At wb%t rate per cent will £225 amount to £260 : 9 : 3,3
qrs. in 3 years ? Ans. 5 per cent.
260,465625
=1,157625, the cube root of whicli
225
(it being the 3d power):*=l,05=5 per cent.
10. At what rate per cent, will £200 amount to £243 : 2,025«.
in 4 years ? An». 5 per cent.
11. At what rate per cent, will £450 amount to £547 : 9 : 10
2,0538368 qrs. in 5 years ? Ans, 4 per cent.
12. At what rate per cent, will £500 amount to £619 : 8 : 2
3,8323 qrs. in 4 years ? Ans. 5 J per cent
IV. When P A R are given to find T.
a which being continually dirided by R till no-
RuLK. — ^=rt thing remains, the number of those divisions
p will be equal to T. .
EXAMPLES.
13. In what time will £225 amount to £360 : 9 : 3 3 qrs. at
5 per oent. ?
260,465625 1,157626 1,1025 1,05
=1,157625- =1,1026 =-^1,06-
225 1,05 1,06 1,05
=1, the number of divisions being three times sought
14 In what time will £200 amount to £243 2,0258. at 5 per
cent ? Atis, 4 years.
15. In what time will £450 amount to £547 : 9 : 10 2,0538368
qrs. at 4 per cent ? Ans. 6 years.
16. In what time will £500 amount to £619 : 8 : 2 3332S
qrs. at SJ per cent t Ans. 4 years.
ANNUITIES, OH PENSIONS, IN ARREARS.
Note. TJ represents the annuity, pension, or yearly rent t
\ li T as before.
168
COMPOUMO INTEREST.
A Table showing the amount of£l annually, for any number
of years under 31, af 6 and 6 per cent, per annum.
Y£AR8.
1
2
3
4
5
6
4
8
9
10
11
13
13
14
15
5 RATES.
1,00000
2,05000
3,16350
4,31012
5,52563
6,80191
8,14200
9,54910
11,02656
12,57789
14,30678
15,91712
17,71298
11>,59868
21,57856
1,(>0000
LVXJOOO
3,18360
4,37461
5,(13709
6,97532
8,39383
9,89746
J 1.49131
13,18079
14,97164
16,86994
18,88213
21,01506
23,27597
YEARS.
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
5 RATES. 6
23,65749
25,84036
28,18238
30,53900
33,06595
35,71925
38,50521
41,43047
44,50199
47,72709
51,11345
54,66912
58,40258
62,32271
66,43884
35,67252
28,21288
30,90565
33,75999
36,78559
39,99272
43,39229
46,99582
50,81557
54,86451
59,15638
63,70576
68,52811
73,63979
79,05818
Note. The above table is made thus :--take the first yeer'e
amount, which is £1, multiply it by l,06+l=2,05=8econd
year's amount, which also multiply by 1,05+1 =2, 1626=third
year's amount.
I. When U T R are given to find A.
ur* — u
Rule. =A, or by the table thus :
r— 1
Multiply the amount of £1 for the number of years, and at the
rate per cent, given in the question, by the annuity, pension,
&c. and It will give the answer.
EXAMPLES.
17. What will an annuity of £50 per annum, payable yearly,
amount to in 4 years, at 5 per cent. ? ^ ^ j
Ans. 1,05 X 1,05 X 1,05 X 1,05 X 50=60,77531250
60,7753125—50
then =£215 : 10 t 1 2 qrs. ; or^
1,05—1 HI-.
by the table thus, 4,31012 X 50=£216 : 10 : 1 1,76 qrs.
18. What will a pension of £45 per annum, payable yearly,
amount to in 5 years, at 5 per cent. ?
COMPOUND INTEREST.
t60
19. If a salary of £40 per annuip, to be paiJ yearly, be '"or*
borne 6 years, at 6 per cent., what is the amount?
_ _ Aw5. £379 : : 3,0679fl096d.
ao. If an annuityof £76 per annum, payable yearly, be omit-
ted to be paid for 10 years, at 6 per cent., what is the amount ?
II. When A R T are given to find U.
ar — a
Rule. =U.
rt— 1
EXAMPLES.
31. What annuity, being forborne 4 years, will amount to
£315 : 10 : 1 3 qrs. at 5 per cent. ?
316,50636X1,05—316,60635
atis. — _ .^c:o,
1,05X1,05X1,06X1,06' -I
33. What pension, being forborne t v ?Ar», v ill amount to
£348 : 13 : 3,37 qrs. at 5 per cent. ? Am, £45.
33. What salary, being omitted to be paiu <5 years, will amount
to £379 : : 3,06796096d. at 6 per cent, ? Ans, £40.
24. If the payment of an annuity, being forbome 10 years,
amount to £986 : 11 : 3,33d. at 6 per cent., what is the annuity?
III. When U A R are given to find T.
ar-|-u — a which being continually divided by R till
Ryuj. -jt nothing remains, the number of those
u divisions will be equal to T.
EXAMPLES.
35. In what time will £50 per annum amount to £316 : 10 :
1 3 qrs. at 6 per cent, for non-payment ?
Ans. 316,50635 X 1,05+50 315,50636 =1,31650635
- ^
which being continually divided by R the number of the divi-
sions will be=4 years.
36. In what time will £45 per annum amount to £348 : 13
337 qrs, allowing 5 per cent, for forbearance of payment ?
08
Ana, 5 yCure*
160
:??MPOUND INTERbST.
37. In -what time "flrUl £40 per annum amount to £279:0:
8,05796096(1, at 6 per cent. 1 Ans. 6 years.
28. In what time will £76 per annum amount to £988 : 11
2,22d. allowing 6 percent, for forbearance of payment t
Ans. 10 years.
PRESENT WORTH OF ANN JITIES, PENSIONS, &«.
A Thble ehming the present worth of £1 annuity for any num'
her of years under 31, rebate at B and 6 per cent.
TEAWI.
.*> RATES. 6
YEARS.
5 BATES. G
1
0,95238
0,94339
16
10,83777 10.10589
3
1,85941
1,83339
17
11,C7406
10,47726
8
2,72324
2,67301
18
11,68958
10,82760
4
3,54595
3,46510
19
12,08532
11,15811
6
4,32947
4,21236
90
12,46221
11,46992
6
5,07569
4,91732
21
12,82115
11,76407
7
5,78637
5,58238
22
13,16300
12,04168
8
6,46321
6,20979
33
13,48857
12,30338
,J
7,10783
6,80169
24
13,79864
12,55036
to
7,72173
7,36008
25
14,09394
12,78336
11
8,30641
7,88687
Q6
14,37518
13,00317
13
8,86325
8,38384
27
14,64303
13,21053
13
9,39357
8,85268
28
14,89812
13,40616
14
9,89864
9,29498
29
15,14107
13,59072
15
10,37965
9,71225
30
15,37245
13,76483
NoTB, The above table is thus made : — divide £1 by 1,05=
,95238, the present worth of the first year, which-*-l, 05=90753,
added to the first year's present worth=l ,85941, the second
year's present worth ; then, 90703-*-l,05, and the quotient added
to 185941=2,72327, third year's present worth.
I. When U T R are given to find P.
u
u-
RVLB.-
=P.
r— 1
or by the table thus :
Multiply the present worth of £1 annuity for the time and rate
per cent, given by the annuity, pension, &c. it will give the an-.
:279:0:
yeare.
:988 : 11
?
years.
&«.
it.
"6
10589
17736
32760
15811
16992
76407
34158
30338
}5036
78336
X)317
21053
10616
)9072
76483
)y 1,06=
•=90753,
) second
Qt added
and rats
i the an-.
COMPOVirD INTEREST.
EXAMPLES.
29. What is the present worth of an annoity of £30 per an-
iram, to continue 7 years, at C per cent T
Ans. £167 : 9 : 6 ,184d.
30
1,50363
«167,4716.
■«19,9517
30— 19,9517=-10,0483.
10,0483
1,06—1
By the table 6,68238X30=167,4714.
30. What is the present worth of a pension of £40 per annum,
to continue 8 years, at 5 per cent. ?
Ans, £258 : 10 : 6 3,264 r s.
31. What is the present worth of a salary of £35, to continue
T years, at 6 per cent. ? Ans. £196 : 7 : 7 3,968 qrs.
32. What is the yearly rent of £50, to continue 5 years, worth
in ready money, at 6 per cent. ? Ans, £216 : 9 : 5 2,56 qrs.
II. When P T R are given to find U.
-I <■! IMIIWIB II ll»l,ll W liiMM
prt X r— pr»
RiftE. =U.
ft— 1
EXAMPLES.
33. If an annuity be purchased for £167 : 9 : 5 184d. to be
Qontinued 7 years, at 6 per cent what is the annuity ?
Ans. 167,4716 X 1,50363 X 1,06—167,4716 X 1,60363
1,50363—1
=£30.
34. If the present payment of £258 J 10 : 6 3,264 qrs. be
made for a salary of 8 years to eome, at 6 per cent., what is the
Mlaryt Ans, £40.
35. If the present payment of £195 : 7 : 7 3,968 qrs. be re-
quired for a pension for 7 years to eome, at 6 per cent, what is
the pension ? jins. £35.
36. If the present wofth of an annuity 5 years to come, be
£216 : 9,: 5 2,66 qrs. at 6 per cent., what is the annuity ?
Ans. £50.
08
im
COatPOUND liNTEREST.
IIL When U P R are given to find T.
n which being continually divided by R till
RtTtB.-,-.^ — «ft nothing remains, the number of those di-
p-ft' — pt visions will be equal to T.
EXAMPLES.
37. How long may a lease of £30 yearly rent be had foi
£167 : : 6 ,184d. allowing 6 per cent, to the purchaser?
30
107,471frf 30— 177,6188
which being continually
=lf 50363 ^^^^^®^» *^® number of
' those divisions will beas
to T=7 years.
3a If £258 : 10 : 6 3,264 qrs. is paid down for a lease of £40
per annum, at 5 per cent., how long is the lease purchased for!
Atis. 8 yearf .
89. If a house is let upon lease for £35 per annum, and the
l«esee makes present payment of £105 i 7 : 8, he being allowed
6 per cent., I demand how long the lease is purchased for ?
Ans. 7 years*
40. For what time is a lease of £50 per annum, purcha^
when present payment is made of £216 : : 5 2,56 qrs. at 6 per
cent ' Ans. 5 years.
ANNUITIES, LEASES, &c TAKEN IN REVERSION.
To find the present worth of annuities, leases^ ^c, taken in
reversion.
Rule. Find the present worth of the annui-
ty, &c. at the given rate and for the time of its u^-
o(Hi^inuanc6 : thus,
u
8. Change P into A, and find what principal
being put to interest will amount to P at the
same rate, and for the time to come before the
annuity oommenceft, which will be the present
MVtf^lirn ^\w 4n<% «k vk •>« avi 4«r Av ^ft Ai««««ia
H-'l
-=p.
a
^=p.
t.i'
COMPOUND INTEREST.
Ifi3
by R till
those di-*
had foi
atinually
^ber of
(fill beos
»eof£40
ised for?
yearf.
, and the
allowed
for?
ye&r&.
ircha<»ed
at 5 per
years.
ISION.
iken in
u
-l
EXAMPLES.
41. What is the present worth of a reversion of a lease of £40
per annum, to continue for six years, but not to commence till
the end of 2 years, allowing 6 per cent, to the purchaser?
Ans. £175 : 1 : 1 2, 048 qrs.
40 40-28,1984 106,6933
— «28,1984 =196,6933
=176,0663.
42. What is the present worth of ft reversion of a lease of £60
•er annum, to coiftinue 7 years, but not to commence till the end
of 3 years, allowing 6 per cent to the purchaser ?
.„ _ , Ans. £299 : 18 : 2,8d.
43. There is a lease of a house at £30 per annum, which is
yet in being for 4 years, and the lessee is desirous to take a lease
in reversion for 7 years, to begin when the old lease shall be ex-
pired, what wUl be the present worth of the said lease in rever-
sion, allowing 6 per cent, to the purchaser ?
Ans, £142 : 16 : 3 2,688 qrs.
To find the yearly iticome of an annuity, ^c, taken in rever \
Rule. Find the amount of the present
worth at the ^ven rate, and for the time be-
fore the annmty commences : thus, pr*=A.
Change A into P, and find what yearly rent
being sold will produce P at the same rate,
and for the time of its continuance, which will pr» X r prt.
be the yearly sum required : thus, ^zj].
rt— 1.
EXAMPLES.
44, What annuity to be entered upon-2 years hence, and then
to continue 6 years, may be purchased for £176 : 1 : 1 2,048 qrs.
at 6 per cent. ?
>ln«. 176,0563X1,1236=196,6933 ..
theh 196,6933 X 1,41862 X 1,66—279,01337
164
COMPOVND INTEREST.
45. The present worth of a lease of a house is £299 : 18 : 2 8d.
taken in reversion for 7 years, but not to commence till the end
of 3 years, allowing 5 per eent. to the purchaser, what is the
yearly rent? Ans. £60.
46. There is a lease of a house in being for 4 years, and the
leasee being minded to take a lease in reversion for 7 years, to
begin when the old lease shall be expired, paid down £142 : 16 :
3 2>689 qrs. what was the yearly rent of the house, when the les-
see was allowed 6 per cent, for present payment ? Ans. £30.
PURCHASINa FREEHOLD OR REAL ESTATE, IN SUCH AS ARE
BOUGHT TO CONTINUE FOR EVBll.
'■.-■" '^
I. When U R are given to find W.
u
Rule. —W.
r— 1
EXAMPLES.
47. What is the worth of a freehold estate of £50 per annum,
allowing 5 per cent, to the buyer ?
50
Ans. —=£1000.
1,05—1
48. What is an estate of £140 per annum, to continue for ever,
worth in present money, allowing 4 per cent, to the buyer ?
Ans, £3500.
49. If a freehold estate of £75 yearly rent was to be sold, what
is the worth, allowing the buyer 6 per cent. ?
Ans. £1250.
II. When W R are given to find U.
RuLs. wXr— 1=U.
EXAMPLES.
50. If a freehold estate is bought for £1000, and the allowance
of 5 per cent, is made to the buyer, what is the yearly rent?
Ans. 1,06— 1 =,06, then 1000 X ,05=£50.
51. If an estate be sold for £3500, and 4 per cent, allowed to
thA bilVAr. iirhftf ia tha troarlv ve-n* f Amo Ttdfl
=— ^ —s., — - — ,.. ........ .^.jj- . , ^a.fi/o» Ai(X^V.
bOMPOUND INTBRESti
%i
tm
18:28d.
ill the end
bat is th«
IS. £60.
fl, and the
f years, to
:i42 : 16 :
5n the les-
is, £30.
t AS ARB
T annum,
! for ever,
lyer?
£3500.
old, what
£1250.
llowance
rent?
i^£50.
[lowed to
52. If a freehold estate is bought for £1250 present taoney,
and an allowance of 6 per cent, made to the buyer for the same,
whatis the yearly rent ? ^^s, £75.
III. When W U are given to find R.
HULB. =R.
w
EXAMPLES.
53. If an estate of £50 pcJr annum be bought for £1000, what
is the rate per cent. ?
1000+50
Ans, =1,05=5 per cent.
1000
54. If a freehold estate of £140 per annum be bought for
£3500, what is the rate per cent, allowed T
' _ Ans. 4 per cent
5a. If an estate of £75 per annum is sold for £1250, what is
the rate per cent, allovf ed ? Ans. 6 per cent.
PURCHASING FREEHOLD ESTATES IN RETERSION.
To find the worth of a Freehold Estate in reversion :
u
W
Rule. Find the worth of the yearly rent, thus —
Change W into A, ami find what principal, being r— 1
put to interest, will amount to A at. the same rate, and
for the time to come, before the estate commences, and a
that will be the worth of the estate in reversion, Uius: ^P
r'.
EXAMPIJES.
56. Ijf a freehold estate df £50 per annum, to commence 4
years heose, is to be sold, whatis it worth, allowing the purchaser
5 per cent, for the present payment?
60 1000
4ns.— -=1000, then =£822 : 14 : U.
1,05—1 1,2156
57. What is an estate of £200, to continue for ever, but not to
ootnmctMie till the end of 2 years, worth in ready money, allowing
the purchasef 4 per cent. ? Ans. £4622 : 15 : 7 ,44d,
58. What is an estate of £240 per annum worth in ready mo-
ney, to continue for ever, but not to commence till tfie end of 3
yoars, aUo.wance being made at 6 per cent. ?
Arts, £3358 : 9 : 10 2,24 qrs.
'
1C6
B£13aTE or OtflCOtNT.
To jind thR Yearly Rent of an Estate taken in reversion.
Rule. Find the amount of the worth of the
estate, at tke given rate and time before it coin- wr*=!A
oee, thus :
Chaoge A into W, and -ind what yearly rent wr — wsU,
beinff eold will produce U at the same rate, thiis :
which will be the yearly rent required.
EXAMPLES.
60. If a freehold estate, to comm<:mce 4 years hence, is «old
for £822 : 14 : 1^, allowing the purchaser 5 per cent., whai is
the yearly Income T Ane, 823,70626 X 1,2166=1000^
then 1000 X i,05^I0^>$>.^£8a
60. A feehold estate is bought for £4622 : 15 : 7 ,4M. which
does not commence till the end of 2y«ars, the buyer being alk v-
ed 4 per cent for iiis money. I desire to know ihe yeLly In-
come.. Ans. £am.
61. There is a frtiehoW est?.* gold for £3368 : 9 : 10 2,24 qr».,
but not to commence till the « Aplrs tiou of 3 years, allowing 6
per cent, (or present payment i 4'lmkk th« yearly income?
Ans, £240.
^ REBATE OR DISCOUNT.
A Table 'fhowing the present worth of £1 due any number of
yeara hence, under 31, rebate at 6 and tper cent.
5 EATSa. ^
TKARS.
,953381
,^7030
,8G;JS38
,7835^26
,746315
,710683
,676839
,644609
,613913
,584679
,556837
,530331
,505068
,481017
,943396
,889996
,839619
,793093
,747358
,704960
,665057
,637413
,59189^
,55H394
,536787
,496969
,468839
,443301
,417365
NoTX.— -The above table is thus made: l-*-l,0&=,9&238I.
first year'fl present worth ; and ,952381*«-1,06=,90703, second
year ; and ,9070a-*- i,U6=*tJ63838 thi . year, &c.
I
i
ftEBAIl OR DiaCOUK'T.
m
oerston,
VT — Ws=U,
se, is «old
t., whai u
m, which
ling alk V-
yeatly ta-
?. £20C.
illowing 6
Dme?
vumberof
unt.
13646
ri364
>0343
(0513
1804
mb6
7505
11797
f6978
12998
9610
17368
'6630
4556
=,952381,
^« second
I. When S T R are given to find P
RuiB.— «P.
EXAMPLES.
?. What is the present worth of £316 : 18 : 4 ,2d, payable 4
jem-B hence, at 6 per cent. ? -» r / ■»
4/u, 1,06 X 1,06 X 1,06 X 1,08=1,26247, then by the table.
316,6175 316,6176
-=£250 ,192093
1,26247
249,9984124276
2. ir £344 : 14 : 9 1,92 qrs. be payabk in 7 years' time, what
i8 the prcaent worth, rebate being made at 6 per cent T
o rwn- Ans, £245.
3. There is a debt of £441 : 17 : 3 1,92 ys., which is payablt
4 years hence, but it is agreed to be paid in present money ; what
smn mu£t the creditor receive, rebate being made at 6 per cent,!
n. When P T R are given to find S, ^"*' ^^'
RiTLB. p X r*=S.
EXA^klPLES.
4. If a snm of money, due 4 years hence, produce £2&0 for
the.preeent payment, rebate being laade^t 6 per cent., what was
the sum due ? r i 't
Ans. £250 X l,2fl247=£&16 : 12 : 42d.
6. If £245 be Tecdved for a debt payable 7 years hence, an4
tn allowance of 5 per cent, te ^e debtor fot present payment.
•That was the deht T Ans. £344 : 14 : 9 1,92 qrs.
6. There is a^um dT money due at the expiration of 4 years,
but tfie creditor ames totake £350 fo^ present payment, allow-
ing 6 per cent., what was the debt t t J ^
Ans. £441 : 17 : 3 1,92 qrs.
III. When S P R are given to find T.
8 which bemg continually divided by R till nothing
tiVLE.— «4^ remains, the number of those di^sions will be
,p equal to T
168
REBATB OR DISCOUNVi
EXAMPLES.
7. The present payment of £950 is made for a debt of £316:
12 : 4 ,3d., rebate at 6 per cent., in what time wa» the debt pay-
able ? ^^
315,6176 which being continually divided, thosa
Ajis. ■■ =1,86247 dirisions will be equal to 4=th8 num-
96(^ Vs4. In. ber of years.
,8. A person receives £246 now, for a debt of i344 : 14 : 9
r,92 qrs., rebate being made at 5 per cent. I demand in what
time the debt was payable ? Ana 7 years.
9. There is a debt of £441 : 17 : 3 1,92 qrs. due at a certain
time to come, but 6 per cent being allowed to the*debtor for the
present payment of £350, 1 desire to now in what time the sum
should have been paid without any rebate)"
, ■ /'■i«'***^ii<«4 :. ■■- .4.710. 4 years. ^
IV. When S P T are given to find R.
8 which being extracted by the rules of extraction.
RoLB mv* (the time given in the question showing the pow
.ik P er,) will be equal to R.
EXAMPLES.
10. A debt of £315 : 12 : 4 ,2d. is due 4 years hence, but it is
agreed to take £250 now, what is the rate per tent, that the re-
bate is made at ?
315,6175 4
Ans, — ^=1,26247 :Vl,26247=l,06i=6 per cent
360
11. The. present worth of £344 : 14 : 9 1,92 qrs., payable 7
years hence, is ^^M6, at what rate per cent, is the rebate made'7
l^i- ■ ' ■ ■ ■'• . ! . * '•■Am X
Ans, 6 per cent.
12. There is a debt of £441 : 17 : 3 1,92 qrs., payable in 4
years time, but it is agreed to take £350 present payments I de-
sire to know at what rate per cent, the rebate is made at)
Ana, 6 per cent.
160
t of £316 :
debt pay-
cled, tho88
=the num-
44 : 14 : 9
d in what
f years.
t a certain
tor for the
e the sum
I years*
THE
TUTOR'S ASSISTANT
PART IV.
ztraction.
' the pow
DUODECIMALS,
(, but it is
at the re-
rcent.
payable 7
tte madel
IT cent.
able in 4
ijiU Ide-
at)
T cent.
OR, WHAT IS QEWERALLT CALLED
Cross Multiplicationt and Squaring of Dimensions by Arti'
ficcrsand Workmen*
RULE FOR MULTIPLYINO DU0DBCinAJ.LV.
1. Under the multiplicand write the corresponding denomina*
tions of the multiplier.
2. Multiply each term in the multiplicand (beginning at the
lowest) by the feet in the multiplier ; write each result under its
respective term, observing to carry an unit for every 12, from
each lower denomination to its next superiov.
3. In the same manner multiply the multiplicand by theprhnes
in the multiplier, and write the result of each term one place
mwe to the right hand of those in the multiplicand.
4. Work in the same manner with the seconds in the muhl-
pliwr, setting the result of each term two places to the right hand
of thoiie in the muUipiicand, and so on for thirds, fourths, &c,
p
mill 1 Miiifiii I 11
ii
DUODECIMALS.
EXAMPLES.
f.
1. Multiply 7
CniM MaltipUcation.
3^6
in. f. in.
9 by 3. 6.
Practice.
6i7-»
31.0.0=7X3
2.3.0=9X3
3.6.0=7X6
0.4.6=9X6
3
.6
23.
3.
3
10.
6
Duodecimal.
7.9
2.6
Decimals.
7,75
3,5
n
X3
J. 6X6
27 . 1.6
27. 1.6
3875
2325
27,125
27.1.6
2. Multiply
3. Multiply
4. Multiply
5. Multiply
6. Multiply
7. Multiply
8. Multiply
9. Multiply
10. Multiply
11. Multiply
12. Multiply
la Multiply
14. Multiply
15. Multiply
16. Multiply
17. Multiply
18. Multiply
f.in.
8.5
9.8
8.1
7.6
4.7
7.5.9"
10.4.5
76.7
97.8
57.9
75.9
87.5
179.3
259.2
257.9
311.4.7
321.7.3
f. in.
4. 7
7. 6
3. 5
5. 9
3.10
by 3. 5.3"
by 7. 8.6
9. 8
8. 9
9. 5
by 17. 7
by 35. 8
by 38.10
by 48.11
by 39.11
by 38. 7.5
by 9. 3.6
by
bv
by
by
by
by
by
by
Facit,
Facit,
Facit,
Facit,
Facit,
Facit,
Facit,
Facit,
Facit,
Facit,
Facit,
Facit,
Facit,
Facit,
Facit,
Facit,
Facit,
t. iu.pts.
38. 6,11
72. 6
27. 7. 5
43. 1. 6
n. 6.10_,,
25. 8. 6.2.3
79.11. 0.6.6
730. 7. 8
854. 7
G43. 9. 9
1331.11. 3
3117.10. 4
6960.10. 6
12677. 6.10
10?88. 6. 3
il4lr2. 2. 4.11 11
2988. i.10.4.6
TITE APPLICATION.
Artificers' work is computed by diffp; '): , "; measure'^, viz :—
1. Glazing, and masons' flat work, by the foot.
2. Painting, plastering, paving, &c. by the yard.
3. Partitioning, flooTing, roofing, tiling, &,c. 'the iquare of
100 feet.
4. Brick work, &lc by the rdd of 16^ feet, whose square is
272)1^ feet.
59.
Mec
■S .
Decimals.
7,76
3,5
3875
2325
27,125
11
5
6
6.2.3
0.6.6
8
9
3
4
6
10
3
4.1111
0.4.6
viz: —
>quar8 of
square is
/U0DECIMAL8.
171
masnrinff by the Foot Square, as Glazier, d Masons^ Flat
Work.
EXAMPLES.
u '^; JJ'fr i.^ "" ^''"'® "^^^^ ^ ^^^^ of windows, 3 in a tier-the
annM 'fv '. ^D ''Z ^. ^'t' ^^ ^"^^^«' ^h« «-«ond 6feet 8 inches
and the third 6 feet 4 inches, the breadth of each is 3 feet 1 1
inches ; what wifl the glazing come to, at 14d. per foot
Duodecimals.
7 . 10 the
6 . 8 heights
6 . 4 added.
19. 10
3= windows in a tier.
■feet. in. pt«.
233 . . 6 at 14d. per ft.
2d.=f 233 ~ Is.
38 . 10 = 2d.
. Oi =6 parts.
59. 6
3 . 11 in breadth.
178.6
54 . 6 , 6
233.0.6
2|0)27|1 . 1 ,
£13. H . 10^ Ans.
r«?;«vs.^-:.TZT£aS2L~;:;a
8". per
Ans. £1 : 18 : 9.
90 ixru^.' .u . Ans. £1:3 :S,
^Z. What IS the price of a marble slaV vhose length i. fi ft,
7 inches, and the breadth 1 foot 10 inches, t 6s. pef Joot f
Ans. £3:1:5.
^asnringhy the Yard Square, a. Paviers Painters, Plas-
terers, and Joiners.
^ Note. DiTide the square feet by 9. and it will rri.. t,- «.,^
P9
m
DUODECIMALS.
■!
•ii'ii
EXAxVfPLES.
23. A room is to be ceiled, whoso length is 74 feet D inch€«^
and width 11 feet 6 inches ; what will it come to at 3s. lO^d par
yard? ^715. £18 : 10 : 1.
34. What will the paving of a court-yard come to at 4fd. per
yard, the length being 58 feet 6 inches, and breadth 64 feel 9
inches 'i
Ans. £7 : : 10.
25^ A room was painted 97 feet 8 inr " os about, and 9 feet 10
inches high, what does it come to at 28, 83d. per yard 1
Ans, £14 : 11 : 1^
26. "What is the content of a piece of Wainscoting in yards
square, that is 8 feet 3 inches Jong, and 6 feet 6 inches broad,
and what will it come to at 68. 7^d. per yard?
^715. Contents, yards 5.8.7.6 ; comes to £1 : 19 : 6.
37. What will the paving of a court-yard come to at Ss. ^
per yard, if the length be 27 feet 10 inches, and the breadth 14
feet 9 inches ?
Ans. £7:4: 6.
28. A person has paved a court-yard 42 feet 9 inches in front,
and 68 feet 6 inches in depth, and in this he laid a foot-way the
depth of the court, of 5 feet 6 inches in breadth ; the ioot way ia
Isaid with Purbeck stone, at 3s. 6d. per yard, and the rest with
pebbles, at 3s. per yard ; what will the whole come to ?
Ans, £49 : 17.
29. What will the plastering of a ccaling, at lOd. per yard,
come to, supposing the length 31 feet 8 inches, and the breadtli
14 feet 10 inches? ^
M
Ans, £1 : 9 : 9.
30. What will the wainscoting of a room come to at 6s. pe
square yard, supposing the height of the room (taking in the cor-
nice and moulding) 1^ 12 feet 6 inches, and the compass 83 feet 8
inches, the three window shutters each 7 feet 8 inches by 3 feet
6 inches, and the door 7 feet by 3 feet 6 inches ? The shutters
and door being worked on both sides, are reckoned work and
/4*.« roa .10.01
li
DU0DKCIMAL9.
in
Uea^uri^by tke Square of 100 feet, as Flooring, Partition^
tng. Roofing, Tiling, J^c.
EXAMPLES.
81. In 173 feet 10 inches in lenffth, and 10 feet 7 in/.»,«- i«
height of partitioning, how many square" ? ^" *"
Ati^, 18 square*, 39 feet, 8 inches, 10 p.
8?l. If a house measure* within the walls^RQ ^P» *fi^4^ 'i?^' •
^Sf Wt ^ilf ft^' *"r ^" ,^-dt^nd^h1ro^^^^^
PUUI, what wiUiMorae tp rooang at 10s. 6d. per square?
^^*' £12: 13: ll|.
of Aeroof of thatbuilding XLX aKu 0^^
^e. when the rafter, are J of the breadthof IbuUd neCt^f
tae roof is more or less than tho fm*. «;*-k *i! """"^"8 » out it
one side to the other wU a" od „ "trfng?*"' "'*'' """"^ ^""^
34. What will the tiling of a barn cost at 2fi« m r^
^?w. £24 ; 9 : 5|.
Measuring by the Rod,
^v'^^'^ Bricklayers always value their work at thp
ick and a half thir-k . ««/! t/^u^ .u.- ., - r*^ " '"«
5fi. it must h. r.j.;;:7;:"^ "*7.r."v^"^^« .'^^ ^^^ wan is
brick ^ ,
ImrU muM be reduc^.d to that thickness by this
^3
rate of a
more or
in
DUODECIMALS.
Rule. Multiply the area of the wall by the number of half
bricks in the thickness of the, wall ; the product divided by 3,
gives the area.
EXAMPLES.
35. If the area of -a wall be 4085 feet, and the thicknej^s two
bricks and a hal^ how many rods doth it contain?
Ans. 25 rods, 8 feet.
26 I^ a garden wall be 254 feet round, and 12 feet 7 inches
high, and 3 bricks thick, how many rods doth it contain ?
Ans> 23 rods, 136 feet.
37. How maijy squared rod^ are there in a wall 62| feet long,
14 feet 8 inches high, and 2^ bricks thick ?
Ans. 5 rod's, 167 feet.
38. If the side walls of a house be 28 feet 10 inches ia length,
arid the height of the roof from the ground 55 feet 8 inches, and
the gable (or triangular part at top) to rise 42 course of bricks,
reckoning 4 course to a foot. Now, 20 feet high is 2^ bricks
thick, 20 feet more at two bricks thick, 15 feet 8 inches more at
1^ brick thick, and the gable at 1 brick thick; what will the
whole work come to at £5 16s. pe^ rod ?
Ans. £48 : iS : 5^.
Multiplying several figures by several, and the product to he
produced in one line only.
RtLE. Multiply thB units of the multiplicand by the units of
the multiplier, setting down the units of the product, and carry the
tens ; next muMply the tens in the multiplicand by the units of
the multiplier, to which add the product of the units of the multi-
plicand multiplied by the tens in the multiplier, and the tens car-
ried ; then multiply the hundreds in the multiplicand by the units
of the multiplier, adding the product of the tens in the multiplicand
multiplied by the tens in the multiplier, and the units of the multi-
plicand by the hundreds in the multiplier ; and so proceed till yo^i
the multiplier.
ify cyp ry iigUrc i
DUODECIMALS.
175
EXAMPLES.
'
Multiply 35234
by 52424
Product, 1847107216
Common wo
35234
52424
140936
70468
140936
70468
176170
' 1847107216
EXPLANATION.
First, 4 X 4=16, that is 6 and carry one. Secondly, 3X4-1-
4X2, and 1 that is carried, is 21— set down 1 and carry 8.
Thirdly 2 X 4+3 X 2+4 X 4+2 carried=32, that is 2 and car-
ry3. Fourthly, 5 X 4 + 2x2 + 3X4 +4 X2+3 carried=47.
set down^7 and carry 4. Fifthly, 3X4 + 5X2 + 2X4 + 3X2
+ 4.x 5 + 4 carried=60, set down and car: t 6. Sixthly, 3X2
+ 5X4 + 2x2+3X5+6cai:ried-51, setdown 1 and carry
5. Seventhly, 3X4 + 5X2 + 2X5 + 5 carried=37, that is 7
and carry 3. Eighthly, 3X2+5X5 + 3 carried=34, set down
4 and carry 3. Lastly, 3X5+3 carried=18, which being mul-
tiplied by the last figure in the multiplier, set the whole down,
and the work is finished.
.
il O 4
176
THE
TUTOR'S ASSISTANT
PART V.
A COLLECTION OF QUESTIONS.
1. What is the value of 14 barrels of soap, at ^d. per lb., each
barrel containing 254 lb. ? Arts. £66 : 13 : 6.
2. A and B trade together ; A puts in £320 for 5 month©, B
£460 for 3 months, and they gained £100; what must each roan
recbive t Arts. A £53 : 13 : 9ff^, and B £46 : 6 : 2^%^
3. How many yards of cloth, at 17s. 6d. per yard, can I hare
for 13 cwt. 2 qrs. of wool, at I4d. per lb. ?
Atis. 100 yards, 3^^ qr».
4. If I buy 1000 ells of Flemish linen for £90, at what may I
sell it per 6ll in London, to gain £10 by the whole?
. ' ^Tis. 3s. 4d. per ell. '
$.^ A has 648 yards of cloth, at 14s. per yard, ready money,
but in barter will have 16s. ; B has wine at £42 per tun, ready
money : the question is, how much wine must be given for the
cloth, and what is the price of a tun of wine in barter ?
Ans. £48 the tun, and 10 tun, 3 hhds. 12f gals, of
wine must be given for the cloth.
6. A jeweller sold jewels to the value of £1200, for which he
received in part 876 French pistoles, at 16s, 6d. each ; what sum
remains unpaid ? Ans, £477 : 6.
7. An oilman bought 417 cwt. 1 qr. 15 lb., gross weight, of
train oil, tare 20 lb. per 112 lb., how many neat gallons were
there, allowing 7^ lb. to a gallon? Ans. 51^ gallons.
8. If I buy a yard of cloth for 14s. 6d., and sell it for 16s. IW.,
what do I gain per cent. ? Ans. £16 : 10 : ^^f^.
9. Bought 27 bags of ginger, each weighing gross 84f lb., tare
at If lb. per bag, tret 4 lb. per 104 lb., what do they come to
at 8|d. per lb. ? Ans. £76 : 13 : ^.
■
n
n
'
A COLLECTION OP atJESTlONS. I77
colli '^^°^ *" '^"'"''^ *''''' « ^^ * '*""""&» ^**** ^>" t Of a lb.
cost ? "^ • ""^ * ^*"^" ^'^^^ 8 of a pound, what witt ^ of a tun
13. A gentleman spends one day with another^^^r- 7^^ni
and at the year's end layeth up £34^, what^r^s y;^^^^^^^^^^
"rj A u to ^ 1 ^^s. £848 : 14 : 4*.
tim^s m Ih ^nt%o ^'f V^"^ ^^'^^^^ '^^^ being * 9i
a^nrP« i?i .^?u^^ ^.^'K' °^ *^"' ^^^^ 388 lb., how mani
<mnce8 difference is there m the weight of these coimoditiesT
14 A captain and 160 sailors took a prize'^wonh £r%0^*nf
which the captain had f for his share, and t^eTeLt wfs eoukllv
divided among the sailors, what was each manWr' ^ ^
!«; A . T* ^ ''^^^''' ^^^ ^2^» »"d each sailor £6 : 16,
7A vpar^ r/ • T-P^' ^^"!- ^^" ^956ampunt. to £1314 : 10, in
7^ years, at simple interest? a^o ik „„, « "'
£n'; ^ hath 34 cows, worth 72s. each, andl'^'h^ worth
£13 a piece, how much will make good the differenrV n 1-2
they interchange their said drove of'ca" ''""LTd'-ir
^nA P o ' V ^ ^ ^^^^^ unknown ; B twice as much as A
and C as much as A and B ; what was the share of each ? '
1ft /-innft • . u ^. .^ , ^^^- ^ ^^' B ^40, and C £60.
10 A • /^^- ^ ^^^^ ' ^^^ S ^312 : 10, and C £500
19. A piece of wainscot is 8 feet 6^ inches long, and 2 fee^^'94
inches broad, what is the superficial content ? ^ '^^^^ -^ *««* 9f
2n If Q«n I. . ^^*^- 24 feet : 3" : 4 : 6.
men must depart that the provisions may last so much the longer »
le , oxen at £11, cows at 4O3., colts at £1 : 5, and lioffs It T\-
.0 each, and of each a like number, how man'y of each' soJt^did
"i^^'^Who* V, I, J J .^'^^' *^ ^* e^ch sort, and £8 over.
^. What number added to 1 1| will produce 36ft|^?
-4w5.24fif.
178
A COLLECTION OF aVESTIONS.
34. What number multiplied by f will produce U-iV ?
Ans. 26H-
25; What is the value of 179 hogsheads of tobacco, each weigh
ing 13 cwt. at £2 : 7 : 1 per cwt. ? Ans. £5478 : 2 : 11.
26. My factor sends me word he has bought goods to the va-
lue of £500 : 13 : 6, upon my account, what will his commission
come to at 3^ per cent ? Ans. £17 : 10 : 5 2 qrs. -f^.
27. If i of 6 be three, what will i of 20 be? Ans. 7^.
28. What is the decimal of 3 qrs. 14 lb. of a cwt.?
Ans. ,875.
29. How many lb. of sugar, at ^d. per lb. must be given in
barter for 60 gross of inkle, at 8s. 8d, per gross ?
Ans. 13861 lb.
30. If I buy yarn for 9d. the lb. and sell it again for 13id. per
lb., what is the gain per cent. ? Ans. £50.
31. A tobacconirt would mix 20 lb. of tobacco at 9d. per lb.
with 60 lb. at 12d. per lb., 40 lb. at 18d. per lb., and with 12 lb.
at 2s. per lb., what is a pound of this mixture worth ?
Ans. Is. 2^d. -jSi-.
32. What is the difference between twice eight and twenty,
and twice twenty-eight ; as also, between twice five and fifty, and
twice fifty-five ? Ans. 20 and 50.
33. Whereas a noble and a mark just 15 yards did buy ; how
many ells of the same cloth for £gi0 had I ? Ans. 600 ells.
34. A broker bought for his principal, in the year 1720, £400
capital stock in the South-Sea, at £650 per cent., and sold it
again when it was worth*but £130 per cent. ; how much was
lost in the whole ? Ans. £2080.
35. C hath candles at 6s. per dozen, ready money, but in bar-
ter will have 6s. 6d. per dozen ; D hath cotton at 9d. per lb. ready
money. I demand what price the cotton must be at in barter ;
also, how much cotton must be bartered for 100 doz. of candles t
Ans. The cotton at 9d. 3 qrs. per lb., and 7 cwt. qrs.
16 lb. of cotton must be given for 100 doz. candles.
36. If a clerk's salary be £73 a year, what is that per day ?
Ans. 4s.
37. B hath an estate of £53 per annum, and payeth 5s. lOd.
to the
per annum ?
J5
£100
.
Ans. lis. Od.
58*
A COLLECTION OP QUESTIONS.
179
38. If I buy 100 yards of riband at 3 yards for a shiUinir, and
iOO more at 3 yards for a shilling, and sell it at the rate of 5 yards
for i shillings, whether do I gain or lose, and how much ?
on ^TTx. 1 . , ^^^* ^^ose 3s. 4d.
39. What number is that, from which if you take f , the re-
mainder will be i- ? ^ ^^'^^ 2Jl
40. A farmer is willing to make a mixture of rye at 4s. a bush-
el, barley at 3s., and oats at 2s. ; how much must he take of each
to sell It at 2s. 6d. the bushel ?
/ii Tf9 r ,. ^/^^•^^('•ye, 6ofbarley, and24ofoats.
41. Iff of a ship be worth £3740, what is the worth of the
whole J ^^^ £9973 " • 8
42. Bought a cask of wine for £62 : 8, how many gallons were
in the same, when a gallon was valued at 5s. 4d. ?
Ans 234
43. A merry young fellow in a short time got the better of ^ of
his fortune; by advice of his friends, he gave £2200 for an ex-
erapt s place m the guards ; his profusion continued till he had no
more then 880 gmneas left, which he found, by computation, was
f^ part of his money after the commission was bought ; prav what
was his fortune at first ? /ns £10 450
♦».o1!'-^*'"''k"'^" ^^""^ V""" ^^ '"'^"^y t« ^« divided amongst
! ZTJ"!? x^ '"?'!I!^'; ^^V^^ ^^^^ «^*" *»^^« i ^'f it» th« second
i, the third i and the fourth the remainder, which is £28, what
w the sum? ^^^ ^^^^
simlielllLVelt^ --'^*-^^1000for3i Y^^^^^.
46. Sold goods amounting to the value of £700at two 4 months,
what IS the present worth, at 5 per cent, simple interest ?
Ans. £682 : 19
H
V: ^ ^^.r^Ofeet long, and 18 feet wide, is to be covered with
painted cloth, how many yards of % wide will cover it ?
48. Betty told her brother George, that though her for^unt on
her marriage, took £19,312 out of her family, it was but i of wo
r/that?'' " ^' P'"^^'^ ' ^^i^^^ y-^ly income ; pray what
40 A .1 t . . -^4715. £16,093 : 6 : 8 a year.
49. A gentleman having 503. to pay among his labourers for a
day's work, would give to every boy 6d., to every woman 8d
r„l 'ZT^I''^ \^^' ' '>' ^^-^-r of boys, womL, and mTn!
.»«. „,c aaiuc. 1 uerrr.na t i; iiunibe* of each ?
Ans. 20 of each.
ido
A COLLECTION OF QUESTIONS.
50. A Stone that measures 4 feet 6 inches long, 2 feet 9 inches
broad, and 3 feet 4 inches deep, how many solid feet doth it con-
tain ? Ans. 41 feet 3 inches.
61. What does the whole pay of a man-of-war's crew, of 640
sailors, amount to for 32 months' service, each man's pay being
22s. 6d. per month ? Ans. £23,040.
52. A traveller would change 500 French crowns, at 4s. 6d.
per crown, into sterling money, but he must pay a halfpenny per
crown for change ; how much must he receive ?
Ans. £111 : 9 : 2.
53. B and C traded together, and gained £100 ; B put in £640,
C put in so much that he might receive £60 of the gain. I de-
mand how much C put in ? Ans. £960.
54. Of what principal sum did £20 interest arise in one year,
at the rate of 6 per cent, per annum ? Ans. £400.
55. In 672 Spanish gilders of 2s. each, how many French pis-
toles, at 17s. 6d. per piece ? Ans, 76ff .
56. From 7 cheeses, each weighing 1 cwt. 2 qrs. 5 lb., how
many allowances for seamen may be cut, each weighing 5 oz. 7
drams? Ans. 356ff.
67. If 48 taken from 120 leaves 72, and 72 taken from 91
leaves 19, and 7 taken from thence leaves 12, what number is
that, out of which when you hav o taken 48, 72, 19, and 7, leaves
12? -4ns. 158.
68. A farmer ignorant of numbers, ordered £500 to be divided
among his five sons, thus: — Give X^ myw^hi»i^ 'Blr^^-J^'^. .
and £ f part ; divide this equitably among them, according to
their father's intention.
Ans. A £152f|i, B £114if|, C £91^,
D £76iif , E £65iH.
59. When first the marriage knot was tied
Between my wife and me,
My age did hers as far exceed,
As three times three does three ;
But when ten years, and half ten ^ars,
We man and wife had been,
Her age came then as near to mine,
As eight is to sixteen.
Ques. What was each of our ages when we were married
Ans. 45 years the ma^j, 15 the woman.
181
<*»
A Table for finding' the Interest of any sum of Money, for any
number of months, weeks, or dar% at any rate per cent.
Year.
Calm. Month.
Week.
Day.
£
£ 9. d.
£ a. d.
£ 8. d.
1
1 8
4i
0|
2
3 4
9
li
3
5
1 1}
2
4
6 8
1 6
2}
5
8 4
1 11
3i
6
10
2 31
w w -mr ^
4
7
11 8
2 8i
4i
8
13 4
3 1
5i
9
15
3 51
6
10
16 8
3 lOi
6}
20
1 13 4
7 8i
1 li
30
2 10
11 6i
1 71
40
3 6 8
15 4i
2 2i
50
4 3 4
19 2f
2 9
60
5
1 3 1
3 3^
70
5 16 8
1 6 11
3 10
80
6 13 4
1 10 91
4 4i
90
7 10
1 14 7i
4 Hi
100
8 6 8
1 18 5i
ft 5{
200
16 J3 4
3 16 11
10 m
300
25
515 4J
Q 16 5i
400
33 6 8
7 13 10
1 1 11
500
41 13 4
9 12 3J
1 7 4|
600
50 J
11 10 9
1 19 10|
700
58 6 b (
13 9 2|
V V II
I 18 4i
800
66 13 4
15 7 8i
2 3 10
900
75
17 6 1|
2 9 3}
1000
83 6 8
19 4 11
2 H 9k
2000
166 13 4
38 9 5»|
a 9) 7
9000
250
57 13 10 i
9 4 4h
4000
333 6 8
76 18 5i
^' ■• X Y
i? 19 2
5000.
416 13 4
96 3 Oj
ji IS Hi
6000
TjOO
115 7 8\
16 8 9
7000
583 6 8
134 12 3i
19 3 6t
8000
6(;6 13 4
153 16 11
m» ** ** *
21 18 4i
9000
50
173 1 6i
24 13 11
10,000
833 6 8
192 6 If
27 7 lU
20,000
1666 13 4
384 12 3i
54 15 lOj
30,000
2500
576 18 5i
62 3 10
t82
Rule. Multiply the principal by the rate per cent., and the
number of months, weeks, or days, which are required, cut off
two figures on the right hand side of the product, and collect from
the table the several sums against the different numbers, which
when added, will make the number remaining. Add the several
sums together, and it will give the interest required.
N.B. For every 10 that is cut off in months, add twopence i
for every 10 cut off in weeks, add a. half penny ; and for every
40 in the days, 1 farthing.
EXAMPLES.
1. What is the interest of £2467 10s. for 10 months, at 4 per
^ent. per annum ?
2467 : 10 900=75 : :
4 80=6:13:4
7=0:11:8
9870:
10
987|00
987=82: 6:0
2. What is the interest of £2467 10s. for 12 weeks, at 5 per
< int. ?
2467 : 10 1000=19 : 4 : 7|
5 400=± 7 : 13 : 10
80= 1 : 10 : 9^
12337 : 10 50= : : 2^
12
1480|50=28: 9: 5
1480160:
3, What is the interest of £2467 10s., 50 days, at 6 per cent. ?
2467 : 10 7000=19 : 3 : 6^
6 400= 1 : 1 : 11
2= : : U
14805 ; 60= : : 0|
50
7402|50=20 : 5 : 7
7402150 :
To find what en Est fit-, from one fo £60,000 /7er annum will
' ' ' to for one day.
Rule 1. ^ t( t the annual r^ mt or income from the table for
.. _.i,:,»i. *,.i.^ iU^ 1 /•_„ J
together, and it will g v^e the answer
1 J
% *
d the
Lit off
from
rhich
vera)
ince,
jvery
I per
>per
int.?
will
! for
183
An estate of £376 per annum, what is that per day ?
300=0 : 16 : 5:^
70=0 : 3 : 10
6=0: 0: 4
376=1 : : 7i
To find the amount of any inconf salary ^ or servants' wagts^
for any number of mora'tSf weeks, or days.
Rule. Multiply the yearly income or salary by the number
)f months, weeks, or days, and collect the product from the table.
What will £270 per annum come to for 1 1 months, for 3 weeks,
and for 6 days ?
270
11
2970
270
6
1620
For 11 months.
2000=166 : 13 : 4
900= 75 : 0:0
70= 6 : 16 : 8
2970=247 : 10 :
For 6 days.
1000=2 : 14 : 9J
600=1 : 12 : 10^
20=0 : 1 : 1^
1620=4: 8: 9^
For 3 weeks.
270 800=15: 7: 8^
3 10= : 3 : 10^
810 = 15 : 11 : ^
For the whole time.
247 : 10 :
15: 11 :6^
4: 8:9^
267 : 10 : 3i
A Table showing the number of days from any day in the
month to the same day in any other month, through the year.
rnoM
January
February.. ,
March
April
May
June
July
August
September ..
Octfshflr
November . ,
December. . .
TO
365
334
306
275
245
214
184
153
U3
31
365
337
30G
276
245
215
184
S
122 153
QOI lOO
61
31
92
62
59
28
365
334
304
273
243
212
181
1 CI
120
90
90
59
31
365
335
304
274
243
212
151
121
^
120
89
61
30
365
334
304
273
242
181
151
02
S
151
120
92
61
31
365
335
304
273
212
182
A
181
150
122
91
61
30
365
335
303
242
bo
s
<
212
181
153
122
92
61
31
365
334
uUi
273
2121 243
2l
243
212
184
153
123
92
62
31
365
u
O
273
242
214
18:^
153
122
92
61
30
ot55| obu
3041 334
274' 304
304 334
273i303
245275
214244
18^1214
1531183
123
92
61
3i
365
153
122
91
Gi
30
335 365
184
A COMPENDIUM OP BOOK-KEEPING.
BY SINGLE ENTRY.
Book-keeping is the art of recording the transactions of i)crsonS
m business s > as to exhibit a stnte of their aflairs iu a concise
and satisfactory manner.
Books may be kept either by Singh or by Double Entry, but
Single Entry is the method chiefly used in retail business.
The books found most expedient in Single Entry, are the Day-
Book, the Cash-Book, the Ledger, and the Bill-Book.
The Day-Book begins with an account of tiie trader's property,
debts, &c. ; and are entered in the order of their occurrence, the
dafly transactions of goods bought and sold.
The Cash-Book is a register of all money transactions. On the
left-hand page, Cash is made Debtor to all sums received ; and
on the right, Cash is made Creditor by all sums paid.
The Ledger collects together the scattered accounts in the Day-
Book and Cash-Book, and places the Debtors and Creditors upon
opposite pages of the same folio ; and a reference is made to the
folio of the books from which the res^ ctive accounts are ext ic-
ted, by figures placed in a column &Mmithe sums. References
are also made in the Day-Book ancl C'dsli-Book, to the folios in
the Ledger, where the amounts ai* Uected. This process is
called posting, and the following general rule should be remem-
bered by the learner, when engaged in transferring the register
of mercantile proceedings from the previous books to the Ledger :
The person from whom you purchase goods, or from whom
you receive money, is Creditor; and, on the contrary, the person
to whom ycu sell goods, or to whom you pay rnoney, is Debtor.
In the Bill-Book are inserted the particulars of all Bills of Ex-
change ; and it is sometimes found expedient to keep for this pur-
pose two books, into one of which are copied Bills Receivable,
or such as come into the tradesman's possession, and are drawn
upon some other person ; in the other book are entered Bilh
Payable, which are those that are drawn upon and accepted b>
the tradesman himself.
an
185
DAT BOOK,
,3 6
o bc
it*
1
January Ist, 1837.
I commenced buBinwB with • capital of Five Hundred
Pounda m Cash
sa_
Bennett and Sona, Lonu. t.*
By 2 hhdf of sugar
Cr.
dot. qr. lb. ctDt. gr. lb.
13 1 4 12
13 3 16 116
gtoM wt. 26 20
tarb 2 3 6
neat wt. 23 1 14 at 636. per cwt.
2 chests of t
cwt. qr. lb.
1 15
1 12
lb.
96
S5
2 27
1 22
I 3 5at6«.per 'h.
2
3d^
Hall and Scott, JLdverpool,
By soap, 1 cwt. at 688
candles, 10 dozen at 78. 9d.
Cr.
6th
Ward, WiUiam
To 1 cwt. of sugar,
14 lbs. of tea,
i cwt. of soap,
at 708..
at 8s...
at 748.
Dr.
6th
Cooper, William
Tol
(folio 1.)
£
TjOO
'I.
iU
60
8
17
6
10
sugar hogshead,
Dr.
10
12
18
6
6
6
.n!l I^J ^y*^^"* ?K Tv,^ directed to fill up this and similar blanks in this bc^k
and t^ Ledger with the names of places familiar to }»im,
a3
e>.
^>
IMAGE EVALUATION
TEST TARGET (MT-3)
A
1.0
I.I
1.25
l^|28 12.5
|50 "^ !■■
1^ 1^ 112.2
S: lis. 12.0
1.8
1.4 IIIIII.6
V]
v]
7J
%
%^'^> > -^<^ ^"^^
.V
w
'/
ftiotographic
Sciences
Corporation
33 WEST MAIN STREET
WEBSTER, N.Y. MSBO
(716) 872-4503
d^
\
(V
\\
V
^'^^ ^ >. '<^q\
"^ ^%. ^:^ '^^
>*
°:^^^
^^^
i/..
186
DAY BOOK.
(folio 2.)
p
January 9th, 1837.
£
1
1
4
17
17
1
6
1
8.
16
8
5
5
9
8
4
8
10
2
1
2
1
2
2
Johnton^ Richard Dr.
To 2 dozen of candles, at 89, 3d
d.
6
i cwt. of Boap, at 14»
'
h cwt. of suffar. at 708
6
1
10th.
Ward, William Dr.
To sugar, 1 cask
cwt. qr. lb.
gross wt. 5 2 10 cask
tare 2 10
neat 5 at68B
6
9
3
6
12th.
Smith, John Dr
To 14 lb. of sugar „
12 lb. of candles '
7 lb. of soap
1 lb. of tea
14th.
16
13
16
10
9
4
10
6
4
2
2
Q
3
Hall and Scott, Liverpool, Cr.
By 2 cvyt. soap, at 688
17th.
Newton, John Dr.
To 21 lb. of soap, at 748. per cwt. ..... .
2 dozen of candles, at 88. 3d
19th.
Smith, John . n_
To 14 lb. of sugar
ilb. of tea ..'*.*..'*".!
1
13
18
8
6
2
21st.
Smith, John Dr
To 28 lb. of sugar
^ V ST>a Ot CtUxUlCO, •• ..•.. .... .•.••.....
—J
c
6
'
6
9
3_
6
10
4
A
2
9
187
DAY BOOK.
(folio 3.)
January 23d, 1837.
Yates <f» Lane, Bradford, Cr.
By 4 pieces of superfine cloth, each 36 yards,
^ at 248. per yard . .
£
172
23d.
Edward*^ Benj. Manchester~ Cr.
By 2 pieces of calico^each 24 yards, pt Is. per yard. .
~23d.
2
Smith, John
T o 14 lb. of soap.
Dr.
24th.
».
8
d.
Johnson, Richard
To 2 dozen of candles,
1 cwt. of soap,
IJ cwt (^ sugar,
at Ss. 3d.
at 748 . . .
at 708...
Dr.
24th.
Smith, John
To 1 lb. of tea.
Dr.
26tb.
Mason, Edward />^_
To 3 pieces of superfine cloth, each 36 yards,
o . , r I.O. at 27s. per yard...
2 pieces of cahcp, each 24 yards,
at Is. 2d. per yard.
3
16
14
5
15
6
~6
145
2
27th.
148
Parker, Thomas, JOff.^
To 1 piece of superfine clpth, 36 yards, at SSsy , . . ,
31st.
3
Bills Payable, Cr.
_^yYate8 & Lane's Bill at 2 months, due April 2... .
Inventory) January 31, 1837.
Raw suffar,
Tea,
Soap,
Candles,, 2 dozen,.
cwt. gr. lb.
14 3 14 at 638
1 2 16^ at 68. per lb.
3 14 at 688
at 73. 9d. . . .
50
172
46
55
2
105
8
16
16
12
8_
16
17
7
19
15
19
1
6
6
irJ
!88
CASH BOOK.
■
II
I
■ (
O
O
o
«
<«:
oo
00 A
eoo
00
ss
G«0*i4
f2SS
fiN •NW MG»
i
s
B
ll
"" Bt3 «* S w
•-< f^cSeo en
00^6 6 o
lAQOOiieeo <o
??S^"®55S P
■<5
00
i '.
I
J
iV
199
INDEX TO THE LEDGER.
r
N
Newton, John
77721
T^ Bernard &Co i
O 5«?»«t' & Sons, London! '.'.'.'. I
Bills payable 3
C
^p«, William .'777^
O
Jfarker, Thdinaa 3
D
Q
Edwarda, B. Manchester. a
^tock account ' .", ^ — f
O SmHh,JehB ,*.*!.*"**' a
G
H
Hall & Soott, Liverpool.
I
JoluMOD, Richard 2
K
W
Waid, Wiiua -j
Ifates & lane, Bradbid 3
I Maaon, Edward 3
iVl
E
J
,i.
Jit
If
I
100
o
Pi
o
§
LBIKIER.
Of*? M«
O |0
09 o
«fj? s
'u")
ococ
CO -f^
CO I-
i-» CO
CO
I-
00
CO
CO
vo
o»
^g
•-(
r^o
1^
«6
«
-N(N
J3
i-i
eS
a
•■3
9 « »
§PQ
(55
oeo
;^
SC5
6
:3
d
o
a
B
.«3
CO C!
00 rt
CO a
00 <4
. CO *^
00 c«
.0
B3
«»i ^^ 1— I
1—1
o
04
CO
QOO
COO
CO
00
1—1
CO
CO
0«£)
rj<©
CO
O©
©O
©t^
CO CO
I -
-HOI
o
a «
tj 3 >
"^ S C
02 g.S
t: « o
13 i
CO
" s
si w ~ v!
eg
C5
•?
I
■-S 5 5
m
00. eS
^«5
SO ^
^ 3
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00 S
i-Hl-4
S
o
P
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Q
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o
• Pi*
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Ift
k«
SJ
(?)
O
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4r
Li^nazn,
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