!
STORAGE
195
J
ok you y
an
1
ARTES
18.17
SCIENTIA
LIBRARY
VERITAS
OF THE
UNIVERSITY OF MICHIGAN
SE PLURIOUS UNUM
TUEBOR
SI QUERIS PENINSULAM AMŒNAM,
CIRCUMSPICE
ПИНИНИН
Минпины
A
QAY
だそ
​3.5
нь
John. Birkatt 1739
John
ounter Fort
iFitt
Birkett 174
by Sectt
Joseply
Burkitt
¿ i
thikeres Book 1803
友
​HEWIT T's
ARITHMETIC
Fuft published, by Mr. HEWITT,
(Price 1s. 6d. in Sheep, and 2s. in Calf)
T
HE Trader's Pocket Companion: Containing
Correct Tabies, ready calculated, of univerfal
Ule to Merchants, Shopkeepers, Mechanicks, and to
all other Perſons in any Kind of Buſineſs.
A Table calculated, to fhew at one View, the Va-
Jue of any Quantity of Goods, Wares, or Merchan-
dife, at any Price, adapted to all Capacitics and its
particular, general, and extenfive Ufe, fhewn by ma-
ny and various Examples.
A Table of univerfal Ufe, demonftrated, by the
Solution of various Queſtions in Multiplication, Di-
vifion, Reduction, Merchandifing, meaſuring Super-
ficies and Solids, Gauging, Surveying, &c.
Twenty-five Geometrical Problems, with their af-
figned Figures, applied to Meaſuring, Gauging, Sur-
Geying, &c.
A Table calculated, to diſcover at one View, the
different Difcompts upon any of the Branches of the
Cuftoms, upon imported Go
upwards.
from one Farthing
reckoning Salaries or
View, what any year-
A Table for the more eafy
Wages, by difcovering, at one
ly Salary, Wages, or Eftate, amounts to, by the
Month, Week, or Day: an
daily Salary amounts to, by the Month, Week, or
Year.
sontrary, what any
A Table for Cafting up Intereft at any Rate, for
any Number of Days.
The Rates and Fares of Coachmen, Carmen, and
Watermen, with their Rules and Reſtrictions.
Si quid novifti rectius iftis,
Candidus imperi, fi non, his utere mecum
HE WIT T's
ARITHMETIC
I N
Whole Numbers,
AND
FRACTION S
VULGAR and DECIMAL:
SHEWING
The shortest Operations made uſe of
in REAL BUSINESS;
WITH
The Method of EXTRACTING the
Square and Cube ROOT S.
For the Ufe
HOOLS.
By 70H
HE WIT T.
AUTHOR of the Trader's Pocket-Companion.
LONDON
Printed for J. CLARKE, under the Royal-Exchange;
S. BIRT, in Ave-Mary-Lane; T. ASTLEY, in
St. Paul's Church-Yard; J. WOOD, in Pater-nofter
Row; and J. HODGES, on London-Bridge.
[Price One Shilling bound.]
Jesyon Scott ilwe
Anne Fon.
and
ini
Meat Sci.
Sabhekd
12-17-29
au635
(v)
TO
WILLIAM CARRE,
of St. Helen-Auckland, in the
Bifhoprick of Durham, Eſq;
SIR,
ด
AM fenfible an Addrefs
of this Nature, to a Gen-
tleman of your refined
Taſte, and diſtinguiſhing Judg-
ment, is very difficult to attempt;
and however common it may be
for an Author to publiſh an E-
piſtle of this kind; yet, in my
A 3
humble
vi DEDICATION.
humble Opinion, it is feldom
rightly underſtood, or very often
miſtaken.
It is for this Reaſon, I think,
I am, at prefent, in a very odd
Situatio, and find my felf un-
equal to the Task I have under-
taken.
The grand Foible of human
Nature is fuch, that ADULATION,
has oftner fucceeded, and done
greater Execution, than any o-
ther Art whatever; and yet,
could I deviate from my felf fo
far, as to touch, or border here
in the leaſt upon it, inftead of
finding a Reception, I am con-
vinced
DEDICATION. vii
vinced I ſhould very juftly draw
upon my ſelf, your higheſt Con-
tempt.
Should I prefume to point
out your many excellent Quali-
fications, adorned with the ut-
moſt good Nature and Huma-
nity, it would be a kind of ta-
cit Confeffion, that I fet my ſelf
up for a Judge, of what, I ſhould
at beſt, but very faintly deſcribe;
or, to give it a more favourable
Turn, I fhould only repeat, what,
all, who know you, are very well
acquainted with already.
To avoid theſe Objections, Sir,
give me leave to enjoy that in
my Mind, which, were I to ex-
prefs,
viii DEDICATION.
prefs, would but offend your
Modesty, and expofe my Weak-
nefs.
However, I fhould be want-
ing in Gratitude, fhould I mifs
this publick Opportunity of de-
claring my felf greatly indebted
to you for many Favours I have
received; but it is hard to fay,
whether, the Favour, or, the
Polite Manner, in which you
beſtow it, pleaſes moſt.
with profound Reſpect,
SIR,
I am
Your most Obedient,
And Devoted Servant,
J. HEWITT.
(ix)
THE
PREFACE.
HE following Treatife
Tis compofed for the Ufe
and Improvement of all
thofe, who would attain to the
Knowledge of fo uſeful and ex-
cellent a Science: The Exam-
ples to each Rule, are not many,
to puzzle the Learner, but few,
eafy, and clear.
I
Χ
The PREFACE.
I have differed from most
Writers in regard of the RULE
of THREE: They make it two
diftinct Rules, under the Titles
of Direct, and Indirect: The
Learner is inftructed here, to
proceed to the Operation of any
Question propofed in the afore-
mentioned Rule, without confider-
ing the Diftinction Spoken of
(xi)
CONTENTS.
Definition of Arithmetic
Numeration
Addition
Subtraction
Multiplication
Page.
I
2
4
ΙΟ
13
Divifion
Reduction
Vulgar Fractions
Decimal Fractions
Of Proportion, or the Rule of Three 58
The Double Rule of Three
18
24
29
44
65
The Rules of Practice
71
Practice by Divifion
79
Practice by Multiplication
80
Short Methods in Bufinefs
81
Of Simple Interest
90
Rebate, or Diſcount
Of Compound Interest
Equation of Payments
96
100
Lofs
94
xii
CONTENTS.
Page.
Lofs and Gain
ΙΟΙ
Barter
105
Fellowship without Time
106
Fellowship with Time
108
Alligation Medial
110
Alligation Alternate
112
Single Pofition, or the Rule of Falfe 116
Double Pofition
The Extraction of the Square Root
The Extraction of the Cube Root
118
120
124
(1)
HEWIT T's
ARITHMETIC.
CHA P. I.
DEFINITION of ARITHMETIC.
RITHMETIC is deriv'd, and takes
its Name from the Greek, ('Aestrès,
Numerus) and is the Art of Number-
ing, or may be called the Doctrine
of accompting by Numbers; for as
Magnitude, or Greatness, is the Sub-
ject of GEOMETRY, fo Multitude, or Number, is the
Subject of ARITHMETIC.
UNIT (notwithſtanding fome Opinions) I humbly
conceive to be the BEGINNING, and LEAST of Num-
ber.
Subtract
from 8, and 7 will remain:
1 to 7, and it will make 8.
-add
If UNIT is no Number, it will neither decreaſe
any Number it is fubtracted from, or encreaſe any
Number it is added to: But as it is evident, that Unit,
UNIT,
being fubtracted from, or added to any Number, de-
creafes, or encreaſes it, fo it is a Demonftration, that
UNIT, is Number.
B
ARITK-
HEWITT's ARITHMETIC.
ARITHMETIC is compos'd of five Parts, viz. Nu-
meration, Addition, Subtraction, Multiplication, and
Diviſion.
Numeration teacheth to read, write down, expreſs,
or value any Number given, or propos'd.
The Characters, or Figures, by which all Num-
bers may be expreſs'd, are Ten, viz.
One, Two, Three, Four, Five, Six,
1
2
3
4
5
6
Seven, Eight, Nine, Nought.
7
8
9
There are three Sorts of Numbers, viz. a Digit,
an Article, a mix'd, or compound Number.
All Numbers not exceeding the nine Units, are
call'd DIGITS, as 1, 2, 3, 4, 5, 6, 7, 8, 9.
ARTICLES are Numbers confifting of a Digit and
a Cypher, plac'd on the right Hand, as, 10, 20,
80, 40, ốc.
Mix'D, or COMPOUND NUMBERS are compos'd
of both, as 12, 13, 14, 15, 102, 103, &c.
In order to exprefs, or value any Number
pro-
pos'd, or fet down, it will be proper to confider well,
and get perfect, in the following
TABLE.
9
8.
Hundreds of Millions.
Tens of Millions.
Millions.
o Hundreds of Thouſands.
5 4, 3
Tens of Thouſands.
Thouſands.
→ Hundreds.
~ Tens.
Units.
When
HEWITT's ARITHMETIC.
3.
When any Numbers are given to value, or ex-
prefs, divide them into Periods, beginning from the
right Hand, or Place of Units, allowing 3 Figures
to a Period, by making a Comma at the End of every
Period, as in the Table-
-thus, the firft Period
ends in Hundreds, the fecond in Thouſands, and the
third in Millions. So, the Table is to be thus va-
lued, or exprefs'd.---Nine Hundred Eighty-feven
Millions, Six Hundred Fifty-four Thousand, Three
Hundred Twenty-one.
Before I proceed any farther, I will infert ſome
Few Marks or Characters, which in fome Operations
hereafter, I may more conveniently make uſe of,
than the Words they are made to fignify.
More, or added to.
Lefs, or fubtracted from.
Into, or multiply'd by.
Divided by.
Equal to.
So is, or the Sign of Proportion.
AXIOM S.
THINGS equal to the fame Thing, or to equal
Things, are equal to one another.
If equal Things be added to equal Things, or to
one and the ſame Thing, the wholes will be equal to
one another.
If from equal Things be taken away equal Things,
or one and the fame Thing, the Remainders will be
equal to one another.
If to unequal Things, equal Things, or one and
the fame Thing be added, the wholes will be une-
qual.
If from unequal Things, equal Things, or one and
the fame Thing be taken away, the Remainders will
be unequal.
B 2
This
HEWITT'S ARITHMETIC.
Things which are double to the fame Thing, or
to equal Things, are equal one to another: The fame
is to be underſtood of Triple, Quadruple, &c.
Things, which are the Halfs of one and the ſame
Thing, or of equal Things, are equal the one to the
other: The fame is to be understood of Subtriple,
Subquadruple, &c.
Every whole is greater than it's part.
Every whole is equal to all it's parts taken to-
gether.
A
CHA P. II.
ADDITION of whole Numbers.
DDITION teacheth to bring feveral diffe-
rent Sums into one
RULE.
Be fure to place Units under Units, Tens under
Tens, Hundreds under Hundreds, and ſo on.
EXAMPLE.
Receiv'd at one Time
At another Time
More
More
1.
5246
371
42
8
The Aggregate, or whole Sum amounts to, l. 5667
Thus, I begin with the bottom. Figure on the right
Hand, which is in the Place of Units, and ſay, 8
and 2 is 10, and 1 is 11, and 6 is 17, this being all
that is to be added together in the Place of Units, I
fet
HEWITT's ARITHMETIC.
$
5,
and
fet down 7, and carry 1 Ten to the next bottom Fi-
4 is
gure in the Place of Tens; faying 1 and
7 is 12, and 4 is 16, putting down 6 at the Bottom
under the Figures in the Place of Tens; then I carry
the 1 to the next bottom Figure in the Place of Hun-
dreds, and fay 1 and 3 is 4, and 2 is 6, which I fet
down at the Bottom under the Place of Hundreds ;
and nothing remaining to add to the laſt Figure 5 on
the left Hand of the uppermoft Row, I bring it down,
and then find thofe different Sums I receiv'd, amount
in all to 5667, viz. Five Thoufand, Six Hundred,
and Sixty-feven Pounds.
ADDITION of Pounds and Shillings.
1.
S.
4
7
19
6
5
18
17
15
13
ΙΟ
16
1. 60
I begin at the bottom Figure in the Shillings on
the right Hand, and fay 5, 8, 6, 7, make 26; ſo I fet
down 6 in the Place of Units, and carry the 2 to the
other 3 Tens, which make 50; then I fet down i
Ten on the left Hand of the 6, and carry 2 for the
40 Shillings to the Pounds, fo 2, 3, 7, 5, 9, and
make 30, I put down the o Cypher on the right Hand
at the Bottom, and carry 3 to the 3 ones, which make
6, which being plac'd on the left Hand of the Cy-
pher, make 60-So thoſe different Sums of Pounds
and Shillings, make Sixty Pounds, Sixteen Shillings.
4
ADDI
HEWITT's ARITHMETIC.
DDITION of Pounds, Shillings and Pence.
ADDITION of
1.
S.
di
13-
-17-
4
10-
5
14-
16—
II
30
I
Shillingence and Farthings.
S.
d..
qr.
16.
4-
I
2 N
275
89
31
クー
​18-
·10-
༢
-13-
II
-I
9
9-
82
14-
3
15-
-15-
5-
2
7
1. 775- 2-
AGENERAL RULE for ADDITION of ſeveral
Denominations.
As in whole Numbers, Units muſt be plac'd under
Units, Tens under Tens, &c. So here, Farthings muft
be plac'd under Farthings, Pence under Pence, Shil-
lings under Shillings, and Pounds under Pounds, and
fo of any other Denominations and remember to
begin always with the Denomination on the right
Hand, and as many of the firft Denomination, as
make one of the fecond, carry one to the fecond,
and the fame of the fecond to the third, and ſo on; -
As here, 2, 3, 2, 1, 3, 1, Farthings make
3 Pence, fo you fet down o under the Farthings, and
carry 3 to the Pence, faying 3, 5, 4, 8, 1, 4, inake
25, then come down the Tens, faying 35, 45, 551
which is 7 Pence above 4 Shillings, fet down the 7 un-
dex
HEWITT'S C
T
ARITHMETIC.
der Pence, and carry 4 to the Shillings, 4, 5, 7, 9, 3,
8,6, make 42; then come down the Tens 52, 62,
72, 82, which is 2 Shillings above 4 Pounds; fet
down the 2 under the Shillings, and carry 4 to the
Pounds, faying 4, 5, 1, 9, 5, 7, 4, make fet down
359
5, and carry 3, faying 3, 1, 3, 8, 7, 3, 2, make 27 ; .
make
fet down 7, and carry 2, faying 2, 2, 2, 1, 7.
which in Value make l. 775:2:7.
One Fourth
I
ftands for
Three Fourths
{
2 Farthings.
3
One Half
F
The Proof of ADDITION.
After adding up the whole Sums, cut off the up-
per Sum by a Line drawn thro', and then odd up all
the others, and that Line add to the
as in the foli.
t, and
ns, it.
Ad-
if it agrees with the first Addition of ai
is right; if not, it is falſe
dition, the whole amounts to /. 332:7:10, 1s up-
per Line being 1. 247:6:84, is cut off, and all the
other Sums make 7. 85: 1:24, which being added to
the uppermoft Line, makes the third anfwerable tɔ
the first.
1.
S.
247
d.
6 8/1/1
3夏
​U N
32-
17-
4
15
18- 12-
10-
14-
7-11
4-
ΙΟ
II
Total-1. 332-
85-
I
2
Proof-332-
7101
But
8
HEWITT's ARITHMETIC.
But Men well acquainted with Accompts and Bufi-
neſs, generally add from the Bottom, and then from
the Top to the Bottom; and if a Miftake happens, it
is found out by this means.
In order to render a Perfon quick at Addition, it
will be proper to get perfect in the following Table.
Pence.
Shillings.
I
12
48
2346 78
+6∞ ON +∞
24
36
60
72
make
84
2 M to 7∞
8
3
5
6
96
108
1 20
132
144
9
10
II
12
ADDITION of TROY-WEIGHT.
A Table of Troy-Weight.
24 Grains,
20 Penny-weight,
}
make
{
1 Penny-weight.
I Ounce.
12 Ounces
¡ Pound.
By this Weight, are weighed all Kinds of Jewels,
Pearls, Gold, Silver, Corn, Bread, Liquors, and Elec-
tuaries; and from hence all the Meaſures of wet and
dry Commodities are taken.
lb.
22--
13-
12-
02. dwt. gr.
918—21
II- 14 -19
6-11-
23
9-
·10-
-17 ——— 13
*
59 3- - 3·
3- - 4
A D.
HEWITT's ARITHMETIC. 9
ADDITION of AVERDUPOIZE-WEIGHT.
A Table of Averdupoize-Weight.
16 Ounces,
28 Pounds,
56 Ditto,
make
84 Ditto,
4 Quarters,
zo Hundred,
1 Pound.
1 Quarter.
2 Ditto.
3 Ditto.
1 Hundred Weight.
I Tun.
Note well, This Ounce is lighter than the Ounce
Troy by 42 Grains in 480; the Ounce Averdupoize
being but 438 Grains, bears a Proportion to the
Ounce Troy, as 73 to 80.
Tuns
C.
17—18-
13-14-
grs. lb.
317-
2- 135
02.
·14·
15-
19-
9-
·17-
I
8-
T
II
10:
Q-250
·2513-
·13-
2- ·276 15.
4-
7-
I
5-
4
70-
9-
0-20-
20 I
ADDITION of TIM E.
A Table of Time.
60 Minutes,
24 Hours,
365 Days,
} make {
1 Hour..
1 Day..
1 Year.
Years.
10
HEWITT's ARITHMETIC.
Years.
Days. Hours. Minutes.
7-
-230-
·21·
54
2
191
7
47
3.
84
19-
·36
5-
14-
-29
14
147- -15-
46
S'
CHA P. III.
SUBTRACTION of whole Numbers.
UBTRACTION teacheth to take a leffer
Number from a greater, and to know what re-
inains.
RULE.
Take care to place the leffer Number under the
greater, and be fure to put Units under Units, Tens
under Tens, &c. and every Denomination under the
like Denomination, as Pence under Pence, Feet under
Feet, &c.
EXAMPLE.
1.
Receiv'd 45679
Paid away 14467
Remains 31212
Begin with the Bottom Figure on the right Hand
(as in Addition) and fay, 7 from 9, remains 2
6 from 7, remains 1 -4 from 6, remains 2
4
from
5, remains 1-
remains 1-1 from
1 from 4, remains 3. But
it
HEWITT's ARITHMETIC.
11
it very often happens, that feveral of the Figures are
greater in the Sum ſubtracted from, than in the Sum
fubtracted: In which Cafe you muſt borrow 10 (in
whole Numbers) from the upper Figure on the left
Hand, to lend it to the Figure on the right; thus
-9 from 5 I cannot, but borrowing 10 added to
makes 15, 9 from 15 remains 6, which 10 you pay
again as an Unit, that is (1 Ten) 1 and 5 is 6, 6 from
2 I cannot, but 6 from 12 and there remains 6, 1 and
3 is 4, 4 from 1 I can't, but 4 from 11 remains 7
I and 1 is 2, 2 from 4, refts 2.
Receiv'd 4125
Laid out 1359
Remains 2766
SUBTRACTION of feveral Denominations.
1.
S.
d.
From 247
Subtract 214-
·17-
14-
8
Remains 33 3 — 3
8 from 11 Pence, and there remains 3 Pence, 14
Shillings from 17 Shillings, and there remains 3 Shil-
lings, 4 Pounds from 7 Pounds, and there remains
3 Pounds, 1 Pound from 4 Pounds, and there remains
3 Pounds.So that, when 214 Pounds, 14 Shillings,
and 8 Pence, is fubtracted from 247 Pounds, 17 Shil-
lings, and 11 Pence; 33 Pounds, 3 Shillings, and 3
Pence remain. But if the Pence in the lower Line
happen to be more than thoſe in the upper Line, you
muſt borrow I Shilling, which making 12 Pence,
add 'em to the Pence in the upper Line, and then ſub-
tract the lower Line from the upper, paying the
12
HEWITT'S ARITHMETIC.
1 Shilling to the next Denomination on the left Hand,
thus
d.
1.
S.
From 547
Subtract 459
II
4
18 — II
Remains 87-12—— 5
Take 11 Pence from 4 Pence I cannot, but borrow-
ing 1 Shilling, which being 12 Pence, and 4 Pence
make 16 Pence, take 11 from 16, and 5 remains ;
then 1 Shilling borrowed, and 18 makes 19, from 11
I can't, but borrow 1 Pound which is 20 Shillings,
and 11 is 31, 19 from 31, and 12 remains; Pound
borrowed and 9 is 10, from 7 I can't, but 10 from 17,
and 7 remains; 1 and 5 is 6, from 4 I can't, but 6
from 14, and 8 remains; 1 and 4 is
is 5 from 5 nothing
remains.
Proof of SUBTRACTION.
ì
Add the Remainder to the Sum fubtracted, and if
both make up the Sum fubtracted from, it is right;
1.
if otherwife, 'tis falfe, as in the laft Example . 87:
12:5, being added to 1. 459: 18:11, they will
make 1.547: 11:4
SUBTRACTION of Troy-Weight.
lb.
02.
dwt.
gr.
1.27--
·II-
17-
-2 I
IOI-
8—— 21 —
14
26——2—16———— 7
SUB-
HEWITT's ARITHMETIC.
13
SUBTRACTION of A-verdupoize-Weight.
Tuns. C. qrs.
246———6————3—
-15- I
194-
lb.
21-
02.
-10
27—————14
12
Years.
367-
SUBTRACTION of Time.
Days. Hours.
218–
218-
·311▬▬▬▬▬▬23·
148- 271
Min.
·14·
41
55
14-
-46
CHA P. IV.
MULTIPLICATION.
ULTIPLICATION is a Compendium of
M Addition-and teaches of two Numbers given
to encreaſe the greater as often as there are Units con-
tain'd in the leffer: Thus, 6 multiplied by 3 makes
18.
6
Add
{
6
6
6x3=18
There are three Parts to be obſerved in Multipli-
cation.
1. The Sum to be multiplied, is call'd the Multi-
plicand.
C
2.
14
HEWITT's ARITHMETIC.
2. The Sum by which you multiply, the Multi-
plier.
3. And what is produced from the Work, the
Product.
The first Step to enable you to proceed in this Rulę,
is to get perfect in the following Table.
The MULTIPLICATION TABLE.
4
2 Times
8 Times
3
2 3 4 7∞ a
9
1Ο
are
12
8
+6∞ ∞ N
14
16
18
are
3+56 7 9
0-0
1.8
ON 200
4
-0-0
Times
9
are
are
28
32
36
25
30
35
40
-}-{}
5 Times
7
8
9
45
6 Times
HEWITT's
ARITHMETIC.
36
6
6 Times
7
are
8
9
Times
{1}-{}}
8
are
· { } } ==
9
8
8 Times { {; }
9
are
42
48
54
49
56
{{#3} }
63
64
{ // }}
72
9 Times 9 are 81 >
22
11 Times
12 Times
7
Nm tio não a
2
3
4
33
44
55
66
are
8.
9
10
II
110
121
78
77
88
99
5
8
9
2 3 4 SO NO σ
10
I I
12
are
24
36
48
60
72
84
96
108
120
132
144%
When there are two Numbers to be mutiplied by
one another, you may make which of them you pleafe
C 2
the
25
HEWITT's ARITHMETIC.
the Multiplier and Multiplicand, tho' the ſhorteſt way
will be to make the leaſt Number the Multiplier, as
if 2496 and 48 were to be multiplied together, I would
make 2496 the Multiplicand, and 48 the Multiplier.
Multiply 346
By 4
1384
Say, 4 Times 6 are 24, fet down 4; and fay 4 Timės
4 are 16, and 2 you carried are 18, fet down 8 and
carry 1; 4 Times 3 are 12, and 1 is 13, which fet
down as you fee in the Work, becauſe there is no
other Figure left to multiply.
When ever your Multiplier contains a Cypher or
Cyphers, and a fingle Unit, bring down the Multi-
plicand, and place as many Cyphers on the right
Hand of it, as are in the Multiplier, and the whole
is the Product, fee the Work.
Multiplicand 7294
Multiplier
10
Product 72940
Multiplicand 4965
Multiplier
100
Product 496500
Multiplicand 98746
Multiplier
1000
Product 98746000
But where more Units with a Cypher or Cyphers
are concern'd, bring down the Cypher, or Cyphers,
and then proceed to multiply with the firft-Figure on
the left Hand of the Cyphers, as
5679
HEWITT's ARITHMETIC. 17
5679
30
170370
35648
3900
32083200
106944
139027200
4576
204
18304
91525
933504
If Man ſhares 297 1. how much Money muſt there
I
be in all to pay 869 Men the fame ?
Anfwer 258,093 1.
869
297
6083
7821
1738
258,093
There is a Method of multiplying by any two Units,
to 19, and producing no more Figures than the Pro-
duct, as appears by the following Operation; but as
it is more curious than uſeful, I would recommend the
C 3
com
18
HEWITT's ARITHMETIC.
common Way of Working, being lefs liable to Mi-
ftakes.
579643127
19
11C13219413
The Proof of MULTIPLICATION.
Exchange the Multiplier for the Multiplicand, and
work as before, and if this Product anſwers the firft,
it is probably right, if otherwife, it is wrong-There
is another Way of proving Multiplication, by cafting
away the Nines in the Multiplicand, aud what remains
above, or under Nine, fet it on the right Hand of a
Crofs; then proceed to do the fame by the Multi-
plier, and place what remains on the left Hand, then
multiply one by the other, and ſet down at the Top
of the Crofs, what is under Nine, or over as many
Nines as can be caft away; then proceed to do the
fame with the Product; and if what remains over or
under Nine, anſwers the top Figure, your Work may
be probably right-But the moſt certain Proof is by
Divifion, as will hereafter be fhewn.
D
CHAP. V.
DIVISIO
N.
IVISION teacheth to find how often one Num-
ber is contain'd in another: as if it were requir'd
to know how often 4 is contained in 16, the Anſwer
wou'd be 4 Times; or if 4 was fubtracted 4 Times
from 16, nothing will remain, as here under: There-
fore Divifion may be juſtly ſaid to be a Compendium
of Subtraction.
From
HEWITT's ARITHMETIC.
19
From
Subtract
16
I 2
8
4
4
4
4
4
12
8
4
There are four Things to be obferved in this Rule.
1. The Sum to be divided, is call'd the DIVI-
DEND.
2. That, by which you divide, the DIVISOR.
3. That, which fhews how often. the Diviſor is
contained in the Dividend, the QUOTIENT.
4. The REMAINDER, which must be always lefs
than the Divifor.
EXAMPLE.
How many Pence are contained in 264 Farthings,
I confider that 4 Farthings make 1 Penny; fo that as
often as 264 contains 4, which is expreffed in the
Quotient, there are ſo many Pence.
Dividend
Diviſor 4)264(66 Quotient
24
24
24
o Remainder.
I first place down 264 which is the Dividend, or
Sum to be divided; then at the Beginning and End, 1
draw two Semi-Circles, as in the foregoing Example;
and place 4, the Diviſor, before the left Hand Semi-
Circle; then, as I can't have 4 in 2, I fay, how
many Times 4 in the two firſt Figures 26, I put down
6 in the other Semi-Circle, faying 6 Times 4 make
24, which place under the two firft Figures in the Di-
vidend
20
HEWITT's ARITHMETIC.
vidend 26; draw a Line under them, and ſubtract 24
from 26, faying 4 from 6, there remains 2; then 2
from 2, nothing remains; for which, place a Point
as you fee in the Example.-Then bring down the re-
maining Figure 4 in the Dividend, and fay, how
many Times 4- in 24, I put down 6 by the other 6,
which is called the Quotient, and fay, 6 Times 4
make 24, which being placed under the other 24, and
fubtracted from it, there remains o nought.
But when the Learner comes to be expert in Di-
vifion, where the Divifor confifts of any Number not
exceeding 12, as 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12.
-he will produce no more Figures than the Quotient,
and the Remainder, if any-which is owing to the
Uſe of the Multiplication Table.
EXAMPLE.
Divide 2448 . between 12 Men.
Dividend
Divifor 12)2448(204 Quotient
I fay 12 in 24, I put down 2 in the Quotient, and
fay 12 Times 2, or twice 12 is 24, from 24 nothing
remains; then I fay 12 in 4, which is the next Fi-
gure, I cannot, therefore put down o a Cypher in the
Quotient; and taking the 2 Figures, fay, how many
Times 12 in 48, I put down 4 in the Quotient, and
fay 4 Times 12 make 48, from 48, and nothing re-
mains.
Divide
HEWITT's ARITHMETIC.
2-1
Divide 764831925 by 4619
Dividend.
Diviſor 4619)7648,3,1,9,2,5,(165583 Quotient
4619
30293
27714
.25791
23095
.26969
23095
.38742
36952
•
17905
13857
4048 Remainder.
This is call'd long Divifion; but I would recom-
mend the following, which is call'd the fhort Italian
Method, and will prove as eafy, by Practice, as the
other—the foregoing Method having Abundance of
uſeleſs Figures, and when the Dividend and Divifor
are large, the Operation extends to an unfeemly
Length.
4619
22 HEWITT's ARITHMETIC,
4619)764831925(165583
30293
.25791-
26969
.38742
•
17905
4048
I begin with the first 4 Figures in the Dividend,
which I find contain the 4 Figures in the Divifer,
and put down in the Quotient-faying, once 9
from 8, I cannot, but borrowing 1 from the Place of
Tens, it makes the 8 Eighteen, then 9 from 18 there
remains 9; once I and the 1 you borrowed make 2,
from 4 there remains 2; then once 6 from 6, there
remains o, once 4 from 7, there remains 3
-then
I bring down the next Figure in the Dividend, which
is 3, making a Point as you fee to prevent miſtaking
the laft Figure you brought down-then I fay how
many Times 4619 in 30293, and I find I can have it
6 Times, which 6 I put in the Quotient, and ſay 6
Times 9 make 54 from 3> I cannot, but 6 from the
place of Tens added to 3 makes 63, take 54 from 63,
and there remains 9; then ſay, 6 Times i make 6,
and 6 borrowed make 12 from 9 I cannot, but from
19, and there remains 7; then 6 Times 6 make 36,
and 1 is 37 from 2, I cannot, but from 42, and
there remains 5; then 6 Times 4 make 24, and 4 is
28 from o, I cannot, but from 30, and there re-
mains 2 -and fo proceed thro' the whole.
When the Divifor ends with a Cypher, or Cyphers,
cut 'em off, and cut off as many Figures on the right
Hand
HEWITT's ARITHMETIC. 23
Hand of your Dividend, as you cut off in the Divifor,
and then proceed as before, only bring down thoſe
cut off in the Dividend, to the Remainder.
EXAMPLE.
4000)5315·067(Remainder.
Quotient 1328-1067
2242
4500)6187 | 42(137 238 23
168
•
· 337
22
By this it appears, that when the Divifor is 10,
100, 1000, or 10000-cut off as many Figures on
the right Hand in the Dividend, as you cut off in the
Divifor, and the Remainder is the Quotient.
1 |000)475 | 361) 7361
1040)67983 | 1(653 718
·558
383
· 71
Proof of DIVISION.
The fureft Way is by Multiplication—that is,
multiply the DIVISOR by the Quotient, or the Qua-
TIENT by the Divifor, and take in the Remainder,
if
2.4
HEWITT's ARITHMETIC.
if any, and the Product, if the Work is right, will
prove the fame as the Dividend-
Example.
-fee the foregoing
653
1040
26831
6530
679831
R
CH A P. VI.
REDUCTION.
EDUCTION teacheth to bring Numbers of
different Denominations into one; or alter Num-
bers, Weight, Mcaſure, Time, Money, &c. from one
Denomination to another: Therefore obferve,
First, All great Denominations are brought into
Small by Multiplication, as,
Pounds,
f 20
Shillings,
12
Pence,
Pence,
multiply'd by
2 4
Pounds,
240
Pounds,
480
Pounds,
960
are
[Shillings.
Pence.
Half pence.
Farthings.
Perce.
Half-pence.
Farthings.
Secondly, All Small Denominations are brought into
great by Divifion; as,
Shillings,
HEWITT's ARITHMETIC. 25
Pounds.
Shillings,
20
Pence,
I 2
Shillings.
Half-pence,
2
Pence.
Farthings,
4
Pence.
Pence,
240
Pounds.
Half-pence,
480
Pounds.
Farthings,
1960
Pounds.
In 4367. 175. 6d. how many Shillings and Pence.
First, Confider, whether the Sum propofed is to be
brought into a greater or leſſer Denomination; as here
Pounds, Shillings, and Pence, are to be brought into
Pence, which is reducing greater Denominations to a
less, and confequently according to the Rule laid down,
is to be done by Multiplication-but then confider
how many Shillings a Pound makes, viz. 20———
then multiply the Pounds by 20, and take in the 17 s.
and they make 8737 s. then confider how many Pence
a Shilling makes, viz. 12; then multiply 8737s. by
12, and take in the 6, and they make 104850 d. the
Anſwer required. See the Work.
1.
S.
d.
436:17:6
20
8737 Shil.
1 2
104850 Pence.
The Proof of this, as in all others, is by reverfing
the Question, thus-
In 104850 Pence, how many Shillings and Pounds.
12)104850
210)87317-6
436--17-6
1.
D
In
26 HEWITT'S ARITHMETIC.
In 588 Pounds, how many Shillings, Pence, Groats,
and Nobles?
588 Pounds.
20
11760 Shillings.
12
4)141120 Pence.
203528 | Groats.
1764 Nobles.
Obferve, this Queſtion was anſwer'd by Multiplica-
tion and Diviſion – as far as it related to Pence, by
Multiplication, which is bringing great into small,
then by Divifion, to find the Groats and Nobles,
bringing Small into great.
In 1764 Nobles, how many Groats, Pence, Shil-
lings, and Pounds?
1764
20
35280 Groats.
4
12) 141120 Pence.
2 c)11760 Shillings.
588 Pounds.
REDUCTION of TIME.
As to the Table of Time, I refer the Reader to the
zd. Chap.
How many Days, Hours, and Minutes, fince the
Birth of our SAVIOUR to this prefent Year 1738 ?
1738
HEWITT's ARITHMETIC.
27
1738
365
8690
10428
5214
634370 Days
24
2537480
1268740
15224880 Hours
60
Answer 913492800 Minutes.
N. B. According to the true Method, there is loft
in this common Operation, 1 Year, 69 Days, and
6 Hours, a Year being truly 365 Days, 6 Hours.
REDUCTION of LAND-MEASURE.
A Table of Land-Meafure.
3 Barley-Corns
12 Inches
3 Feet
161 Feet
18 Furlongsmake
I Inch.
I Foot.
I Yard.
1 Pole, Perch, or Rod.
I Furlong.
1 Mile.
All Circles are divided into 360 Degrees, and each
Degree into 60 Minutes, which, upon the Superficies
of the Earth, are equal to 60 Miles,
D 2
In
28
HEWITT's ARITHMETIC.
In the Circumference of the Earth (being 360 De-
grees) how many Miles, Furlongs, Poles, Yards, Feet,
Inches, and Barley-Corns?
360 Degrees.
60 Miles in a Degree.
216co Miles.
8 Furlongs in a Mile.
172800 Furlongs.
40 Poles in a Furlong.
6912000 Poles.
11 Half Yards in a Pole,
2)76032000
38016000 Yards.
3 Feet in a Yard.
114048000 Feet.
12 Inches in a Foot.
1368576000 Inches.
3 Barley-Corns in an Inch.
4105728000 Barley-Corns.
Thefe Examples are fufficient to inftruct the Learn-
er in any of the other Rules of Reduction, as Cloth-
Meafure, Wine-Meaſure, Troy-Weight, Averdupois-
Weight, &c. becauſe hanging too long upon one and
the fame Purpoſe, is rather apt to give Pain than
Pleaſure, and often difcourages the Learner from pro-
ceeding.
CHA P.
HEWITT's ARITHMETIC. 29
CHAP. VII.
Of VULGAR FRACTIONS.
A
FRACTION, or broken Number, is a Part,
or Parts of an Integer, or whole Number; for
as whole Numbers from their Beginning, may con-
tinue without End, fo any Integer, or whole Num-
ber, by Imagination, may be diffolved, or divided
into Parts infinite.
I 2
4"
A Fraction is expreffed by two Numbers, as thus
1,3,4, the uppermcft Number is called, the Nume-
rator, and the lowermoft the Denominator; fo in theſe
Fractions
3
ž, 3, 4, 1, 2, 3, are the Numerators, and
2, 3, 4, are the Denominators.
The DENOMINATOR is fo called, becauſe it ex-
preffes the Number of PARTS into which the INTE-
GER is divided.
3
·
The NUMERATOR, is fo called, becauſe it tells,
or expreffes how many of thoſe PARTS (denominated,
muſt be taken: Thus, fhews that the Integer is
divided into four Parts, which, the Denominator ex-
preffes, and the Numerator fhews that three of thoſe
four Parts muſt be taken.
When the Numerator is equal to the Denomiuator,
that Fraction is faid to be equal to Unity, thus
4
4
I.
When the Numerator is less than the Denominator,
that Fraction is faid to be less than Unity, and is cal-
led a SIMPLE, or PROPER FRACTION.
When the Numerator is greater than the Denomi-
nator, fuch a Fraction is more than Unity, and is cal-
led an IMPROPER FRACTION; as thus, = 2+},
which, when fo expreffed, is called a MIXT NUMBER.
When an Integer is divided into any Number of
Parts, and each of thofe Parts, fubdivided into other
Parts,
30
HEWITT's ARITHMETIC.
Parts, fuch Fractions are called, Compound Fractions,
or Fractions of Fractions, and are always connected
together by the Particle (OF) as, 3 of 4 of %, and
as it is abfolutely neceffary to know how to bring
Fractions of feveral Denominations into one, before
we can proceed farther in the Doctrine of Vulgar
Fractions, I fhall begin with,
REDUCTION of Vulgar Fractions.
REDUCTION teaches to bring Integers into Frac-
tions, or improper Fractions, into equivalent whole,
or mixed Numbers, or Fractions of many Denomi-
nations into one.
1. To reduce proper Fractions.
RULE.
Multiply all your Denominators together, and the
laft Product will be your common Denominator,
then multiply your firit Numerator into all the Deno-
minators, except its own: then multiply the fecond
Numerator into all the Denominators, except its own,
and fo on with the reft, if there are more.
EXAMPLE.
Reduce, and according to the foregoing
Rule, the Work will ftand thus,
120 192 320
44
ΤΟ
P
8
480
22
92
So that 110 19 320 are equal to TT
☀ Tô 12:
2. To
HEWITT's ARITHMETIC.
31
4. To reduce Compound Fractions, or Fractions of
Fractions into one Denomination.
RULE.
Multiply all the Numerators into one another, and
that Product is your new Numerator; then multiply
all your Denominators one into another, and that
Product is your new Denominator.
EXAMPLE.
Reduce of of of 30 Shillings to a proper Fraction.
24
of of of 30 Shil. or 12 Shil.
60
3. To reduce Improper Fractions into its equivalent
whole, or mix'd Number.
RULE.
Divide the Numerator by the Denominator, and the
Quotient is a whole Number, and the Remainder (if
any) is a new Numerator to the old Denominator.
EXAMPLE.
Reduce 27
5)27(5
2
So that 27 are equal to 5 3.
4.90
32
HEWITT's ARITHMETIC.
4.
To reduce a whole Number into an Improper
Fraction.
RULE.
Let the Number propos'd be your Numerator,
1 the Denominator.
Reduce 9 into an improper Fraction.
Thus.
5. To reduce a whole, or mix'd Number into one
Denomination.
RULE.
and
Multiply the whole Number into the Denominator
of the Fraction, adding thereto the Numerator, and it
makes a new Numerator to the old Denominator,
EXAMPLE.
Reduce 7 and, and it makes 3.5
Multiply 7
5
35
Add
I
36
6. To reduce a great Fraction into the lowest Denomi-
nation, of the fame Value.
RULE.
Take half of the: Numerator, and half of the De-
nominator, as often as you can; then confider if any
other Number can be found, that will divide both Nu-
merator and Denominator.
E X-
HEWITT's ARITHMETIC.
33
Reduce
48
EXAMPLE.
288
576
I 2
144
I
72
24 fometimes, the Re-
duction of a great Fraction in to a fmall, is more ef.
fectually done, by finding a Number that will at firſt
divide the Numerator and Denominator, than by hal-
ving it, for Example,
6
Reduce 28 13.
24 | 1881
It is eafier done thus
15
divide 24 the Numerator
by 12, and the Quotient is 2 for a new Numerator ;
then divide 60 by 12, and the Quotient is 5 for a new
Denominator.
So that 24
Another Way,
Divide the Denominator by the Numerator, and the
Diviſor of every Divifion by the Remainder, 'till no-
thing remains -then the laft Divifor will divide
-but I would
both your Numerator and Denominator-
not adviſe he Practitioner to ufe this Method, it be-
ing very tedious and troubleſome.
When a Fraction, whofe Numerator and Denomina-
tor have a Cypher, or Cyphers, in order to reduce it
to its loweſt Term, and retain the fame Ratio, cut off
as many Cyphers from the Denominator, as you do
from the Numerator, and the remaining Fraction will
be equal to the firſt.
45
Reduce 48. Reduce 1% = $.
운동 ​| 응응
​56
윽
​7. To find whether one Fraction is GREATER or LES-
SER in Value than another.
RULE.
Multiply the Numerators into each other's Denomi-
nator, and if the Products are equal, the Fractions are
fo;
34
HEWITT's ARITHMETIC.
fo; if not, you'll find that the Numerator of the
greateſt Fraction multiplied by the Denominator of the
other, will make the greateſt Product.
EXAMPLE.
is more in Value, than, becauſe 7 multiplied
I
II2.
by 16
And 9 multiplied by 9=81.
So, is equal in Value to 12, becauſe 9x16=144
And 12×12-144.
8. To find the Value of any Fraction, either in Money,
Weight, Meaſure, &c.
RULE.
Multiply the Numerator of the given Fraction, by
the known Parts of the next inferior DENOMINATION,
and divide that Product by the given Fraction's Deno-
minator, and the Quotient will exprefs the Value of
the propos'd Fraction in that Denomination-and
if any Thing remains, multiply that by he known
Parts of the next inferior Denomination, and divide as
before, and ſo on, 'till you bring it into the loweſt
Terms.
EXAMPLE.
What is the Value of of a Shilling?
12
Here I confider the next inferior Denomination of a
Shilling are Pence, and the known Parts are 12,
therefore,
7x12=84+12=7.
That is, 7 multiplied by 12 is equal to 84; and 84
divided by 12 is equal to 7.
So that of a Shilling is to 7 d.
What
HEWITT's ARITHMETIC.
35
What is the Value of of a Pound Sterling?
I
Firſt confider, that the next inferior Denomination
of a Pound are Shillings, and the known Parts are 20;
therefore multiply 20 by 2, and the Product is 40;
which divide by 3, the Denominator of the given Frac-
tion, and the Quotient is 13 Shillings, and 1 remains;
which muſt be multiplied by the known Parts of the
next inferior Denomination, which is 12, the Pence
in a Shilling; but as I neither multiplies, nor divides,
proceed to divide the 12 by the Denominator 3, and
the Quotient is 4 d.
So that of a Pound Sterling in Value is 13 s. 4 d.
When a Fraction is to be brought from a leffer to a
greater Denomination, make it a compound Fraction,
by comparing it with the next fuperior Denominations.
between it, and that you would have it reduc'd to; then
proceed to reduce your compound Fraction, to a fimple
Fraction, by the fecond Rule in this Chapter, and
your Work is done.
EXAMPLE.
What Part of a Pound Sterling is 3 of a Penny ?
According to the fecond Rule in this Chapter it will
Aand thus,
2 of 2 of 2 for Anſwer.
CHAP.
36 HEWITT's ARITHMETIC.
I'
CHAP.
VIII.
Addition of Vulgar Fractions.
F your Fractions to be added have a Denominator
common to all, then add all the Numerators toge-
tner, and the Total is a new Numerator to the com-
mon Denominater; and if it is an improper Fraction,
reduce it to a whole or mix'd Number, as taught in
the third Rule of the feventh Chapter.
But if your Fractions are proper, or improper, or
have different Denominators; before you can add them
together, reduce them to a common Denominator by
the foregoing Rules.
3
Example of SIMPLE FRACTIONS.
Add 2 reduced by the firſt Rule in Reduction,
4
ड 6 7
630 672 700 720
they will ſtand thus
34
4
5
6
دانه
7
840
Then 630+672=1302+700=2002+720=2722.
2722 being an improper Fraction, reduc'd by the
third Rule of the feventh Chapter, will be 3 33.
16
840
Example of COMPOUND FRACTIONS.
Add and of 3.
202
84
Firft,of, then and reduced will be 42 and
18, which added will be 1+24.
489
Example
HEWITT's ARITHMETIC. 37
Example of MIXED NUMBERS.
3
Add 3 and 4 together.
7
Reduced to improper Fractions, they1934.
Reduced to a common Denominator, they = 13
+, or 8+33.
35
35
•
:
T
CHAP. IX.
Subtraction of Vulgar Fractions.
HE fame Rule of reducing Fractions to one De-
nomination muſt be here obſerved, as in Addi-
tion: And before one Fraction can be fabtracted from
another, the Fractions must be reduced to one common
Denominator; then fubtract one Numerator from ang-
ther, and place the Remainder over the common De-
· nominator, which Fraction will be the Difference be-
tween the two given Fractions.
Example of SIMPLE FRACTIONS.
Subtract from 7.
5
40
Reduced, they will ſtand thus 24 and 25.
So that 24 fubtracted from 25 there remains
6
40
Example of COMPOUND FRACTIONS.
Firſt
and 18.
Then
?.
of
S
Subtract of from 3.
23
6
reduced, 19, and 1 and 354
ނ
42
fubtracted from there remains 3
gg
E
Example
39
HEWITT'S ARITHMETIC.
Example of MIXED NUMBERS.
4
Subtract 4 from 9%.
그믐​,
Reduced 4 = 24, and 9 7—28, then 24 and zo
reduced to a common Denominator 122 and 195.
Then 122 fubtracted from 325 there remains 203
5 43.
40
ΤΗ
CHAP.
X.
Multiplication of Fractions.
HE Preparation that is abfolutely neceffary for
this Rule, is to reduce all compouud Fractions
to fimple Fractions, and all whole, or mixed Numbers,
to improper Fractions: Then follows this general
Rule; multiply all the Numerators together for a new
Numerator, and all the Denominators together for
a new Denominator.
As whole Numbers multiplied by whole Numbers
encreaſe the Product, fo Fractions multiplied by Frac-
tions decreaſe the Product.
EXAMPLE.
Maltiply of a Pound Sterl. and 2 of a Pound to-
gether.
Here is no Preparation required, the Fractions be-
ing fimple.
So that multiplied by
Note, of a Pound
by the Multiplication of
produces 12125.
16 s. and 2
16s. and 15 s. which
Fractions produces only 125.
To
HEWITT's ARITHMETIC.
39
To multiply compound Fractions.
3
Multiply of by of, being reduced,
3
They are and 30,
And being multiplied, make 128=1.
To multiply a whole Number by a Fraction.
RULE.
Multiply the Numerator by the whole Number,
and divide the Product by the Denominator.
EXAMPLE.
Multiply 5 by 4.
5
3
7) 15(2 +/
플
​To multiply a mixed Number by a whole Number.
RULE.
Reduce the mixed Number into an improper Frac-
tion; then work, as in the laſt Example.
Multiply 4 by 7.
43=24×7 = 32 3.
To multiply a mixed Number by a mixed Number.
RULE.
Reduce both the mixed Numbers to improper Frac-
tions, and then work as in fimple Fractions.
E 2
E X-
40
HEWITT'S ARITHMETIC.
EXAMPLE.
6
Multiply 49 by 53,
49-34 and 5 424, then 34 x 23 makes 28%
2728 or 12.
14
=27
26
3
A
CHA P. XI.
Divifion of Vulgar Fractions.
LL Fractions that are not ſingle, muſt be reduced
to fuch, both for the Dividend and Divifor ;
then multiply the Numerator of the Dividend by the
Denominator of the Divifor, and place that Product for
a new Numerator, then multiply the Denominator
of the Dividend by the Numerator of the Divifor,
and that Product is a new Denominator.
Divifion in vulgar Fractions differ from Divifion in
whole Numbers; for, as the Dividend in whole Num-
bers muſt be always greater than the Divifor, fo here
it may be lefs: And as Multiplication of Vulgar
Fractions decreaſes the Product, fo Divifion encreaſes
the Quotient.
EXAMPLE.
What is the Quotient of
divided by &?
+) { (24 = 1 24.
동
​To divide a whole Number by a Fraction.
3
What is the Quotient of 7 divided by ?
Reduce 7 to an improper Fraction, and it ftands thus,
33) 7 ( 5/2/3 = 183.
HEWITT's ARITHMETIC.
4I
To divide a mixed Number by a mixed Number.
What is the Quotient of 8 3 divided by 7 ?
83 reduced,
2 and 7 /
6
36
I
244
244°
61) 35 (280
8
To divide Fractions of Fractions.
What is the Quotient of of divided by of?
{ 3
of reduced, = 14, and 4 of
reduced = 13.
35
2
35
3333) 1942 (2583
62
= 1
28
CHA P. XII.
The RULE OF THREE direct in Vulgar
F
Fractions.
IRST, Take care that the Fractions con-
cerned, of what Kind foever, be reduced to
fimple Fractions, according to the feveral Rules laid
down in Reduction of Vulgar Fractions. Then obferve,
as in the Rule of Three in whole Numbers, fo like-
wife in Fractions, to let the first and third Numbers.
be Fractions of the fame Denomination, then mul-
tiply your ſecond and third Numbers together, and
divide by the first, and the Quotient is the Anfwer.
EXAM-
42
HEWITT's ARITHMETIC.
EXAMPLE.
4
If of Yard coft . what will coft?
76
3/44
114-464
3
4
42/336
3)14 (338-3-15 s.
8 641448
An EASIER WAY.
Multiply the Numerator of the first Fraction into
the Denominator of the fecond and third, and the
Product is a new Denominator; then multiply the
Denominator of the first Fraction, into the Numera-
tors of the ſecond and third, and the Product is a new
Numerator; and this new Fraction, is the Anfwer
fought, as in the foregoing Example, appears by the
following Operation.
31
148
335
448
If 14 2 Yards of Velvet coft 117. how much
will 29 Yards coft at that Rate ?
59
1392423334
5
After reducing the three mixed Numbers into im-
proper Fractions, multiply 59, the Numerator of the
firft Fraction, into 5 and 2, the Denominators of the
fecond and third Fractions, and the Product is 590 for
a new Denominator: Then multiply 4, the Denomi-
nator of the first Fraction, into 59 and 59, the Nu-
merators of the fecond and third Fractions, and the
Product is 13924 for a new Numerator = 23
23 354.
If
HEWITT's ARITHMETIC.
43
If 7 Flemish Ells make 5 Ells at London, how
many Ells at London will 56 Flemish Ells make?
7
21
1178=42.
CHA P. XIII.
The RULE OF THREE indirect in Vul-
gar Fractions.
I
N Order to difcover whether a Queſtion belongs
to the Rule of Three DIRECT, or INDIRECT,
obferve,
If the third Number be greater than the first, and
if the Anſwer requir'd be greater than the fecond, it
is in the Rule of Three DIRECT.
And if the third Number be less than the firſt,
and the Anſwer requir'd be less than the ſecond, it
belongs to the ſame Rule.
But if the third Number be less than the first, and
the Anſwer requir'd be greater than the fecond, it be-
longs to the INDIRECT Rule.
And if the third Number be greater than the first,
and the Anſwer requir'd be less than the fecond, it
belongs to the fame Rule.
1
If 5 Yards of Cloth
Cloaths, how many Yards
do the fame ?-
As Z
4
3
wide make a Suit of
of 3 of a Yard wide will
14011 Yds..
When
44
HEWITT'S ARITHMETIC.
When you find the Queſtion propoſed belongs to
the indiret Rule, ftate it fo, as that the first and
third Numbers are of the fame Denomination; then
obferve this general Rule,
Multiply the Numerator of your third Number by
the Denominators of the fecond and firft, and place
that down for a new Denominator: Then multiply
the Denominator of the third Number into the Nu-
merators of the fecond and first Numbers, and place
that for a Numerator over the new Denominator :
And this NEW FRACTION is the fourth Proportio-
nal, or Anſwer to the Queftion.- As in the forego-
ing, 14 which is an improper Fraction, but reduc'd,
is equal to 11, and fo many Yards of any Thing
3 of a Yard wide will as readily make a Suit of
Cloaths, as 5 Yards of any Thing 1 of a Yard
wide.
4
2
If 18 Men can reap 29 Acres of Corn in 143
Days, in how many Days will 9 Men do the fame ?
As 18
5
36
106229 Days.
CHA P. XIV.
Of DECIMAL FRACTIONS.
T
HE Word Decimal comes from DECEM, Ten,
becauſe an Integer is fuppofed to be divided
into 10 Parts, and every Tenth, into 10 Hundredth
Parts, and every Hundredth, into 10 Thoufandth
Parts, and fo on, ad infinitum.
An
HEWITT's ARITHMETIC.
45
An Integer
A Prime
A Second
A Third
10 Primes.
10 Seconds.
10 Thirds.
10 Fourths, &c.
Any Thing whatever may be divided into 10, 100,
1000, &c. equal Parts; and the greater Number of
Parts that the Unit is divided into, the nearer the
Decimal is to the true Value.
A Decimal Fraction is known from a whole Num-
ber by a Comma, thus, 0,5-tho' fometimes by a
Point, thus, 0.5; and fometimes, thus, oL5; but let
their Number be what it will, take their Denomina-
tion from the Place of their laft Figure on the Right
Hand.
0,5
Thus, 0,50
0,500
0,5
Thus, 200,005
55 Tenths.
}are {3
are
50
• Hundredths.
500 Thouſandths.
And,
{
5 Tenths.
5 Hundredths.
5 Thousandths.
The Denominator of a Decimal Fra&ion is never
exprefs'd, as in Vulgar Fractions, but is known to be
an Unit with a Cypher, or Number of Cyphers,
which the Numerator always diſcovers.
CYPHERS on the Right-Hand of a Decimal Frac
tion never alter the Value; for .5 .50 .500 .5000
are all of the fame Value, and are equal to or 1.
CYPHERS on the Left-Hand of a Decimal Frac-
tion decreaſe the Number in a Ten-fold Proportion;
thus, a Cypher prefix'd before .18, makes it in Va-
lue
which before was but 8.
TOCO
018
I
To
46 HEWITT'S ARITHMETIC.
To reduce a DECIMAL FRACTION to a VULGAR.
RULE..
Place the Denominator underneath the Numerator,
and then reduce it to its loweft Terms.
EXAMPLE.
Reduce .75 to a Vulgar Fraction, thus, 5)751-3.
3
So that .75 = 4:
To reduce a VULGAR FRACTION to a DECIMAL.
RULE.
Place on the Right-Hand of the Numerator of the
given Fraction, as many Cyphers, as you pleaſe, and
divide it by the Denominator, and the Quotient is the
Numerator to the Decimal Fraction.
EXAMPLE.
Reduce to a Decimal Fraction,— thus,
5)4,0(0,8 So that 4 = 0,8;
But it often happens, that a Fraction occurs, which
can't be eaſily expreffed in decimal Parts, without a
very troubleſome Operation, yet the Work may be
carried on 'till what remains is fo trifling, as that the
decimal Fraction may be expreffed near enough.
As
HEWITT's ARITHMETIC.
47
As is
Operation.
=
0,8888, as appears by the following
9)8,0000(0,8888.+
80
80
80
·8
To turn Money into Decimals.
What decimal Parts of a Pound Sterl. ase equal to
15 Shillings?
RULE.
Firſt, Turn it into a Vulgar Fraction, by placing
under the Number given, the known Parts of the In-
teger, as a Denominator; then proceed as before
taught, in reducing a VULGAR FRACTION to a
DECIMAL.
Thus, 15 Shil. turn'd into a Vulgar Fraction, are
15 of 1 7.
20)15,00(,75 Anſwer.
What decimal Parts of a Pound Sterl. are 15 s.
9 d. 2?
Reduce them to vulgar Fractions, by placing the
known Parts of their Integers, for a Denominator un-
der each, and they will ſtand thus, 18 40 80.
3
20
48 HEWITT's ARITHMETIC.
20) 15,00(,75
· 240)3,0000(,0375
1800
1200
.00
960)3,0000(,003 1
1200
240
>75
,0375
,0031
,7906
OR THUS,
S. d.
15: 9:30
I 2
鳌
​189
4
759
960)759,0000(,7906
8700
.6000
240
To
HEWITT's ARITHMETIC.
49
To value any Number of Decimals.
RULE.
Multiply the Decimal given by the known Pares
of the next inferior Denomination, feparating in the
Product by a Comma, as many Figures on the Right-
Hand, as your Decimal confifts of; then multiply
that Product (the Decimals only) by the known Parts
of the next inferior Denomination, ftill obferving the
fame Rule, 'till you have brought it into the leaſt known
Parts of the Integer, and the Figures ftanding on the
Left-Hand of the Comma, are the known Parts of
the Integer, or Integers, in Money, Weight, Measure,
Time, &c.
EXAMPLE.
What is the Value of ,7906, or the Shillings,
Pence, and Farthings, that are equal to ,7906 Parts
of a Pound Sterl. ?
,7906 Parts of a Pound
Multiplied by 20 Shillings in a Pound
Produce Shillings 15,8120 and Parts of a Shilling
Which multip. by 12 Pence in a Shilling
produce Pence 9,7440 and Parts of a Penny
which multipl. by 4 Farthings in a Penny
produce Farthings 2,9760 and Parts of a Farthing.
So that the Value of ,7906 decimal Parts of a
Pound Sterl. is 15 s. 9a.
F
To
50
HEWITT's ARITHMETIC.
To value the Decimal Parts of a Pound Sterl. by
INSPECTION.
Double the firft Figure on your Left-Hand in the
Decimal, and that is fo many Shillings, and if the
econd Figure is, or exceeds 5, then add one more to
the Number of Shillings; the fecond Figure (if un-
der 5) or its Excefs (if above 5) join'd with the
third, make fo many Farthings; only deduct 1 if
they amount to 25, or 2 if near 50.
And the Reafon of this Deduction is, that as 1000
is the Denominator of every Decimal, whofe Nume-
rator confifts of 3 Places, fo confequently by valuing
the Figure ftanding in the third Place as fo many
Farthings, we allow 1000 Farthings to the Pcund,
whereas there are no more than 960.- The Overplus
therefore being 40 in 1000, makes 4 in 100, or i
in 25.
As in the laft EXAMPLE.
What is the Value of,7906 Parts of a Pound Ster.?
Double 7,
and it is 14, the fecond Figure being a-
bove 5, add 1 to the 14, and it makes 15 Shillings;
then 9 the fecond Figure, exceeding 5 by 4, join it to
the third Figure, which is a Cypher, and confequent-
ly makes it 40; but 40 being nearer 50, than it is
to 25, deduct 2, and there remains 38, which is fo
many Farthings, being 9 d.
So that ,7906 Parts of a Pound Sterl. by Infpec-
tion, in Value, is, 15 s. 9 d. answerable to the
common Operation, in the fame Example before.
CHA P.
HEWITT's ARITHMETIC.
51
CHA P. XV.
Addition of Decimals.
ET down your propofed Numbers, Units under
S Units, Yens under lens, and Parts under Parts
of like Value, add them as if they were whole Num-
bers obferving to feparate fo many decimal Parts
in the Total, as were in any of the given Numbers.
EXAMPLE 1.
Add 0,7; 0,38; 0,847; 0,029; 0,007 together.
Place them thus,
0,7
0,38
0,847
0,029
0,007
1,963
EXAMPLE 2.
Add 0,0756; 0,3299; 0,0415; 0,1983; 0,2547*
together.
0,0756
0,3299
0,0415
0,1983
0,2547
0,9
F 2
In
52
HEWITT's ARITHMETIC.
In this laſt Example, you may, if you pleaſe, put
down all the Cyphers in the Aggregate, on the Right
Hand of the 9, thus, 0,9000, which however is on-
ly of the fame Value with 0,9; becauſe, as has been
before obferved, Cyphers on the Right-Hand of any
Figure in a decimal Fraction, can neither decreaſe,
or encreaſe it.
EXAMPLE 3.
Add 2,47586; 41,3524; 372,161; 22,18; 9,73
together.
Thus,
2,47586
41,3524
372,161
22,18
9,7
447,86926
Or, thus,
2,47586
41,35240
372,16100
22,18000
9,70000
447,86926
CHAP.
HEWITT's ARITHMETIC. 53
CHAP. XVI.
Subtraction of Decimals.
AVING placed the Numbers, as directed in
H Addition, work as if they were all whole Num-
bers, obferving ftill to cut off from the Difference, or
Remainder, for DECIMAL PARTS, all the Figures
on the Right-Hand of the Place of UNITS.
EXAMPLE 1.
From 34,5
Take 21,9
Remains 12,6.
EXAMPLE 2.
From
127,579624
Take 92,894711
Remains 34,684913
EXAMPLE 3:
From 7654
Take ,3742
Remains,3912
CHAP.
F 3
54
HEWITT's ARITHMETIC.
P
CHA P. XVII.
Multiplication of Decimals.
LACE them one under another as in whole
Numbers, ſtill obferving to cut off on the Right
Hand in the Product as many decimal Parts as were
in both Multiplicand and Multiplier together.
Multiply 24,76
by 5,34
9904
7428
14380
152,2184
Multiply 5943
by ,3164
23772
35658
5943
17829
,18803652
T
CHAP. XVIII.
Divifion of Decimals.
HE Operation of Divifion in DECIMALS, is
the ſame with that of whole Numbers; the
only Difficulty is, to know the true Value of the
Quotient,
HEWITT's ARITHMETIC.
55
Quotient, which may eafily be removed by obferving
this general
RULE.
There must always be as many Places of DECI-
MAL PARTS in the Divifor and Quotient together, as
there 'are in the Dividend alone.
There are 4 PARTICULAR CASES, which may
happen in Divifion of Decimals.
CASE 1.
When the Places of decimal Parts in the Dividend,
do, in Number, exceed thoſe in the Divifor, thoſe
that are wanting to compleat the general Rule, muſt
be cut off in the Quotient.
EXAMPLE 1.
Divide 589,467 by 48,6; thus,
48,6)589,518(12,13
1035
•631
1458
CASE
56 HEWITT's ARITHMETIC.
CASE 2.
When it happens that the Number of Places of
decimal Parts in the Dividend, is equal to the Num-
ber of thefe in the Divifor, the Quotient will be. IN-
TEGERS.
EXAMPLE
Divide 583,68 by 2,56; thus,
2,56)583,68(228
· 716
2048
2.
O
CASE 3.
When it happens that the Number of Places of
decimal Parts in the Dividend, is lefs than the Num-
ber of thoſe in the Divifor; Cyphers must be placed
on the Right-Hand of the Dividend, 'till the Num-
ber of decimal Places in it, is either equal to, or
greater than that in the Divifor; and then the Qua-
tient, muſt be either all Integers (as in CASE 2.) or
muſt contain a determinate Number of decimal Parts,
(as in CASE 1.)
EX
HEWITT's ARITHMETIC. 57
EXAMPLE 3.
Divide 2,695 by 6,125; thus,
6,125)269,500(44
24500
CASE 4.
When it happens that the Quotient does not con-
tain fo many Figures as the general Rule requires to
be affigned, or cut off for decimal Parts therein;
ſupply that Defect with Cyphers, placed on the Left-
Hand of the Figures in the Quotient, which then will
be the true Product required,
EXAMPLE 4.
Divide 3,25717 by 58,9; thus,
58,9)3,25717(,0553 the true Quotient
3121
•1767
CHAP.
58
HEWITT's ARITHMETIC.
CHAP. XIX.
Of PROPORTION,
OR
The RULE of THREE.
Commonly call'd the GOLDEN RULE; and
very deſervedly fo, from its extenfive Use, and Su-
periority over all other Rules.
T
HIS Rule is either DIRECT, or INDIRECT;
and theſe again are either SIMPLE, or COM-
POUNDED.
It is called the Simple Rule of Three Direct, when
there are three Numbers given, to find a fourth, that
fhall bear the fame Proportion to the third, as the
Second does to the firft.
It is call'd the Simple Rule of Three, INDIRECT,
when the Numbers are in reciprocal Proportion, that
there are three Numbers given to find a
But, that fhall bear the fame Proportion to the fe
as the third does to the firft.
fating all Queftions in the Rule of Three, the
bird Numbers must be of the fame Deno-
if the first be Days, the third muſt be
and be fure always to reduce your fecond
Number Into its loweſt Name mention'd— thus, if
your fecond Number be Pounds, Shillings, Pence, and
Farthings, you. muft reduce it to Farthings.
Moft of our Writers on this Subject, have, in their
oks, fet down the Rule of Three DIRECT, and
MPIRECT, as two diftinct Rules: But I fhall treat
of
HEWITT's ARITHMETIC,
59
of both promifcuoufly, and lay down one general
Pale, which will enable the Learner to difcover at
once, whether the Queftion propefed be DIRECT,
or INDIRECT.
I app ehend, this Method will fix a ftronger Im-
preffion on the Memory and Judgment of the Practi-
tioner, than that hitherto rade ufe of.
Becauſe, by making them two diftin&t Rules, you
have only Queſtions propofed, peculiar to each Rule,
and without employing your Judgment to know whe-
ther the Queftion be direct or indirect, you follow the
Method of Operation laid down to each particular
Rule, which often puzzles the Learner, when he
leaves either his Mafler, or Book- But as the Quef-
tions I fhall propoſe, both direct, and indirect, will
be promifcuous, the Judgment will be employed to
know which Rule they belong to, and what Method
of Operation must be taken.
RULE.
When a Queſtion is ſtated, if your third Term
(being more than the firft Term) requires MoR E, er
being lefs, requires LESS, 'tis DIRECT; But if
third Term, being more, requires LESS, or being lefs,
requires MORE, 'tis INDIRECT.
your
However, if MORE is required, multiply the mid-
dle Term by the greater of the two Extremes, aud
divide by the leffer: But, if LESS is requir'd, multi-
ply the middle Term by the leffer of the two Ex
tremes, and divide by the greater, and the differe
Quotients will be the Anſwers.
EXAMPLES.
If 9 lb. Tea coft 11. what will 18 ib. coft ?
I I
9)198
22/. Anfwer.
Τ
60
HEWITT's ARITHMETIC.
If 18 lb. Tea
221.
9 lb.
9
If 22 lb.
18)198
117. Anfw.
181.
I I
22)198(9 7.
o
11 16.
If 11 7.
117.
916.
22 1.
9
11) 198
18 Anſw.
If 14 Men finiſh a Piece of Work in 26 Days,
how long will 7 Men do the fame ?
Men.
Days.
Men.
If 14
26
7
14
104
26
7)364
52 Days, for Anſwer.
If
HEWITT's ARITHMETIC.
61
If I fpend 87. 17 s. in 4 Weeks, how much will
that amount to, at that Rate, in 52 Weeks?
Weeks.
If 4
7.
S.
8:17
20
177
52
354
885
Weeks.
52
49204
2301
Now, becauſe this Anſwer 2301 are Shillings, they
muſt be reduced to Pounds.
2 | 0)230 | г
115 l. : Is. Anſwer.
If I ſpend 428 l. 175. 6 d. per Year, what does
that amount to, one Day with another?
Days.
If 365
1. 5. d.
428: 17: 6
Day.
I
20
8577
12
( 12
365)102930 (282
2993 2|0)2|3—6
730
1. 35. Od. Anſwer.
G
Two
62
HEWITT's ARITHMETIC.
Two Ships fet Sail at one Time from the fame
Port, one fails 44 Leagues per Day North, and the
other 57 Leagues per Day South; the Queftion is in
how many Days will they be 1384 Leagues afunder?
44+57=101.
Leag.
If 101
Day
I
Leag.
1384
7 I
101)1384(13 TŰ Days. A wer.
374
71
A Garrison, confifting of 4672 Men, being be-
fieged, have Provifions only for 17 Days, but it be-
ing neceffary they ſhould hold out 5 Weeks, how
many Men muſt be fent out, to answer the End?
Days.
Men.
If 17
4672
Days.
35
17
32704
4672
35)79424(2269
94
242
324
From 4672
Subtr: 2269
9
Anſwer 2403 Men.
Now
HEWITT's ARITHMETIC.
63
Now it is very plain, that if the Provifions will
fupport 4672 Men 17 Days, confequently, by -he
Operation above, the fame Provifions will ferve 2269
Men 35 Days; fo that 2269 fubtracted from 4672
leaves the Number 2403 Men to be feat out of the
Garrison.
Sold 3 Bags of Pepper, containing 19 C. 32, 27th.
viz. Tare each 36 lb. per Bag, and Tret 4 lb. per
104, at 161d. per lb. Neat, how much does it come
to Neat?
Ct. 9.
lb.
3-22
1
Number 2 -5—1—14
3—7—2—19
3 Bags containing 19-3-27
× 36 Allowance
*108 Tare
4)104
26
4
70 Quarters
28
659
158
2239 lb. Groſs in all the Bags.
108 Tare.
26)2131 6. Subtle. 81 Trett.
lb. Subtle
2131
· 51
Tret
81
25
b. Nett.
2059
If
64 HEWITT'S ARITHMETIC.
16.
5.
d.
1.
If 1
1 : 4 : //
2050
12
33.
16
6150
2
6150
2)67650
12)33825
33
2:0)28118-9
Anſwer 140-18-9
A Merchant finding himſelf indebted to ſeveral
Creditors 4617 7. and not being able to pay the whole,
propofes to pay 13 s. per Pound, how much pays the
Compofition?
1.
1.
1.
As I
13
4617
20
20
20
92340
13
277020
92340
2|0)1 200420
210)6002|1 I
Anfwer 3001, 1 s.
If a Penny white Loaf ought to weigh 11 Ounces
Troy, when Wheat is at 4 s. per Buſhel, what ought
it to weigh, when Wheat is 6s. 9 d. per Buſhel?
Anſwer 614 Ounces.
27
CHAP.
HEWITT's ARITHMETIC.
65
CHA P. XX.
The DOUBLE RULE of THREE.
TE
HIS is the COMPOUND Golden Rule, and
confifts of Two, or MORE Analogies, either
direct, or reciprocal; Five Numbers being propofed,
to find a SIXTH.
When a Queſtion is compounded of two or more
Analogies DIRECT, obferve this general
RULE.
Multiply the first Terms of both fimple Analogies
together, and make that Product the first Term of
the COMPOUND one; likewife multiply the third
Terms of both fimple Analogies together, and make
that Product the third Term of the COMPOUND one;
and make the remaining Term HOMOLOGOUS to that
fought, the Second.
EXAMPLE.
If 16 Horſes in 12 Days eat 80 Bushels of Corn,
how many Bushels will 24 Horfes eat in 48 Days?
Let your first compound Term be 192
16 x 12,
which is the Product of the firft Horfes multiplied
into the first Days: Let your third compound Term
be 11
1152 24 x 48, which is the Product of the fe-
cond Horſes multiplied into the fecond Days: Then
let your fecond Term be 80, being the Term homolo-
gous to that fought.
G 3
THUS,
66 HEWITT's ARITHMETIC.
THUS,
fes.
16.
Bufhels.
Horſes.
80
24
Day 12
1152
Days 48
192
192)92160(480 Buſhels.
192
96
1536
00
1152
If 36 Bufhels of any Seed yield 684 Bufhels in 2
Years, how much will 144 Bufhels yield in 8 Years,
fuppofing every Year's Crop to meet with the fame
Succefs.
Bufhels.
36-
Bufhels.
Bufhels.
684
144
8 Years.
2
72
1152
684
4608
9216
6912
72)787968(10944 Bufhels.
• 679
316
• 288
The
HEWITT'S ARITHMETIC. 67
The fame Method muſt be uſed, as in the forego-
ing Examples, in cafe the propofed ANALOGY be
yet more compounded.
EXAMPLE.
Suppoſe the Weight of a Stone be 1539 Pounds,
whofe Length is 5 Feet, Breadth 2 Feet, and Thick-
;
nefs 2 Feet: What will the Weight of another Stone
be, whofe Length is 11 Feet, Breadth 3 Feet, and
Thickness 3 Feet?
THUS,
Feet.
lib.
Feet.
Length 5
- L539
11 Length
Breadth 2 X
99
Thickneſs 2 X
X 3 Breadth
X 3 Thickneſs
13851
20
13851
99
2|0)15236 | 1
lib. 7618
I
Anſwer.
20
It fometimes happens that one of the compofing Ana-
logies is DIRECT, and the other RECIPROCAL; in
which Caſe obſerve the following
RULE.
Multiply the third Number in your ftating by that.
Number you would otherwife have placed under your
firft, and multiply your firft Number, by that, you
would have placed under your third.
EXAM-
68 HEWITT's ARITHMETIC.
EXAMPLE.
If 16 Men, in 23 Days, can mow 224 Acres of
Grafs, how many Men will mow 4000 Acres, at that
Rate, in 20 Days?
Inftead of placing them thus,
Acres.
224
Days 28
Days
Acres.
224
Men.
16
Place them thus,
Men.
20
16
4480
{
Acres.
4000
20 Days
Acres.
4000
28
Days
II 2000
16
672000
112
448|0)179200|0(400 Men
000
Doctor HARRIS, in his Lexicon Technicum, lays
down an infallible Rule for the Solution (by one Ope-
ration) of any Queſtion in the Double Rule of Propor-
tion, without any Regard to its being DIRECT, or
INDIRECT; which is as follows,
The
HEWITT's ARITHMETIC.
69.
The given Terms in the DOUBLE Rule of Pro-
portion being five, there are three of them always
conditional, or fuppofitious, and antecedent; the re-
maining two demand the Queftion, and are Confe-
quents.
The Antecedents must be firft ftated- let the Ante-
cedent, which is the principal Cauſe of Lofs or Gain,
Encreaſe or Decrease, Action or Paffion, be put in the
FIRST PLACE; and that, which betokeneth the Space
of Time, Diſtance of Place, &c. be put in the SE-
COND PLACE; and the remaining Part in the THIRD.
The Antecedents thus ftated, the other two Confequents,
wherein the Demand lies, muſt be placed under the
Antecedents of the fame Denomination.
RULE.
Then, if the Blank, or Term fought, fall under the
third Term, multiply the three laft Terms together,
for a Dividend, and the two firft for a Divifor; and
the Quotient gives the fixth Term required..
RULE 2.
But, if the Blank fall under the first or second Term,
multiply the first, fecond, and fifth Terms for a Di-
vidend, and the third and fourth for a Divifor; the
Quotient gives the Anſwer.
EXAMPLE I.
If 24 Cannon require 168 Barrels of Powder in 1
Day, how many Barrels will 72 Cannon require in
36 Days?
Here, the three conditional or fuppofitious Terms,
and Antecedents, are, 24, 168, 1.- And the Antece-
dent, which is the principal Caufe of Action, is, 24
Cannon; the Space of Time, 1 Day; and the re
maining
70
HEWITT's ARITHMETIC.
maining Antecedent, 168 Barrels of Powder-the
other two Terms, which are Confequents, 72 Cannon,
and 36 Days, each of which being placed under the
fame Denomination, they will ſtand thus,
Cannon.
Day.
[
Barrels.
24
168
Can. 72
36 Days
36
1008
504
6048
72
12096
42336-
24)435456(18144 Barrels
195
34
105
•96
Q
CHA P.
HEWITT'S ARITHMETIC.
The RULES of PRACTICE.
CHAP. XXI.
PRACTICE, is a
Р
RACTICE, is a Compendium, or Contrac
tion, of the common Rule of Proportion, when
the firit Term is 1; and fo call'd (I believe) from
its general Ufe, in the Practice and Exercife of Trade.
The even Parts of a Shilling.
6
2
is
miez mefing meft
F====
8
I
The even Parts of a Pound.
10
6:8
5
4
3:
2:6
2
1 : 8
I
is
CASE I.
ས
When the Price of the Integer is a Farthing, di-
vide the given Number by 4, and what remains will
be Farthings, and the Quotient will be Pence.
E X-
72
HEWITT'S ARITHMETIC.
EXAMPLE 1.
What are 44 Yards, at 1 Farthing per Yard, worth?
Farthing is of 1 d.
I 4 144
11 d. Anſwer.
2.
EXAMPLE
What are 88 Yards worth, at d. 1 per Yard?
2
is of 1 d.
플 ​188
44 d. or 3 s. 8 d.
EXAMPLE 3.
3
What comes 147 lib. to, at d. 2 per lib.?
14 147
mp
73-3
95.: 24 d.
•
Here obſerve, the Price being 4 d. I took Half of
the given Number, which, you fee, are 73 Three
Haif-pences, and I three Farthings remain; then
1 d. being of a Shilling, I divide the 73 by 8,
and the Anfwer is 9 s. and I remains, which is one
1 d. added to the 2 d. makes 2 1 d.
½
CASE II..
I
When the Price of the Integer is an even Part of
a Shilling, divide the given Number by that Part,
and the Anſwer is Shillings.
E X-
HEWITT's ARITHMETIC.
73
EXAMPLE 1.
At 2 d. per lib. what comes 438 lib. to ?
2 d. is of a s. 1438
73 s. = 3 %. 13 s.
EXAMPLE 2.
At 3 d. per Yard, what comes 218 Yards to?
3 d. is of a s.
4
| 218
54:6=27. 14s. 6 d.
3.
EXAMPLE
At 4 d. per Ounce, what comes 99 Ounces to ?
4 d. is of a s. 199
33 s. = 1 l. 13 s.
EXAMPLE 4.
5 d. per lib. what comes 120 lib. to?
At
3 d. is of as.
1120
2 d. is ½ of a s.
30
20
50 s. = 2 l. 10 s
H
E X-
74 HEWITT'S ARITHMETIC.
EXAMPLE 5.
6 d. is of a 5.
|240
120 s. = 61.
CASE III.
When the Price of the Integer is not an even Part
of a Shilling, divide the given Number by the feve-
ral Parts thereof.
EXAMPLE 1.
At 7 d. per lib. what comes 89 lib. to?
Take and of
89
29: 8 d.
22: 3 d.
51 : 11 d.=2/. 11s. iid.
EXAMPLE
2.
At 8 d. per Yard, what comes 319 Yards to?
Take and of 1319
106: 4 d.
106: 4 d.
212: 8 d. 10l. 1zs. 8d.
E X-
HEWITT's ARITHMETIC.
75
EXAMPLE 3.
At 9 d. per Ounce, what comes 517 Ounces to?
Take for 6 d.
14
1517
for 3 d.
258 6 d.
129: 3 d.
3879 d. 197. 75. 94.
EXAMPLE 4.
At 10 d. per Yard, what comes 76 Yards to?
6 d. is ½ of
176
4 d. is of
38
25:42.
634 d. 31. 3 s. 4 d.
EXAMPLE 5.
At 11 d. per Barrel, what coft 314 Barrels ?
1/
6 d. is 314
4 d. is
121 152
i d. is
104: 8 d.
26: 2 d.
287 10 d. 147. 75. 10d.
H 2
:
E X.
76
HEWITT'S ARITHMETIC.
CASE IV.
When the Price of the Integer is Pence and Far-
things under a Shilling, work for the Pence (as in
CASE II. and III.) and then work for the Farthings
(as in CASE I.)
EXAMPLE.
At 5 per Yard, what coft 24 Yards ?
4 d. is
is
124
1 d. is
8.
8 3
115.
CASE V.
When the Price of the Integer is an even Number
of Shillings, multiply the given Number by half the
Price of the Unit, or Integer valuing the firſt Fi-
gure on the Right-Hand in the Product, double, for
Shillings, and the Remainder is Pounds.
EXAMPLE 1.
At 25. per Yard, what coſt 517 Yards?
Now here obſerve, the Price is 2 s. the half is 1;
but as neither multiplies, or divides, the Number
given is the Product, making the laft Figure 7 dou-
ble for Shillings; fo that the Anfwer is 517. 14 s.
E X-
HEWITT's ARITHMETIC.
77
EXAMPLE. 2.
At 4s. per Ct. what come 416 Ct. to.
2
1.83,4s.
EXAMPLE 3.
At 16 s. per Hogfhead, what coft 816 Hogfheads?
8
1. 652,165.
CASE VI.
When the Price of the Unit´is any odd Number
of Shillings, proceed as in CASE V. and add of
given Number to your Product.
EXAMPLE 1
At 17 s. per Yard, what coft 486 Yards ?
8
20
388,16
24, 6
1. 413, 25.
CASE VII.
When the Price of an Unit is Shillings and Pence,
work for the Shillings, and then for the Pence- un-
leſs the Price happens to be an even Part of a Pound.
H 3
E X.
78
HEWITT's ARITHMETIC.
EXAMPLE 1.
At 9s. 4 d. per Gallon, what coft 220 Gallons?
4
88,0
I
20
I s. is of 220
11
4 d. is
of 11 Z.
3: 13:4
Anfwer /. 102: 13:4
EXAMPLE 2.
At 2s. 6d. per Ounce, what coft 144 Ounces ?
2 s. 6 d. is of a 7. 187. Anſwer.
EXAMPLE 3.
At 3 s. 4 d. per Yard, what coaft 828 Yards?
3. 4 d. is of a 7. 1387. Anfwer.
EXAMPLE 4.
At 5 s. per Ell, what coft 317 Ells?
55. is of a 7. 791. 5s. Anſwer.
4 1.
EXAMPLE 5.
At 65. 82 per Ct. what cok 324 Ct. ?
6s. 8 d. is of a 7. 108 7. Anfwer.
†
E X-
HEWITT's ARITHMETIC.
79
EXAMPLE 6.
At 135. 4 d. per Barrel, what coft 182 Barrels?
6 s. 8 d. is
of a 1.
60:13:4
6 s. 8 d. is
½ of a 1.
60:13:4
13:4
7. 121: 6:8
PRACTICE by DIVISION.
1.
s. d.
42 Pieces of Holland cost 219 14 6½ what coft
If
1 Piece?
6×7=42
7)219 14 61
6)31: 7:9
15: 47 Anfwer.
1. s.
If 144 Anchors of Brandy coft 296 5 what cofts
1 Anchor ?
12 X 12 = 144
12)296: 5
12)24 139
1.2: 1:12 Anſwer.
PRAC
80 HEWITT's ARITHMETIC.
PRACTICE by MULTIPLICATION
Abbreviated.
1. s. d.
At 1
17
to ?
6 per Piece, what comes 45 Pieces
1:17:6
9
16: 17
: 17: 6
5
1. 84: 7:6 Anſwer.
S.
At 5
d.
9×5=45.
: 4 per Ounce, what comes 72 Ounces to?
5:4
8
2:28
9
19:40 Anſwer.
1.
S. d.
8×9 = 72.
At 2: 13: 11 per lib. what comes 54 lib. to ?
2 13 II
9
24 5 3
6
7. 145: 11:
11: 6 Anſwer.
9×6=54.
Gold
HEWITT's ARITHMETIC.
8
1.
Gold at 4:
Ounces to ?
S. d.
2: 7 per Ounce, what comes 12Q
4:27
12
49: 11:0
10
12 X 10 = 120.
495: 10 : 0 Anſwer.
A Short Method to know what 100 comes to at any
Number of Pence, or Pence and Farthings the Unit.
RULE.
Multiply the Price of the Unit by 5, and that Pro-
duct divide by 12, the Quotient is the Anſwer
if the Price of the Unit, is Pence and Farthings, mul-
tiply the Farthings by 5, and the Product is Shillings,
carrying for 1 Farthing, 2 for d. and 3 for 2 d.
to the next Product of 5 multiplied by the Pence.
1
EXAMPLE 1.
At 19 d. per lib. what comes 100 to?
5
12)96: 5
1. 8:05 Anſw.
Here 19 d. is the Price of the Unit - I fay 5
Times is 5, which is fet down as fo many Shil-
lings, and I carry to the next, faying 5 Times 9 is
45
82
HEWITT's ARITHMETIC.
45 and 1 is 46, fet down 6, and carry 4, 5 Times 1
is 5, and
4 carried, make 9, which muſt be valued
as 967. 5 s. and is the Dividend to the Divifor 1 2.
EXAMPLE 2.
At 17 d. per Yard, what coft 100 Yards?
5
12)87: 10
1.7 5 10 Anſw.
EXAMPLE 3.
At 14: 4 d. per Ounce, what coft 100 Ounces ↑
12) 73
5
12)73: 15
6:
2:11 Anfw.
A ſhort Method to know what 100 amounts to, the
PRICE of the UNIT, at any Number of Shillings.
RULE.
Add a Cypher to the Price of the Unit, and halve
it, and that Product is the Anſwer.
EXAMPLE 1.
At 7 s. per Yard, what coft 100 Yards?
75
1. 30 Anſwer.
E X-
HEWITT'S ARITHMETIC.
83
EXAMPLE 2.
At 19s. per lib. what coft 100 lib.?
190
1.95 Anſwer.
Several fhort Ways to know the Amount of GOODS,
bought or fold, at particular Prices.
CASE I.
Goods fold by the Ct. or 112 lb.
RULE.
Multiply 2 s. 4 d. by the Number of Farthings in
the Price of the Pound, and the Product is the An-
fwer required.— or, multiply the Price of one Pound
by 7, and divide that Product by 15, and the Quo-
tient is the Anſwer.
EXAMPLE 1.
3
What comes 112 lb. to, at 2 d. 2 per lb.?
2/
2 d.
3
4
to 11 Farthings.
= 25 s. 8 d.
I
or, or 17. 5 s. 8 d.
2 s. 4 d. x II
the Price required.
EXAMPLE 2.
What comes 1 Ct. to, at 4 d. ½ per lb. ?
4 d. 18 Farthings.
1/1/2
25. 4 d. x by 9
21 S.
and 21 s. x by 2
42 s. or 2 l. 2 s.
E X-
84
HEWITT's ARITHMETIC.
EXAMPLE. 3.
What comes 1 Ct. to, at 8 d. per lb.?
8 × 7=56.
561537. 14 s. 8 d.
Note well, When your Multiplier exceeds 12, divide
it into Parts, as in the fecond Example, 2 s. 4 d.
multiplied by 9, and that Product multiplied by 2, is
equal to 2 s. 4 d. multiplied by 18 at once; becauſe
twice 9 is equal to 18.
CASE II.
The Price of the Ct. or 112 lb. being given, to
know the Price of 1 lb.
RULE.
Multiply the Price of the Ct. by 15, and divide
the Product by 7.
EXAMPLE 1.
At 21. 6 s. 8 d. per Ct. what comes 1 lb. to?
1.
S.
d.
2:
6:8
X
× 5
11: 13:4
x3
7)35 :
5 d.
0:0
E X-
HEWITT's ARITHMETIC.
&
EXAMPLE 2.
At 1 l. 5 s. 8 d. per Ct. what is the Price of 1 H. ?
1. S. d.
I : 5 : 8
× 5
6:8:4
x 3
7)19: 5:0
2 d. 3
CASE III.
Having the Amouut of 100, to find the Price of 1.
RULE.
Multiply the Price of 100 by 12, and divide by 5.
EXAMPLE.
If 100 Fish coft 67. 13 s. 4 d. what coſt 1 Fiſh.
1.
S. d.
6:13:4
X 12
5 )80 :
0:0
16 d. Anſwer.
CASE IV.
The Price of being given, to know the Amount
of 120.
I
RULE
86 HEWITT's ARITHMETIC.
RULE.
Divide the Price of 1 by 2, and the Quotient is
the Anſwer. If remains, it is 10s. if 3 remains,
I
it is 7 s. 6d for 5 s. and for 4 2s. 6d.
EXAMPLE 1.
What comes 120 to, at 4 d. each ?
3 3/
4227 Anſwer.
EXAMPLE 2.
120 at 3 d. 2 each.
2 = 1 l. 17 s. 6 d. for Anſwer.
EXAMPLE
120 at 5 d. each.
3.
5 1 ÷ 2 = 27. 15 s. Anſwer.
EXAMPLE 4
120 at 6 d each.
6 ÷ ÷ 2 = 37. 25. 6 d. Anſwer.
CASE V.
To find the Amount of 200.
RULE.
Place a Cypher on the Right-Hand of the given
Price of 1, and that is the Amount of the Whole in
Pounds.
EXAM-
HEWITT'S ARITHMETIC.
87
EXAMPLE.
What is the Amount of 200 Pair of Stockings at
6 s. per Pair?
60%. Anſwer.
What comes 200 to, at 4 s. 6 d. ?
45. Anfwer.
Note, for 6 d. in the Price of 1, add 5 inſtead of
a Cypher, as in the laft Example, as the Price of 1
was 4 s. 6 d. inſtead of annexing a Cypher to the 4,
I annex 5,-and fo for 3 d. annex 2 7. and 10 s. for
1 d. annex 1 7. and 5 s. for 3 d. annex a Cypher to
the given Price, and 12s. 6d.
CASE VI.
To find the Amount of 300.
RULE.
Annex a Cypher to the Price of 1, then take half,
and add both gether for Anſwer.
EXAMPLE.
300 Chaldron of Coals at 24 5.
240
120
1. 360 Anſwer.
CASE VII.
To find the Amount of 400.
I 2
RULE
$8 HEWITT's ARITHMETIC.
RULE.
Annex a Cypher to the Price of 1, and multiply
that by 2 for Anſwer.
EXAMPLE.
400 Sheep at 11 s. each,
110
2
1. 220 Anſwer.
CASE
VIII.
To find the Amount of 500.
RULE.
Annex a Cypher to the Price of 1, double it, then
take the half of the First, and add both together for
Anſwer.
EXAMPLE.
500 Quarters of Wheat at 35 s.
350
700
175
1.875 Anſwer.
CASE IX.
To find the Amount of 600.
RULE.
Annex a Cypher to the Price of 1, and multiply
it by 3.
E X-
HEWITT's ARITHMETIC. 89
EXAMPLE.
600 at 14s.
140 × 3 = 420 1. Anſwer.`
CASE X.
To find the Amount of 700.
RULE.
Annex a Cypher to the Price of 1, multiply it by
3, then halve it, and add both together for Anſwer.
EXAMPLE.
700 at 18 s.
180
× 3
540
90
7.630 Anſwer.
CASE XI.
To find the Amount of 1000.
RULE.
Multiply the Price of 1 by 50, and divide by 12
EXAMPLE.
1000 at 9 d. each.
I 3
G dė
до HEWITT's ARITHMETIC.
9 d.
50
12) 450
1. 37: 10s. Anſwer.
CASE XII.
Having the Price of 1000, to find the Price of 1.
RULE.
Multiply the Price of the Whole by 12, and divide
that Product by 50.
EXAMPLE.
If 1000 coft /. 37: 10 s. what is 1 worth?
5104510:
12
O
9 d. Anfwer.
I'
CHAP. XXII.
Of INTEREST.
NTEREST is either fimple, or compound.-
SIMPLE, when it arifes only from the Princi-
pal— COMPOUND, when it arifes both from Prin-
cipal and Intereft.
SIMPLE
INTEREST.
The Intereft of any Sum for 1 Year, is found by
this plain Proportion, viz.
As 100 l. is,
To the Rate of Intereft,
So is the given Principal,
To the Intereſt required.
E X-
HEWITT's ARITHMETIC.
91
EXAMPLE
I.
1.
What's the Intereft of 469
s. d.
17 4 for 5
Years at
4 per Cent. per Annum ?
1.
I.
1.
If 100
4
S. d.
469: 17:4
4
18 | 79: 9:4
20
15189
12
10 72
4
288
1. s. d.
One Year's Intereft 18: 15: 10/1/
5
Years.
1.93: 19:
194 Anſwer.
The Reaſon of cutting off two Figures on the
Right, is for the 2 Cyphers in the Divifor 100.
To find the Intereft for Months, divide the Year's
Intereft by the even Parts they make of a Year.
EXAMPLE 2.
1. S.
. d.
What's the Intereſt of 325: 17:6 for 5 Months
at 4 per Cent. per Annum ?
325
92
HEWITT's ARITHMETIC.
1.
S. d.
325:17:6
4
13 03: 10:0
20
0170.
12
8140
4
1 | 60
l. s. d.
13:08 One Year's
3:5:2
23:
10
3
Mon. is
2 Mon. is
5:
00
8
:7
4
Anſwer.
A Method to caft up INTEREST, when the Prin-
cipal has odd Money in it, and the Time, Weeks, or
Days.
RULE.
Reduce the Principal to the loweft Denomination,
and multiply it by the Number of Days the Intere it
is required for; and if the Rate of Intereſt is at 5 1.
per Cent. divide the Product by 7300, and the Quo-
tient gives the Intereft demanded, in the Denomina-
tion the Principal was reduced to the Number of
Days in a Year 365, multiplied by 100l. and divi-
ded by 57. makes the common Diviſor 7300.
E X-
HEWITT's ARITHMETIC. 93
EXAMPLE 3.
1. S. d.
What is the Intereft of
for
547: 16:4
13 Days,
at 51. per Cent. per Annum?
1. 5.
547: 16:4
20
d.
10956
12
131476
13
394428
131476
7300)17091188(12)234
* 249
19s. 6 d. Anſwer.
*301
'9
If what remains, and what is cut off in the Divi-
dend, being multiplied by 4, will make a Number
fufficient to contain the Divifor 7300, the Quotient
will be ſo many Farthings, which may eafily be dif-
cern'd, without making unneceflary Figures.
Note, If your Rate of Intereft be less than 5 per
Cent. as 4, take of the Intereft at 5, and fub-
tract it, the Remainder is the Anſwer at 4
10
at 4, ſubtract, and fo along in Proportion
if
if
your
94
HEWITT's ARITHMETIC.
your Rate of Intereſt ſhould be 6, 7, 8, 9, &c. take
a proportional part of the Interest at 5 per Cent. and
add to it, as in the laſt
EXAMPLE,
The Intereft there of 547 l. 16 s.
at 5 per Cent. per Ann. amounts to
per Cent. it would be 1 l. 3 s. 4 d. 3
Take
5. d.
4
d. for 13 Day
19 s. 6 d. at 6
fee the Work.
19: 6
3:10 2/
3
1. 1 : 3 4
3
4 4
10
If it had been at 4 per Cent. per Ann. the 3
muſt have been fubtracted from 19s. 6d, and
the "Anſwer would have been 15 s. 74d.
CHA P. XXIII.
COMPOUND INTEREST,
OR,
INTEREST upon INTEREST,
Co
COMPOUND INTEREST, as has been before faid,
arifes both from Principal and Intereft; that is,
when the Intereft on any Principal remains unpaid at
the Year's End, it is added to the firft Principal, and
fo goes on at the fame Rate of Intereft, ftill adding
every Year's Intereft to the Principal, 'till the whole
is paid.
E X-
HEWITT'S ARITHMETIC,
95
EXAMPLE.
What will 567 1. amount to, in 3 Years, Com-
pound Intereft, at 5 per Cent. per Annum?
1.
567
5
2835
20
710
1.
5.
595:-7
5
29 | 76: 15
20
15 | 35
12
420
1.
S.
s. a.
625: 2:4
5
31 | 25: 11 : 8
1
20
5 11
1.2
1160
Firk
140
96 HEWITT's ARITHMETIC.
First Principal
First Year's Intereſt
·Second Principal-
1.
S. d.
567
28: 7:
595: 7
Second Year's Intereft 29: 15:4
Third Principal-- 625: 2:4
Third Year's Intereſt 31: 5
4
Anſwer 656: 7:54
First Year's Intereſt
Second Year's Intereſt
Third Year's Intereft
Total Intereſt
Principal
1.
S. d.
28: 7:
7:0
29: 15:4
31: 5:1 /1/20
89: 7:54/4
567
0:0
656: 7:54
CHAP. XXIV.
REBATE, or DISCOUNT.
I
Tis a common Method in Trade to fell Goods for
Time, and fometimes for Part ready Money, and
Part upon Time. And this Time, be it more, or
lefs, in many Cafes, is govern'd according to the Na-
ture of the Goods.
E X-
HEWITT's ARITHMETIC.
97
EXAMPLE.
A Tradefman fells Goods to a Merchant for 7501.
to be paid in 6 Months Time; but the Merchant is
willing to pay ready Money, provided he may have
a Diſcount of 6 per Cent. per Ann. fimple Intereſt.
RULE.
Firſt, fee what the Intereft of 100%. comes to, for
the Time demanded-Then, add the Intereft to 100 7.
which must be the FIRST Term in the Rule of Three,
100 /. the SECOND, and the Sum to be rebated, the
'T'HIRD.
If 103 1.
100 %.
7501.
100
103)75000 (7281.
}
• 290
K
• 840
•16
20
103)320(3
II
12
-
103)132(0
29
4.
103) 116(1
Was
∙13
98
HEWITT's ARITHMETIC.
Was to be paid
Is to be paid
Rebated
7.
S. d.
750
0: o
728: 3:
21: 16: 1024
If you would know the Sum rebated, at once, you
muſt make the Intereſt gain'd in that by 100 7. the
fecond Number, and the Stating would be thus,
1. 1.
1. 1. 5. d.
As 103 3 750: 21: 16:10 3
Or,
As 103 : 100 :
100 :: 750
728: 3
I
+
A Bill of Exchange for 194 7. being due the 19th
of March, and this being the 23d of January, I de-
fire to know how much ready Money I muft receive,
allowing a Diſcount of 5 per Cent. per Annum ?
Days.
1.
Days.
If 365
5
55
5
Jan. 8
Feb. 28
275
20
Mar. 19
55
365)5500(15 s. 0 3d.
1850
*25
12
300
4
365)1200(3
105
HEWITT'S ARITHMETIC.
99
1. s. d.
If 100:15:0 2
20
Then fay,
S.
15:02
12
d.
1.
194.
20
2015
12
24180
180
3880
4
12
723
4
46560
4
96720
186240
723
558720
372480
1303680
9672 | 0)13465152|0(4)1392
12)348
'37931
20219
• 89155
11.95.
*21072
•1728
1.
5.
To be rebated
The Bill of Exchange 194:
O
1 : 9
To be received
192: 11
K 2
CHAP.
100 HEWITT's ARITHMETIC.
CHA P. XXV.
EQUATION of PAYMENTS.
T
HE Intention of this Rule, is, when feveral
Sums are due at feveral Times, to find out, a
rean Time to pay them all at once, without a Lofs,
either to Debtor or Creditor.
EXAMPLE.
A Merchant is indebted the following Sums, pay-
able at ſeveral Times, viz. 140/. in 7 Months; 360°1.
in Months; 830 7. in
5
Months; and 280 l. in
3
Months: At what Time may all the Sums be paid
together, without any Lofs to Debtor or Creditor?
RULE.
4
Multiply each Sum by its refpective Time, and
add all the Products together,
-divide the Total by
the whole Debt, and the Quotient is the mean Time
for the Payment.
1.
140
1 3∞
~ the m∞
360
830
280
1610
140
HEWITT's ARITHMETIC. 101
1.
140
1.
1.
1.
·360830-280
7
5
3
4
980
1800
2490
1120
2490
1800
980
156
1610)63910(3 88
156
15
Anfwer 3 Months, which is very near
4
Months
T
CHA P. XXVI.
LOSS and GAIN.
HIS Rule may be divided into four Parts,
which (if rightly underflood) will inftruct the
Learner how to proceed in the Operation.
1. To know what is gained, or loft, per Cent.
2. To know how any Thing ſhall be fold, to gain or
lofe ſo much per Cent.
3. Having gained or loft fo much per Cent. to
know what it coft.
4. There being fo much gained per Cent. when
fold for fuch a Rate, to know what is gained per Cent.
when fold for more, or what is loft per Cent. when
fold for lefs.
K 3
CASE
192 HEWITT'S ARITHMETIC.
CASE 1.
If I Dozen of Claret is bought for 30 s. and fald
for 39 s. how much is gained per Cent. ?
RULE.
Firft, fee what the Gain or Lofs is by Subtraction;
then let the Price it coft be the FIRST Number in
the Rule of Three, the Gain or Lofs, the SECOND,
and 100 the THIRD.
39
30
If 30
9
100
9
CASE 2.
310)golo
Anſwer 30 per Cent.
If 1 lb. of Tea coft 15s. how much muft it be
fold for, to gain 15 per Cent.?
RULE.
Let 100 be the FIRST Number in the Rule of
Three; the Price, the SECOND; and 100 with the
Profit added, or Lofs fubtracted, the THIRD NUM-
ber.
If
HEWITT's ARITHMETIC. 103
1.
1.
If 100
15
1.
115
15
575
115
17:25
12
3100
Anfwer 17 s. 3 d.
If
CASE 3.
25 lb. of Coffee be fold for 4 s. per lb. and there
is 5 per Cent. Lofs- What did the 25 lb. of Coffee
Coft ?
RULE.
Firft, fubtract the Lofs from the 100 %. Then
let the Remainder, when there is Lofs, or the Gain
added to 100l. when there is Gain, be the FIRST
Number; let the Product of the 25 lb. fold at 4s.
per lb. be the SECOND, and 100l. the THIRD.
100
104 HEWITT's ARITHMETIC.
100
5
95
5
100
5
1. s. d.
95)500( 5:5: 3 15
25
20
95)500(5
25
Anſwer.
12
95)300(3
15
CASE 4.
If Cambrick fold at 16 s. per Yard be 20 per Cent.
Profit; What Gain or Lofs per Cent. would there be,
if fold at 145.?
RULE.
Let the first Price be the FIRST Number, 100%.
with the Profit added, or I ofs fubtracted, the SE-
COND, and the fecond Price propofed, the THIRD.
If 16
120
14
120
16)168¢(105 7.
..80
O
Answer 5 per Cent. Gain.
CHAP.
HEWITT's ARITHMETIC.
. 105
CHAP. XXVII.
The RULE of BARTER.
BA
ARTER is no more than the Exchanging
one Commodity for another.
EXAMPLE.
A hath 5 Ct. 3 grs.
of Indigo, at 17 d. per lib.
B hath Stockings at 39 s. per Doz. how many Stock-
ings must be given for the Indigo?
Ct. qrs.
5:3
4 Quarters in an Hundred.
1
23
28 Pounds in a Quarter.
184
46
S.
d.
644
161
1 : 0
3 is
:3
z is
: 2
107-4
20)91/2-4
45: 12: 4 Value of the Indigo.
SAY,
106 HEWITT'S RITHMETIC.
S.
SAY,
If 39 — 1 Doz. Stockings
12
7.
5.
d.
45
12:4
20
468
912
12
Doz.
468)10948( 23 484.
* 1588
184
CHA P. XXVIII.
FELLOWSHIP without TIME.
F
ELLOWSHIP is no more than many Re-
petitions of the Rule of Three ; for,
As the whole Stock, is,
To the whole Gain, or Loſs,
So is each Man's particular Stock,
To his particular Gain, or Loss.
EXAMPLE.
A, B, and C, join together in Trade, A put in
430 I. B put in 693 . C put in 1997. and they gain'd
481 . what is cach Man's particular Share accord-
ing to his Stock ?
A,
HEWITT's ARITHMETIC. 107
1. 1.
8
1322
189
A, 430-1565
693—252 1 3 2 2
B,
5 3 5
T 322
C, 199— 72 πžžž·
1322-481
1.
1.
If 1322
481
430
14430
1924
1322)206830(156
*7463
•8530
1.
430
*598
1.
1.
1.
If 1322
481
693
481
693
5544
2772
1322)333333(252
.6893
•
2833
→
· 189
H
108 HEWITT'S ARITHMETIC.
1.
If 1322
1.
1.
481
199
481
199
1592
796
1322)95719(72
3179
*535
The Proof of this Rule is evident; for, if all the
Shares exactly aníwer the whole Gain, the Operations
muſt be right, if not they are abfolutely wrong.
CHAP. XXIX.
FELLOWSHIP with TIME.
I
N this Rule, each Man's Stock is multiplied by
his Time- And all the Products added together,
make the FIRST Term in the Rule of Three, the
Gain or Lofs, the SECOND, and each Man's particu-
lar Stock multiplied by its Time, the Third.
EXAMPLE.
A puts in 500 l. for 9 Months, B puts in 780 1.
for 7 Months, and they gain'd 2607. what Share
muft each have?
•
500
HEWITT'S ARITHMETIC. 109
500
780
9
7
A-4500
B-5460
A— 4500
If 9960
260
9960
4500
260
270000
9000
996|0)117000|0(117
• 1740
• 7440
•468
If 9960
260
5460
260
327600
A-117
468
996
528
B-142 996
260
L
10920
996|0)141960|0(142
*4236
*2520
*528
CHAP.
110 HEWITT'S ARITHMETIC.
A
CHAP. XXX.
ALLIGATIO N.
LLIGATION teacheth to mix feveral
Things of different Prices, according to any
required Price or Proportion, its Species is diftinguiſh-
ed by two Names, viz.
ALLIGATION MEDIAL,
And
ALLIGATION ALTERNATE.
As the whole Quantity is to the whole Price, fo is
I to its own Price.
RULE.
Reduce the feveral Prices to one Denomination;
then multiply each Quantity by its Price, and add
all the Products together, which Total, divide by the
Number of all the Parcels that are to be mixed, and
the Quotient is the Anſwer to the Queſtion demanded.
EXAMPLE.
A Grocer hath Sugars of ſeveral Prices, and would
mix them fo, that the Quantity mixed might be one
common Price, viz.
3
4
7
9
}
35
Ct. at
30
26
per Ct.
1.8
What is 1 Ct. of this Mixture worth?
I
HEWITT's ARITHMETIC. III
3×35
= 105
X
4 × 30
120
7×26
182
9 × 18
162
S. d.
23
23)569(24: 82 Anſwer.
109
17
12
23)204(8
20
4
23)80(3
II
A Refiner melts 9 lb. of Silver 10 Ounces fine,
11 lb. of 9 Ounces fine, and 8 lb. of 11 Ounces fine,
and defires to know what Fineneſs a Pound Weight
of this Bullion fhall be ?
lb.
9 × 10 = 90
11 × 9=99
8 x 11
28
88
28)277(92 oz. fine.
8
25
L 2
CHAP.
112 HEWITT'S ARITHMETIC.
CHAP. XXXI.
ALLIGATION ALTERNATE.
A
LLIGATION ALTERNATE, hath three dif-
ferent CASES, vix.
CASE I.
When the Price of each Simple is known, but no
Quantity given, and it is required how much of each
Simple must be mixed, to fell any Part of the Com-
pofition at a mean Price propoſed.
EXAMPLE. 1.
A Tobacconist would mix four Sorts of Tobacco,
of 12 d. of 14 d. of 18 d. of 24 d. per lib. What
Quantity of each must be mix'd, to fell it at 17 d.
per lib.
RULE.
Set down the given Prices under one another, (which
muſt always be of one Denomination) then on the
Left-hand, draw a Line of Connection, and againſt
the Center of that Line ſet down the Price required,
as here under.
12
14
17
18
24
Link
HEWITT's ARITHMETIC. 113
Link them two and two together, always coupling
a greater and a less than the Price required together.
Thus,
I 2
I
14
-7
17
18
24
Or, thus,
12
14
17
18
24
Set down the Difference between the Price required
and every other Price againſt the Nnmber it is yoked
to-the Difference between 17 and 12 being 5, place
it againſt 18, the Number yoked with 12 then
the Difference between 17 and 14 is 3, place it againſt
24 yok'd with 14,- then the Difference between 17
and 18 is 1, place it againſt 12 yoked with 18,-
then the Difference between 17 and 24 is 7, place it
againſt 14 yoked with 24.
So that if he mixes 1 lib., at 12 d. 7 lib. at 14 d.
lib. at 18 d. and 3 lib. at 24 d. he may fell that
Mixture at 17 d. per lib.
5
The Proof of this is very obvious- for the Sum of
the Differences valued at the Price required, will be
found to be equal to the Sum of the particular Diffe-
rences at their given Prices- for 16, the Sum of the
Differences multiply'd by 17 the Price required, will
be found to be 272, and 1, 7, 5, 3, the particular
Differences at 12, 14, 18, and 24, will amount to
the fame Sum of 272.
L 3.
CASE
114
HEWITT's ARITHMETIC.
CASE II.
When the Price of all the Simples is known, and
the Quantity of one given, to find the ſeveral Quan-
tities of the reft, to fell a Quantity of that Mixture
at a Price propoſed.
RULE.
When your Numbers have been rank'd, and their
feveral Differences found, as directed in CASE I. then
proceed thus,
As the Difference of that Number, whofe Quanti-
ty is given, is,
To the reft of the Differences one after ancther,
So is the Quantity given,
To the feveral Quantities fought.
EXAMPLE 2.
A Grocer would mix with 20 lib. of Hyfon Tea
at 18 s. per lib.- Tea of 14 s. 125. and 8 s. per lib.
how much of the three laft Sorts muit he add to fell
it all at 13 s, per lib.
18
14
13
12
8
-5
lib.
S.
5
: 1 :: 20 :
4
at 14
5: I : :: 20:
20:
4
at 12
5:5
: 20: 20 at 9
As
HEWITT's ARITHMETIC. 115
As 5 the Difference againft its Price, is,
To the Difference againſt the Tea of 14 s. per lb.
So is 20 the given Quantity of Hyſon Tea,
To the Quantity of that of 14s, per lb. fought.
This Cafe is proved the fame Way as the former.
CASE III.
When the particular Price of each Ingredient is
given, as alfo the Price of the Compound, and a
Quantity of each Sort required, to make up a Quan-
tity propoſed.
Firft, range your Numbers as directed in CASE I.
then obſerve this,
RULE.
As the Sum of the Differences, is,
To the Total Quantity:
So is each particular Difference,
To its particular Quantity.
EXAMPLE 3.
A Vintner would mix Wine at 6 s. 7 s. 9s. and
10 s. per Gallon, to make up a Quantity of 60 Gal-
lons, to fell it at 8s. per Gallon, how much of each
muft he take ?
I
2
8
9
2
I
As
116 HEWITT'S ARITHMETIC.
As 6: 60: I: 10
Gal.
As 6
6:
60 :: 2 : 20
S
6 s.
75.
at
As 6 60 :: 2 : 20
9s.
As 6: 60 :: I : IO
105.
The Proof of this is the fame, as in the other two
CASES.
1
CHAP. XXXII.
POSITION,
O R,
The RULE of FALSE.
T is fo called from the Method taken to diſcover
the true Anſwer to the Queſtion propoſed, viz.
from fuppofing a Number for the Anfwer required,
which generally happens to be falfe.
This Rule is divided into two Parts, viz.
SINGLE and DOUBLE,
And first of
SINGLE POSITION.
In this Rule one falfe Pofition is fufficient to re-
folve the Queſtion propofed by obferving the follow-
ing
RULE.
Take what Number you pleaſe for the Number
required, and try whether your fuppofed Number be
true or falfe, if true, no more is to be done; but if
falfe,
HEWITT'S ARITHMETIC. 117
falfe, you muſt obſerve what the falfe Refult or Con-
clufion is, and then, by the common Rule of Propor-
tion, fay,
As the falfe Conclufion,
Is to the falfe fuppofed Number,
So is the Number given,
To the true Number fought.
EXAMPLE
2
If three Perfons agree to buy an Eſtate for 2000 /
to be paid for amongst them, in fuch Proportion
that A's Share of the faid Eftate fhall be but of
B's Share, and B's Share ½ of C's Share: What muſt
each Perſon pay?
Suppoſe A muſt pay 2007. upon which Suppofi-
tion, B must pay 500l. and C ioool.
By the Conditions of the Queſtion, A is to pay
of what B is to pay, and B is to pay of what C is
to pay; therefore, if the Suppofition of 2007. for A's
Payment be true, the Reſult muſt be, that theſe three
Payments, viz. A's 2007. B's 500 l. and C's 1000 %.
added together, will juſt make 2000 /. the Sum pro-
pos'd to be expended, but they do not, for
2001. +500 + 1000l. are — = 1700 l.
which is a falſe Reſult, or Conclufion.
1.
:
1.
Therefore,
1.
1.
S.
5
. d.
1019
As 1700 200 :: 2000: 235
As 1700l. (the falfe Refult) is,
To 200 l. (the falfe fuppofed Number),
So is 2000 7. (the whole Number given)
To 235 7. 5 s. 10 d. 19 (the true Number fought.)
Whence
118 HEWITT'S ARITHMETIC.
Whence it is truly concluded, that
1. s. d.
A pays-
235 5
101
17
B pays-
C pays-
588 4
817
1176 9
41
16
Total 7. 2000 o o
I
CHA P. XXXIII.
DOUBLE POSITION.
N this Rule Two Suppofitions are required,
which (if both prove falſe) muft, with their Er-
rors be thus diſpoſed of.
RULE.
Set down both the Suppofitions, and againſt each
of them, their reſpective Errors, which, if too much,
muſt be mark'd thus +, if too little, thus
Then multiply them crofs-ways; the first Suppofi
tion by the fecond Error, and the ſecond Suppofition
by the firft Error; if both the Errors are too little,
or both too much; that is, if the Error each Time is
less than the given Number, or each Time more than
the given Number, then fubtract the leffer Product
from the greater, and the Remainder is a Dividend,
which divide by the Difference of the Errors before
they were cross multiplied. But if the Errors are un-
like, that is, one lefs than the given Number, and
one greater than the given Number, the Sum of thoſe
two Products, (I mean the Errors multiplied croſs-
ways
HEWITT'S ARITHMETIC.
119
ways by their Suppofitions) muſt be divided by the
Sum of the two Errors, and the Quotient will give
the true Number required.
EXAMPLE 1.
A Labourer was hired, upon this Condition, that
for every Day he work'd, he ſhould receive 18 d. but
for every Day he was idle he fhould be mul&ted 12 d.
when 135 Days were paſt, he received 41. 17 s. 6 d.
how many Days did he work, and how many Days
was he idle?
Let us FIRST fuppofe, that he work'd 90 Days,
then he was idle 45 Days: Now yo Days Work,
at 18 d. per Day, amounts to 1620 d. and the 45
Days he was idle, at 12 d. per Day, comes to 540 d.
fo that upon this Suppofition, he would have had to
receive 1620-540=1080 d. which is Less than his
juft Wages come to by 90 d. for 47. 17s. 6d. (re-
duced into Pence) are = 1170 d.
Now, let us fuppofe a SECOND Time, that he
work'd 95 Days, and then he muſt be idle 40 Days ;
and then he earns 95 × 18 d. 1710 d. and he for-
feits 40 × 12 d. 480 d. therefore he has to receive
1710d.. 480 d. 1230 d. which is 60 d. too much.
9095 SECOND Suppof.
FIRST Suppofition
FIRST Error
X95
90-
60+
95
90
8550
5400
+5400
SECOND Error
15|0)139510(93
45
O
ift Error = 90
2d Error
6a
150
So
120 HEWITT'S ARITHMETIC.
d.
So that he work'd 93 Days, at 18 d. per Day =1674
Then he was idle 42 Days, at 12d. per Day = 504
And at the End of 135 Days, he received
or 41. 17 s. 6d.
EXAMPLE 2.
1170
The Ages of A, B, C, together make 114 Years,
but A and B's Age together make 30 Years more
than C, and C and B's Age together make 10 Years
lefs than A. What's the Age of each ?
Anſwer
SA's Age
62
Age
C's Age
10
Years.
42
114
CHAP. XXXIV.
The EXTRACTION of the SQUARE
ROOT.
W
HEN any Number is multiplied into itſelf,
fuch Product obtain'd thereby, is faid to be
the Square of that Number; and that Number, from
whence fuch Square arifes, is faid, to be the Square
Root thereof; thus,
16 is the Square of 4; for 4 multiply'd by itſelf,
produces 16: So, 256 is the Square of 16; for 16
× 16 = 256 :
And
HEWITT'S ARITHMETIC.
121
And, on the contrary, 4 is the Square Root of 16,
and 16 the Square Root of 256.
So, the SQUARE Numbers, whofe Roots are the
9 Digits, are, as expreffed in the following
Squares I 4
Roots
I
TABLE.
T
16 81
9
| 25-| 36 | 49 | 64 | 8 i
| 2 | 3 | 4 | 5 | 6 |
7 | 8
وا
To extract the SQUARE Root then of any propoſed
Number, is to find out a Number, which, being mul-
tiplied into it ſelf, will produce the Number propo-
fed; but it is impoffible to extract the Root out of
every propofed Number; for, there are Numbers in-
finite may be propofed, whofe Square Roots, can't
poffibly be exactly exprefs'd in Numbers; and fuch
Numbers are faid to be SURD, or IRRATIONAL.
But tho' the EXACT Root can't always be extract-
ed, yet it may be very nearly fo,- and we muſt al-
ways fuppofe it, a perfect Square Number, be it fo,
or not; and proceed to the Extracting of its Root af-
ter the following Manner.
When the Square Root of any Number is to be ex-
tracted, distinguish it into Parts, by Points placed o-
ver every other Figure, beginning with that in the
Place of Units: And as many Points as the Number
given will admit of, fo many Figures will the Square
Root fought conſiſt of.
M
EX.
122 HEWITT'S ARITHMETIC.
EXAMPLE 1.
EXTRACT the Square Root of 190096.
190096(436
16
83)300
249
866)5196
5196
PROOF.
436
436
2616
1308
1744
190096
The Operation above is thus performed: Endea-
vour to find a Figure, whofe Square ſhall be equal to,
or the next leſs Square to 19, which I find to be 4,
then 4 multiplied by it felf, is 16, which fubtracted
from 19 leaves 3; then bring down the two oo be-
longing to the next Point, and being placed on the
Right-hand of the 3, they make 300; then to ob-
tain the next Figure of the Root, you muſt divide
this 300 by 8, the Double of the firft Figure in the
Quotient, viz. neglecting the laft o, fay, how many
Times is 8 contained in 30, and you'll find it to be 3,
wherefore
HEWITT'S ARITHMETIC.
123
wherefore place this 3 in the Quotient (being the fe-
cond Figure of the Root) and place it on the Right-
hand of the Divifor, which will make it 83; then
multiply and ſubtract as before, and to the Remain-
der 51 bring down the next two Figures, and it makes
5196, which you muſt divide by 86, the Double of
the two firſt Figures 43, in the Quotient, or Root:
then, neglecting the laft Figure 6, fay, how many
Times 86 in 519, and you will find you can have it
6 Times, then place 6 in the Quotient, and 6 on the
Right-hand of the Divifor 86, and it makes 866,
then multiply and fubtract as before, and o remains;
fo that the Root of 190096 is 436, as is plainly pro-
ved by its producing that Square Number, when mul-
tiply'd by it ſelf.
EXAMPLE 2.
EXTRACT the Root of 20115225.
20115225(4485 Root.
16
84)411
336
888)7552
7104
8965)44825
44825
O
—
So that 4485 × 4485 20115225.
CHAP
124 HEWITT'S ARITHMETIC.
CHAP. XXXV.
The EXTRACTION of the CURE
A
ROOT.
LL Powers encreaſe, according to the Multi-
plication of the SIDE or ROOT, once, or more
Times continually into itself; thus,
As any Number, or Root, multiplied into itſelf,
produces a SQUARE, or fecond POWER: fo again,
that Product, or Square, multiplied into the fame
Root, produces a CUBE, or third POWER; and that
Number, from whence fuch CUBE arifes, is called
the CUBE ROOT thereof.
So 64 is a CUBE Number, whofe Roor is
Times 4
is 16, the SQUARE of 4; and
16 is 64, the CUBE of 4.
4
4: for,
4 Times
The CUBES, as well as the SQUARES, are ex-
preffed in the following
CUBES
TABLE.
154
18 27 54 125 216 343 512 729
SQUARES 149
14916 25 36 49 64 81
ROOTS
I 234 5 6 7 8
9
RULE.
HEWITT's ARITHMETIC. 125
RULE.
Let the propofed Number be properly diſtinguiſh-
ed into Parts by Points, viz. Place a Point over the
Unit firſt, and then over the FoURTH Figure, and
then over every THIRD; and fo many Points, as are
placed in that Manner, of fo many Figures, the CUBE
ROOT required will confift.
EXAMPLE 1.
EXTRACT the CUBE ROOT of 85184.
85184(44
64
21184
192
192
64
21184
O
Here obſerve, the Number, from which the CUB I
Root is to be extracted, is firſt properly marked
then I proceed, by the Table of Cube Roots, to find
the neareſt Root of 85, and find it to be 4; I place
it in the Quotient, and fubtract its Cube Number 64
from 85, and there remains 21, then I bring down
the other three Figures 184, and annex them to 21,
and it makes 21184, which is the next RESOLVEND:
Now to procure a Divifor for the next Operation, I
fquare the Number 4 in the Quotient, and triple that
SQUARE
126 HEWITT'S ARITHMETIC.
SQUARE; thus 4 Times 4 is 16, and 3 Times 16
is 48, which is the next Diviſor; then I ſee how
many Times I can have 48 in 211 (neglecting the
two last Figures here as was done by one, in the
Square Root) and finding it 4 Times, I place 4 in the
Quotient, as the fecond and lait Figure in the RooT,
by which I multiply the Divifor 48, and place the
Product 192 two Places fhort of the laft Figure in the
RESOLVEND (as you fee in the Examples) then ſquare
4 the laft Figure in the Quotient, and it makes 16,
which Square being multiplied by 3 Times the firft
Figure in the Quotient, that is, by 3 Times 4, or by
12, and it makes 192, which I fet one Place ſhort of
the laft Figure in the RESOLVEND; and laſtly, I
CUBE 4, the laft Figure in the Quotient, which is
64, and place it under the laft Figure in the RESOL-
VEND, then I add the Products together, and ſub-
tract their Sum 21184 (which must never be greater
than the RESOLVEND) from the RESOLVEND 21184,
and nothing remains.
×
So that the CUBE ROOT 44 44 = 1936 × 44
85184.
E X.
HEWITT's ARITHMETIC. 127
EXAMPLE
2.
EXTRACT the CUBE ROOT of 33386248.
33386248(322
27
6386
54
36
8
5768
·618248
6.44
384
8
618248
O
X
So that the CUBE ROOT 322 × 322 — 103684
× 322-33386248.
FINI S.
BOOKS printed for John Clarke, under
1.
the Royal-Exchange; S. Birt, in Ave-Mary Lane;
T. Aftley, in St. Paul's Church-Yard; J. Wood,
in Pater-nofter Row; and J. Hodges, on London
Bridge.
ATHEMATICAL LESSONS for the
1M Ufe of Students in the Mathematicks and
Natural Philofophy. Compofed by the Abbot De
Molieres. Delivered at the College Royal of Paris,
and recommended by the moſt famous Mathematicians
there. Done into Engliſh from the French by Thomas
Hafelden, Teacher of the Mathematicks, London.
2. MISCELLANEA CURIOSA. Contain-
ing a Collection of fome of the principal Phænomena
in Nature, accounted for by the greatest Philofophers
of this Age, being the moſt valuable Diſcourſes read
and delivered to the Royal Society for the Advance-
ment of Phyfical and Mathematical Knowledge: As
alfo a Collection of curious Travels, Voyages, Anti-
quities, and Natural Hiftories of Countries, prefented
to the fame Society. To which is added, A Difcourfe
of the Influence of the Sun and Moon on human
Bodies, &c. by R. Mead, M. D. F. R. S. And alſo
Fontenelle's Preface of the Uſefulneſs of Mathematical
Learning. In Three Volumes. The Third Edition.
Reviſed and Corrected by W. Derham, F.R.S.
3. KALENDARIUM UNIVERSALE: Or, the
Gardiner's Univerfal Calendar. Containing an Ac-
count of the ſeveral monthly Operations in the Kit-
chen-Garden, Flower-Garden, and Parterre, through-
out the Year, and alfo Experimental Directions for
performing all Manner of Works in Gardening, whe-
ther relating to Sowing, Planting, Pruning Herbs,
Flowers, Shrubs, Trees, Ever-greens, &c. With the
Products of each Month. Taking in the whole Bu-
finefs of Gardening, in a Method wholly new. The
Second Edition.
4. VADE
BOOKS printed, &c.
•pence,
4. VADE MECUM: Or, the Neceffary Pocket
Companion. Containing, 1. Sir Samuel Moreland's
Perpetual Almanack, readily fhewing the Day of the
Month, and Moveable Feafts and Terms, for any
Year paft, prefent, or to come; with many uſeful
Tables proper thereto, and Rules to find them out for
ever. 2. Directions relating to the Purchafing and
Meaſuring of Land. 3. Remarkable Affairs in Eng-
land, a Tide-Table, and a Table of Expence. 4. The
Years of each King's Reign from the Norman Conqueft
to this Time, compared with the Years of Chrift. 5.
Directions for every Month in the Year, what is to be
done in the Orchard, Kitchen, and Flower-Gardens.
6. The Reduction of Weights, Meaſures, and Coins;
wherein is a Table of the Affize of Bread. 7. A Ta-
ble wherein any Number of Farthings, Half-p
Pence, or Shillings, are ready caft up; of great Ufe
to all Traders. 8. The Intereft and Rebate of Mo-
ney; the Forbearance, Difcompt, and Purchaſe of
Annuities. 9. The Rates of Poft-Letters, both In-
Land and Out-Land, according to the New Eftabliſh-
ment. 10. An Account of the Penny-Poft. 11. The
Principal Roads in England. 12. The Names of the
Counties, Cities, and Borough-Towns in Great-Bri-
tain, with the Number of Knights, Commiffioners of
Shires, Citizens, and Burgeffes, chofen therein to ferve
in Parliament. 13. The uſual and authorized Rates
or Fares of Coachmen, Carmen, and Watermen.
14. Tables for Cafting up Nobles, Marks, and Gui-
neas. The Fourteenth Edition Corrected, with Ad-
ditions. To which is added, Intereſt in Epitome;
or Tables in a fhorter Method than any yet Publiſhed,
from 1 Pound to o Millions, at 5, 6, 7, and 8 per
Cent. by Ifrael Falgate, at the Bank of England.
5. Sir Ifaac Newton's Tables for renewing and pur-
chafing of the Leaſes of Cathedral Churches and Col-
leges, according to the feveral Rates of Intereſt, with
their Conftruction and Ufe explained. Alfo Tables
for renewing and purchafing the Leafes of Land or
Houíes. Very neceffary and uſeful for all Purchaſers,
but
BOOKS printed, &c.
but especially thoſe who are any Way concerned in
Church or College Leafes. To which is added, by a
Right Rev. Prelate, The Value of Church and Col-
lege Leafes confider'd, and the Advantage to the Lef-
ſees made very apparent. The Fifth Edition, Pr. 1 s.
6. A Compendium; or, Introduction to Practical
Mufick. In Five Parts. Teaching by a new and
eafy Method, 1. The Rudiments of Song.
2. The
Principles of Compofition. 3. The Ufe of Difcords.
4. The Form of figurative Defcant. 5. The Con-
trivance of Canon. By Chriftopher Sympfon. With
Additions. The Examples being put in the moſt uſe-
ful Cliffs. The Seventh Edition. Price 2 s.
7. Ogilby's and Morgan's Pocket-Book of Roads,
with their computed and meaſured Diſtances, and the
Distinction of Market and Poft Towns. To which
are added, ſeveral Roads, and above 500 Market
Towns: A Table for the ready finding any Road,
City or Market Town, and their Diſtance from Lon-
don: A Sheet Map of England, fitted to bind with
the Book: And an exact Account of all the Fairs,
both fixed and moveable, in alphabetical Order, fhew-
ing the Days on which they are held. By William
Morgan, Cofmographer to their Majefties. The Eighth
Edition, Price 1 s. 6 d.
8. A Compleat Treatife of Practical Navigation,
demonftrated from its firft Principles: Together with
all the neceffary Tables. To which are added, The
uſeful Theorems of Menfuration, Surveying, and
Gauging; with their Application to Practice. Writ-
ten for the Ufe of the Academy in Tower-ftreet. By
Archibald Patoun, F. R. S. The Second Edition, 8vo.
Price 5 s.
9. Surveying Improv'd: Or, the Whole Art, both
in Theory and Practice, fully demonftrated. In Four
Parts. 1. Arithmetick, Vulgar and Decimal. 2. All
Definitions, Theorems, and Problems; with Plain
Trigonometry, and whatſoever elfe is uſeful in the
Theory of Surveying. 3. The Deſcription and Uſe
of Inftruments neceffary in the Practice of Surveying.
4.
BOOKS printed, &c.
4. How to Meaſure, Caft up, Plot, or Divide any
Parcel of Land; to take inacceffible Heights and
Diſtances; with Surveying Counties, Roads, Rivers,
&c. Alfo to reduce a Plan to a Profpect; and to cor-
rect any Survey by Aftronomical Calculation; with
Directions for making tranſparent Colours for Maps,
c. With an Appendix concerning Levelling, and
conveying Water to any poffible Place affigned. The
Second Edition. To which are now added, Direc-
tions for meaſuring ſtanding Timber at one View,
with Tables ready calculated for cafting up the fame.
10. The Compleat Meaſurer: Or, The whole Art
of Meaturing, very ufeful for all Tradesmen, efpe-
cially Carpenters, Bricklayers, Plaifterers, Painters,
Joyners, Glafiers, Mafons, &c. The Second Edi-
tion. To which is added, an Appendix,
Gauging. 2. Of Land Meaſuring. By William
Hawney, Philomath. Recommended by the Rev.
Dr. John Harris, F. R. S. Price 2 s. 6 d.
1. Of
11. A new Guide to Aftrology; or, Aftrology
brought to Light; being fitted for all Manner of Ho-
rary Queſtions, viz. 1. The Defcription of the twelve
Signs and the ſeven Planets. 2. An Account of all
the Afpects of the Planets one with another, with the
Variety of their Significations. 3. An Account of
every Degree afcending, with Significations and Forms.
4. A Choice of very neceffary Aphorifms. 5. Con
cerning the Alterations of the Weather, and of Elec-
tions fit to begin all Sorts of Work. By Samuel Pen-
fyre, Native of Lauzane in Switzerland, Student in
Aftrology and Phyfick. Price 1 s. 6 d.
•
12. The Gentleman's and Builder's Repofitory;
or, Architecture Difplayed. Containing the moft Ufe-
ful and Requifite Problems in Geometry. As alfo,
The moſt eaſy, expeditious, and correct Methods for
attaining the Knowledge of the Five Orders of Ar-
chitecture, by equal Parts and fewer Divifions, than
any Thing hitherto publifhed. Together, with all
fuch Rules for Arches, Doors, Windows, Cieling-
Pieces, and their particular Embelliſhments as can be
required.
BOOKS, printed, &c.
required. Likewife, A large Variety of Defigns for
Trufs Roofs; with the Method of finding the Hip,
either Square or Bevel. Alſo, the moſt certain and
approved Methods of forming a Number of deficient
Stair-Cafes, with their Twifted Rails, &c. The
Whole embelliſhed, not only with Fourfcore Plates,
in Quarto, but fuch Variety of Cieling-Pieces, Shields,
Compartments, and other curious and uncommon De-
corations as muſt needs render it acceptable to all Gen-
tlemen, Artificers, and others, who delight in, or
practice, the Art of Building. Beautifully printed in
Quarto with a new Frontispiece,. curiouſly engraved,
repreſenting the Manfion Houſe, for the Lord-Mayor
of the City of London. The Second Edition, with
large Additions. The Defigns regulated and drawn
by E. Hoppus, and engraved by B. Cole. Price 10s.
13. The Country Builder's Eftimator: Or, The
Architect's Companion, for Eftimating of New Build-
ings, and Repairing of Old, in a concife and eafy
Method, entirely new, and of Uſe to Gentlemen and
their Stewards, Maſter Workmen, Artificers, or any
Perſon who undertakes, or lets out Work. Wherein
the feveral Artificers Works concerned in Buildings,
and every Article belonging to each of them, are fully,
diftinctly, and feparately confidered, and the Prices
thereof inferted, not only of the Workmanship, but
of the Materials alſo, and what Quantity of Mate-
rials are required to the Performance thereof. With
the Manner of taking Dimenſions, Meaſuring, and
Valuing the fame. Alfo, a new Method, to fhew what
Light is proper for any Room, and the Proportions
that the Windows, Chimnies, and Funnels ought to
have by an univerfal Rule. To which are added,
feveral new Tables (never before publiſhed) for the
Valuing of Oak, or any othe Timber, that is fqua-
redand cut to any Scantling or Size fit for Building.
By W. Salmon, jun. The Second Edition, carefully
revifed and corrected, with many large Additions and
Alterations, interfperfed throughout the Whole. By
E. Hoppus, Surveyor. Price is. 6d.
ME M. Towgood
or Richard Gutback
By Vily of Land End.
Hap
100
20
2000
000
οσ
Niliam
Lin
Own Book Anno
Domini Fish
Exit 1751
1751
or
FOR ME
to Mr Richard
89
3
52
56
во
I John Biritt
Book
Book
Birkitty
7 W
uke th
kv
nkitt
kitt 1740
ㄴ
​Joseph Keot!
744
C
John
erki
7
་
UNIVERSITY OF MICHIGAN
W
Joker
Birkin
John
B..
3 9015 06531 2160
32
12
226407
GB2C X
22
87 that
Johir Birkitt
A 543649
S
23 ce
Terrus
1750