r C: .!i ' w\ r^y^MB PM?.#.^' 3 -^M) :m ;l^ ^N^ Ilmistb Kr-.y/YORK, 'irsk'fT^.iic. iffN^^ ■''■-■wH#ii^ 1 -K' CHARLES SCRIBNER'S SONS, :T)7< ^ '^£>i^ N EW YO RKf^' "^ NATURAL SERIES. THE FIRST LESSOI^TS IN NUMBEES; ILLUSTEMD TABLE. BOOK, DESIGNED FOR elementary instruction. . felter,ia;m.,4 lATE AND POLY'ra^NIC d^TITUW, %■ »< LATB OP THE BROOKLYN COLLEGIATE AND POLYTIBInIC MSTITUW, AND AUTHOR OP THE "arithmetical ANALYSIS," ETC UTHOR ij I \ f NEW YORK: CHARLES SCRIBNER'S SONS, 743 & 745 Broadway. ENTEREdfaccordin^ito Act of Congress, in the year 1865, by S. A. FELTER, In the Clerk's Office of the District Court of the United States for the Southern District of New York. Entered, according to Act of Congress, in the year 18&8, by S. A. FE^^TER, P In the Clerk's Office of the District Court nf the United StateWor the Southern Distiict cf • . N*>wAnrV. ^ • New^^rk. » PEEFAOE. In the preparation of this little boot;^ the au- thor has aimed to make it simply a convenient storehouse from which the Teacher is to draw materials for the instruction of his pupils ; and, therefore, it is not intended to " exempt the teacher from the labor of explaining orally, setting sums, &c." It does not propose ''to teach the pupil how to think, " for this must be done by a living teacher ; and no book, whatever its pre- tensions, can be more than an aid. In the first lessons, but little more should be done than to awaken the senses to the perception of num- ibers as exhibited in surrounding objects, and make the little pupils acquainted with some of the simpler facts. Whoever attempts to force upon them reasons, solutions, definitions, and relations, violates the fundamental law of the de- velopment of the human mind ; and, although the pupils may become learned in the book, they are, nevertheless, on the broad road to conceited ignorance. New York, May 1, 1865. II TO THE TEACHER The teacher will readily perceive that this little book is emphatically an illustrated table-book, and not an elementary Arithmetic ; and that its object is to suggest to the little pupil something to do. While it is impossible in a work so small to do more than give suggestions, the teacher will find little dif- ficulty in supplying the deficiency by the use of the blackboard. Although there is nothing in the book which the children ought to be required to commit to memory as a set task, yet each step should be thoroughly mastered by means of oral and written exercises before proceeding to the next. To accompany the series, there is a Manual pre- pared expressly for the use of the teacher ; contain- ing model lessons suggestive of the best methods of i oral, written, individual, and class instruction. - FIHST LESSONS IN NUMBERS. LESSON I. Note. — Each of the following Le.-sons is illustrated by a Model Exer- cise givoii in detail in a Teacher' b Manual, prepared expressly to accom- pany this work. One stump ; // 1. Two trees ; ^/ 2. Thvee boys; Three kites ; J"/ 3. Four bars ; ^ / 4. Five fowls ; J / 5. COUNTING. liSSSON II. Six stones; ^/ 6. Seven \QdiYQ^\ y/ 7. Eight boats ; §/ 8. i\r^W balls; ^/ 9. T^ti tenpins ; /O/ 10. Note TO THK Teacher.— Questions like the following should be| asked on the foregoing illustrations : How many chickens stand on \ the fence? How many bouts have sails? How many men in the' rowboat? How many tenpins stand up? How many have fallen! down '{ (See Manual of instruction for teachers.) COTJNTING. 7 i.i:ssoN III. # (S Be Manual, Sec. I., ] Exercise I.) Copy and read the following exercises : ; Ex. 1. (1) (2) (3) W («) (6) (7) (8) (9) (10) 3 s / 2 2 3 2 3 3 2 1 / 2 3 2 2 2 J" 2 / 3 / 2 ^ 4 4 ^ 1 / 2 J 2 2 J- 2 J ^ i 2 S / .^ / 3 3 3 -g / / 2 3 2 3 J J J- J" Ex. 2. (1) <2) (3) (4) (5) (6) (7) (8) (9) (10) \ k '^ J ^ ^ d 7 ^ 3 7 4 \ 1 ' 7 P 7 9 3 7 / 7 § P ^ 3 / 7 9 § 7 ^ 7 7 J 3 3 3 3 6 ^ 3 \ 1 s s 7 ^ 7 2 7 ^ J" ^ ^ 7 P 3 / d 2 3 7 i * ^Vof^ /o/* th& Ten cher.— These exercises should be copied neatly on the ■ slate, and read at recitation by the members of the class. Particular atten- i tion should be given to the formation of figures. COUNTING. LESSON IV.* (See Manual, Sec. I., Exorcise I.) J^ = 1, 1, 1. S equals 1, 1, 1, units. ^ == 1, 1, 1, 1, 1. ^or - J equals 1, 1, 1, 1, 1 units ^ = 1, 1. 2 equals 1, 1, units. Copy and read the following exercises : Ex.1. Model. (1) (2) (3) (4) (6) (6) J" = 1,1, 1. ^ p y j^ ^ s .^ = 1,1, 1,1,1. ^ 7 ^ ^ 7 7 ./ = !, 1,1,1. ^ ^ ^ 7 ^ ^ Ex.2. (1) (2) (3) (4) <5) (6) (7) '(8) (9) (10) J ^ p <^ p J,- y^ 4 p 4 7 s / y 4 / / s ^ / S4s^ss^77 ^ p/0S^2dd§7 /S7^74S^s ^ 7§/7S^7S7 s * Note for the Teae?ier.— The teacher should explain the meaning and use of the sign of equality (=) in the following exercises. COUNTING. LESSON V. Fifteen\io6k&\/J^/l?>.EighteenhriQk&\ /S',- 18. Ex. J. (1.) (2.) (3.) (4.) (5.) (6.) (7.) (8.) // // /S /^ /S /S /4 /S /2 /^ // /S' /^ /^ // // /S /p /d // SO /S /d /<$ /^ 20 yp yj /S' // /^ // /^ /4 /3 yd /p /^ /O 20 Yd /J- /^ /S 20 /2 // 20 Questions. — How many books on the upper shelf? How many are lying down? How many bricks in the pile? How many bricks iu the lowest row ? How many bricks in the next row ? How many are lying on the ground ? How many books are standing up? How many books on the lower shelf? How many books on both shelves? If all the books were removed from the lower shelf, how many would remain on the upper shelf? If I should take away three books from the upper shelf, how many would remain ? How many would remain on both ? etc. LESSON VI. One boy and 1 boy are how many boys? Two houses and 1 house are how many ? 3 cows and 1 cow are how many? 4 sheep and 1 sheep are how many ? 5 trees and 1 tree are how many ? 6 fishes and 1 fish are how many ? 7 stones and 1 stone are how many ? 8 posts and 1 ])ost are how many? 9 birds and 1 bird are how many ? ADDITION. 11 LESSON VII.* (See Manual, Sec. I., Exercise II.) ; Copy and complete tke following tables : Ex.1. Model. (l.r (2) (3.) (4.) S-^/^J- ^+/ ^+/ ^+/ ^+/ J-^-Z^S / + ^ /+/ J+Z 2-\-/ 7+/=^ ^+/ /+/ /+j? j'+y 2a-/=j ^+/ /+/ ^+/ ^+/ ^+/ (^+/ / + ^ ^+/ / + ^ ^+/ /+/ ^+/ (^+/ /+/ /+/ J'+Z / + (^ /+^ ^+/ ^H-/ /f/ / + / /+/ /+/ J^+Z /+^ / + / ^+/ J'+Z -^4-/ / + / / + / * iV^o^e /or ^Ae 2Tgr/c7i€/'.— Before copying the following lessons the sign of addition ( + ) should be explained to the pupils. One boy and 2 boys are how many ? 2 girls and 2 girls are how many ? 3 windows and 2 windows are how many ? 4 boats and 2 boats are how many ? 5 chicks and 2 chicks are how many? 6 ducks and 2 ducks are how many? 7 sheep and 2 sheep are liow many ? 8 plates and 2 plates are how many ? 9 birds and 2 birds are how many ? /- ADDITION. 13 m_ LESSON IX. j ■b (See Manual, Sec. I., Exercise II.) i ! ^^Copy and complete the following tables : Ex. 1. (1.) C2.) (3.) (4.) (5.) 1 <6.) 5 + 2= = 3 + 2 2 + 2 4+2 5 + 2 4 + 2 4+2= = 2 + 3 2 + 2 2 + 5 2 + 5 2 + 2 IK 2+4= = 4+2 3 + 2 4+2 3 + 2 1 + 2 ! K 5 + 2= = 2 + 5 2 + 2 1 + 2 2 + 3 2 + 1 ! ■ 2 + 2= = 2+4 2 + 2 2 + 3 1 + 2 3 + 2 ^ 3 + 2= = 3 + 2 1 + 2 1 + 2 2 + 1 4+2 Ex. 2. (1.) (2.) (3.) <4.) (5.) (6-) 2 + 1 1+4 2 + 3 4 + 2 5 + 1 7+1 ■' 1 + 2 3 + 2 3 + 2 5 + 2 4 + 1 4+2 1 + 3 2 + 3 1 + 5 6 + 1 2 + 4 1 + 2 2+2 4+1 5 + 2 1 + 6 5 + 2 + 2 4+1 5 + 1 2 + 5 2 + 5 4 + 2 2 + 3 + 2 1 + 5 3 + 2 5 + 1 2 + 5 4 + 2 Ex. 3. (1.) (2) (3.) (4-) (5-) (6.) 6 + 2 8 + 2 3 + 2 5 + 2 2 + 7 4 + 2 IHL 2 + 6 m 7+2 T 2 + '^ 7 + 2 5 + 2 2 + 3 + 7 2 + 2 6 + 2 2 + 5 2 + 7 + 2 5 + 2 8 + 2 7 + 2 2+9 2 + 7 + 2 i fi 4 + 2 1 + 2 2 + 8 2 + 8 1 + 6 + 2 ; ; 7 + 2 5+2 2 + 7 2 + 6 8+0 84-2 1 14 ADDITION. LESSON X. One boy and 3 boys are how many ? 2 bouses and 3 bouses are bow many ? 3 trees and 3 trees are bow many ? 4 girls and 3 girls are bow many ? 5 caps and 3 caps are bow many ? 6 skates and 3 skates are bow many? 7 posts and 3 posts are bow many ? 8 sleds and 3 sleds are bow many ? 9 boods and 3 boods are bow many? Note.— The teacher should dictate problems referring to the ob- jects in the illustrations, thus : Two boys have hold of hands; how many would there be if another should join them? There are six trees; if two were cut down, how many would remain standing? Two little girls are skating and two are looking on ; how many in all? There are five houses ; if two should be burned up how many would remain? If one boy has two skates, how many skates will two boys have? There are eight boys skating, one of them has fallen ' down; how many remain standing? One house and one house are; , how many ? One tree and five trees are how many ? Four trees (;. and two trees are how many ? Two trees and four trees are how I maoy.t; ! ( 1< I • 1 ^ ADDITION. 15 ! LESSON XI. i (See Manual, Sec. I., Exercise II.) ' Copy, complete, and read the following tables : Ex. 1. (1.) (2) (3.) (4.) <5.) (6.) 1 + 3 3 + 1 4 + 3 1 + 5 3+4 4+3 ' 3 + 1 3 + 4 3 + 2 1 + 3 2 + 4 3 + 2 I 3 + 4 1 + 4 2 + 1 1 + 6 4+3 2+1 6 + 1 3 + 1 1 + 3 2 + 4 4 + 2 3+5 5 + 2 5 + 2 4+3 2 + 5 5 + 2 5 + 2 4+3 2 + 5 5 + 1 3 + 2 5 + 3 3 + 2 Ex. 2. (1.) (2.) (3.) (4) (S.) (6-) 5 + 3 4+3 3 + 9 4+3 7 + 3 6 + 3 3 + 5 5 + 3 7+3 7+3 4+3 7+3 6 + 1 7 + 3 6 + 3 3 + 7 3 + 4 3 + 7 6 + 3 8 + 3 3 + 9 4+3 7+3 5 + 3 5 + 3 6 + 3 7+3 6 + 3 8 + 3 4+3 6 + 3 9 + 3 6 + 3 3 + 6 3 + 4 3 + i Ex. 3. <1.) (2.) (3.) (4.) («•) (6.) 6 + 3 3 + 3 3 + 7 6 + 3 2 + 6 3 + 3 1 3 + 6 7+3 2 + 6 3 + 2 6 + 1 2 + 3 1 9 + 3 2 + 3 3 + 2 2 + 8 1 + 8 4+3 ! 8 + 3 2 + 7 1 + 5 8 + 3 8 + 3 3 + 2 \ 3 + 8 6 + 2 1 + 7 9 + 3 3 + 4 2 + 9 i 6 + 2 2 + 3 6 + 1 4+2 7 + 2 3 + 2 \ i LESSON XII. One ship and 4 ships are how many ? 2 boats and 4 boats are how many ? 3 towers and 4 towers are how many? 4 houses and 4 houses are how many ? 5 logs and 4 logs are how many? 6 barrels and 4 barrels are how many? 7 sea-gulls and 4 sea-gulls are how many ? 8 masts and 4 masts are how many ? 9 men aild 4 men are how many ? ADDITION. 17 LESSON XIII (See Manual, Sec. I. , Exercise II.) ! C^PJ) complete, and read the following tables : Ex. 1. (1.) (2.) (3.) (■4.) (5.) (6.) 4 + 2 3 + 4 5 + 4 0+4 1 + 3 7+1 2+4 2+4 4 + 2 4 + 4+2 6 + 3 3 + 2 2 + 3 2 + 3 7+1 2 + 3 4+2 2;fl 3 + 1 3 + 5 8 + 3 + 1 7+3 3+4 4+2 5 + 2 8 + 1 8 + 1 6 + 2 4 + 3 4+4 2+4 3+1 1 + 8 2 + 3 Ex. 2. (1.) (2.) (3.) <4.) (5.) 1 (6.) ! 6+4 4+6 7+4 2 + 4 4 + 6 + 4 6+4 4+7 3 + 4 + 4 3 + 4 4+6 4+6 4+3 8+4 4+0 + 4 6 + 2 3 + 6 4+8 7+4 8 + 4 9 + 4 6 + 4 4 + 5 4+9 6 + 4 9 + 4 7+4 4+6 5 + 6 4+7 3 + 4 3 + 4 4+7 3 + 4 Ex. a. (1.) (2.) (3.) (4.) (5.) (6.) 6 + 4 4+2 5 + 4 9 + 3 + 4 4+1 IK 4+6 2 + 4 3 + 4 4+3 + 3 1 + H ^+^ 6 + 4 2+4 2 + 2 3 + 2 + 1 ■ 2+4 8 + 2 7+3 3 + 3 2 + 1 + 1 ■ 4+3 2 + 4 6 + 3 4+4 1 + 2 + 2 W 6 + 3 2* 6 + 4 8 + 2 7+3 3 + 2 3+3 18 ADDITION. LESSON XIV. One house and 5 houses are how many? 2 lilies and 5 lilies are how many ? 3 pines and 5 pines are how many? 4 windows and 5 windows are how many? 5\lucks and 5 ducks are how many? 6 islands and 5 islands are 11 islands. TJeaves and 5 leaves are 12 leaves. 8 .flowers and 5 flowers are 13 flowers. 9 doors and 5 doors are 14 doors. To THE Teacher. — Oral questions and problems referring to the above and following illustrations should be given to the class. (See Manual Ex. III. Less. IL) The pupils should be required to ask questions of each other referring to the objects in the illustrations. Problems. — If there are six houses and each house has one door, how many doors have all the houses ? Five of the doors are stand- ing open, how many are shut ? If a hunter should shoot five of the ducks in the pond, how many would escape? If a little girl should pick two of the water lilies, how many would remain ? Five ducks and 3 ducks are how many ? Three trees and 5 trees are how many? Five houses and two houses are how many ? Five men and two I men are how many ? ADDITION. 19 IiESSON XV. (See Manual, Sec L, Exercise 11.) Copy, complete, and read tlie following tables : Bx. 1. (1.) («•) (3.) (4.) (S.) (6.) 5 + 6 6 + 5 6 + 5 5 + 6 6 + 7 3 + 5 6 + 3 7+5 5 + 6 7+5 7+5 6 + 5 5 + Y 8+5 7+5 8 + 5 3 + 5 6 + 6 5 + 8 9 + 5 5 + 8 5 + 6 6 + 5 7+5 6 + 9 8 + 5 9 + 5 5 + 7 7+5 3+5 5 + 6 3 + 5 7+5 5 + 6 5 + 6 6 + 5 Kx. 8. (1.) (2.) (3.) (4.) (S.) (6.) 3 + 5 5 + 2 5 + 3 6 + 2 6 + 4 4+3 5 + 2 6+2 5 + 2 8 + 1 5 + 4 7+2 2+3 7+2 3 + 5 7+2 7+3 4+3 3 + 5 5 + 3 9 + 1 7+3 '6 + 4 4+4 4+2 5 + 5 8 + 2 3 + 2 5 + 5 6 + 2 4+5 3 + 5 7+3 4+3 9 + 1 6 + 2 Kz. 3. (1.) (2.) (3.) (4.) («•) (6.) 7+4 4+6 7+5 9 + 3 4+6 4+3 4+5 6+4 5 + 6 8 + 3 3 + 2 6 + 3 6+4 3 + 5 7+2 7+5 3 + 1 5 + 2 8 + 5 5 + 5 9 + 3 6 + 2 6 + 7 4 + 7 7+6 2 + 2 4+3 9 + 3 6 + 8 4+4 7+3 3 + 3 9+1 7+2 3 + 7 •6 + 5 I 20 ADDITION. LESSON XVI. One branch and 6 branches are 7 branches. 2 stones and 6 stones are 8 stones. 3 cows and 6 cows are 9 cows. 4 sheep and 6 sheep are 10 sheep. 5 trees and 6 trees are 11 trees. 6 lambs and 6 lambs are 12 lambs. 7 feet and 6 feet are 13 feet. 8 men and 6 men are 14 men. 9 birds and 6 bbds are 15 birds. Problems.— If 3 cows were driven home, how many would re- main in the pasture? If a boy should drive away 6 of the sheep, how many would remain ? Since 1 cow has 4 feet, how many feet have 2 cows ? A farmer had 10 sheep, he sold 6 of them, how many had he left? There are 9 cows in the pasture, 6 of the cows have been milked ; how many have yet to be milked ? Two sheep and 3 sheep are how many ? Two cows and 4 cows are how many ? Five trees and "4 trees are how many? How many feet have 2 sheep ? How many feet have 4 sheep ? How many feet have 8 sheep 'i How many horn% have three cows? How many horns have 5 cows? How many horns have 6 cows ? Five boats and 3 boats are how many ? Six boys and 5 boys are how many ? ADDITION. 21 1 i i.x:ssoN XVII (See Manual, Sec. I. Exercise II.) Copy, complete, and read the following tables : Ex. 1. (1.) (2.) (3.) (4.) («•) (6.) 8 + 3 3 + 3 8 + 3 6 + 2 8 + 2 8 + 2 7 + 2 6 + 5 7+4 8 + 3 7 + 3 7+2 9 + 1 2 + 2 6 + 2 7+4 2 + 4 3 + 6 8 + 3 1 + 1 9 + 1 5 + 4 9 + 2 7+2 7+3 7+3 7+4 4+4 6 + 1 4+2 2 + 3 6 + 2 3 + 2 2 + 2 3 + 4+1 Ex. a. (X.) (2.) (3.) (4.) («,) (6) 6+5 4+7 4+6 6 + 9 8+6 4+6 6 + 6 6 + 6 6 + 7 9 + 6 3 + 6 6 + 8 3 + 6 3+6 6 + 8 8 + 6 6 + 7 6 + 9 4+6 8 + 6 6 + 3 7+6 7 + 6 6 + 3 9 + 6 6 + 8 6 + 9 4+6 9 + 6 6+4 7+6 3 + 8 6 + 7 3 + 6 8 + 6 6 + 8 Ex. 3. (1.) (2.) (3.) (4.) («•) («•) 8 + 6 3 + 3 8 + 3 9 + 3 4+7 4+6 6 + 7 4+4 5 + 7 6 + 7 6 + 3 3 + 7 3+4 5 + 5 6 + 9 8 + 6 8 + 3 8 + 3 6 + 3 6 + 6 3 + 7 3 + 7 4+7 4+3 4+4 2 + 2 8 + 6 4+3 6 + 7 7+2 3+3 + 4+7 7+2 4+7 6 + 3 J.ESSON xvm. One rake and 7 rakes are 8 rakes. 2 forks and 7 forks are 9 forks. 3 horses and 7 horses are 10 horses. 4 men and 7 men are 11 men. 5 scythes and 7 scythes are 12 scythes. 6 jugs and 7 jugs are 13 jugs. 7 cups and 7 cups are 14 cups. 8 wagons and 7 wagons are 15 wagons. 9 trees and 7 trees are 16 trees. pROB. — There are five bunches of hay on one side of the wagon and five on the other, how many on both ? There are three rakes, one is standing against a tree, the rest are in use ; how many are in use ? Four rakes and 5 rakes are how many ? Five baskets and 6 baskets are how many ? Six cups and 5 cups are how many ? Eight horses and 3 horses are how many? Seven trees and 4 trees are how many ? Six loads of hay and 2 loads are how many ? ADDITION. 23 LSSSON ZIZ. (See Manual, Sec. I., Exercise II.) Copy, complete, and read the following tables : Ex. 1. (1.) (2.) (3.) (4.) (5.) (6.) 3 + 7 3+4 4+4 3 + 1 4 + 3 8 + 3 4+3 9 + 3 3 + 3 7+2 6 + 4 4+2 IK 6+4 9 + 2 2 + 2 7+4 8 + 4 9 + 3 H ^+^ 7 + 4 1 + 1 7+3 5 + 3 7 + 2 R 8+4 8 + 3 0+0 6 + 3 7+4 3 + 8 j 6+4 9 + 3 + 1 7+2 9 + 3 6 + 2 i. Ex, a. (1.) (2.) (3.) ;4.) («•) (6.) T+4 7 + 8 7+6 9 + 7 7+3 8 + 7 T + 6 7+9 7 + 4 7 + 9 7+0 6 + 7 7+8 7+6 4+7 3 + 7 7+8 3 + 7 ! 7+2 7+2 6 + 7 6 + 7 7+9 7+3 i 7+3 7+3 8 + 7 4+7 6 + 7 7+8 7+2 7+0 3 + 7 4+7 3 + 7 7+3 Ex. 3. (1.) (2.) (3.) (4.) (5.) (6.) 7+8 4+3 4+6 9 + 7 6 + 7 4+6 ^fc 6 + 7 6 + 7 6 + 7 4+7 6 + 8 7 + 8 ^^B 3 + 8 3 + 8 8 + 7 6 + 3 3 + 4 3 + 4 ^^B 9 + 7 4+7 3 + 8 8 + 3 7 + 2 6 + 7 l^m ^'^'^ 6 + 7 3 + 7 9 + 4 4 + 3 3 + 9 P *+'^ 3 + 7 4+3 7 + 8 6 + 7 4+7 ^^^Hk 24 ADDITION. LESSON XX. One melon and 8 melons are 9 melons. 2 peaches and 8 peaches are 10 peaches. 3 cherries and 8 clierries are 11 cherries. 4 bananas and 8 bananas are 12 bananas. 5 clusters and 8 clusters are 13 clusters. 6 leaves and 8 leaves are 14 leaves. 7 plums and 8 plums are 15 plums. 8 vases and 8 vases are 16 vases. 9 vines and 8 vines are 17 vines. Problems. — Two peaches and 5 peaches are how many? Four pine-apples and 6 pine-apples are how many? Eight oranges and 4 oranges are how many ? ! 1 ADDITION. 25 k LESSON XXI. i « (See Manual, Sec. I. Exercise II.) Copy, complete, aud read the following tables: Ex. 1. Cl.) (2.) (3) (4.) (5.) (6.) 6 + 7 5 + 3 8 + 3 8 + 4 1 + 1 3 + 5 + 8 6 + 7 7 + 2 5 + 3 3 + 3 + 7 ! 3 + 7 8+4 6 + 3 6 + 7 4 + 4 8 + ! 4+6 4+5 5 + 3 8 + 3 4+4 6 + 3 4+3 8 + 4 7+4 4+2 5 + 5 3 + 4+7 3+4 6 + 3 6 + 1 6 + 6 8 + 6 Ex. 2. (1.) <2.) (3.) (4.) («.) (6.) :j 8 + 3 8 + 7 8 + 9 8 + 6 8 + 7 8 + 7 1 8 + 4 9 + 9 8 + 6 8 + 7 8 + 8 8 + 6 8 + 3 8 + 3 8 + 7 8 + 4 8 + 3 8 + 8 1 8 + 7 8 + 6 8 + 7 8 + 9 8 + 6 8+4 8 + 6 8 + 7 8 + 6 8 + 7 8 + 8 8+6 1 ! 8 + 3 8 + 8 8 + 7 8 + 6 8 + 9 8+9 Ex. 3. (1.) (2.) (3.) (4) («.) (6.) 8 + 8 8 + 7 6 + 7 4+4 2 + 4+6 8 + 3 6 + 7 9 + 3 3 + 3 7+0 6 + 3 + 7 6 + 9 8 + 7 2 + 2 8 + 9 0+8 ; 3+4 3 + 8 8 + 9 8 + 8 + 8 7+9 1 7+6 8 + 3 6 + 9 6 + 6 7 + 6 + 9 ' 8 + 9 3 7+4 7+8 3 + 3 6 + 8 3+8 26 ADDITION. LESSON xxn. One rock and 9 rocks are 1 rocks. 2 trees and 9 trees are 11 trees. 3 wheels and 9 wheels are 12 wheels. 4 carts and 9 carts are 13 carts. 5 limbs and 9 limbs are 14 limbs. 6 sheds and 9 sheds are 15 sheds. Y icicles and 9 icicles are 16 icicles. 8 posts and 9 posts are 17 posts. 9 crows and 9 crows are 18 crows. Problems.— If there are 14 icicles on the shed, and there are 7 on one side of the post, how many are on the other ? There were 3 crows sitting on the tree, two have flown away ; how many re- main ? Four crows and 5 crows aro how many ? Six carts and 3 carts are how many ? Nine sheds and 4 sheds are how many? Four wheels and 8 wheels are how many ? Eight posts and 7 posts are how many? Five trees and 7 trees are how many ? Nine rocks and 5 rocks are how many ? Four branches and 8 branches are how many ? Nine snow-drifts and 3 snow-drifts are how many ? Three fences and 5 fences are how many ? ADDITION. 27 I.ESSON XXIII • (See Manual, Sec. I. , Exercise 11) Copy, complete, and read the follomng tables : Ex. t . (1.) (2.) (3.) (4.) (5.) (6.) 4 + 3 4+3 4+6 6 + 7 4+6 4+3 7 + 3 7 + 2 7+1 6 + 3 7+4 3+8 : 6 + 1 6 + 7 6 + 6 5 + 3 3 + 4 8 + 3 4+2 5 + 7 5 + 6 8 + 6 4+3 9 + 3 6 + 8 3 + 2 8 + 3 9 + 7 6 + 7 4+8 3 + 2 Q + Q 4 + 7 7+7 6 + 4 7 + 1 Ex. 2. (1.) (2.) (3.) (4.) (5.) (6.) 9+4 4+6 4+6 8 + 6 9 + 6 4+3 9 + 3 7+3 7 + 8 7+9 9 + 8 9 + 9 6 + 9 3+7 8 + 9 9 + 6 3 + 2 6 + 9 ! 3+2 8 + 6 6+4 9 + 4 9 + 8 3+4 1 4+6 6+4 3 + 4 9 + 8 6 + 4 9 + 2 i 5 + 3 3 + 7 7+2 3 + 7 3 + 8 4+3 Ex. 3. (1.) (2) (3.) (4.) («•) (6.) 1 2 + 2 4+2 5 + 6 9 + 9 8 + 8 4 + 6 1 + 1 4+6 6 + 7 7+7 3 + 9 7+3 1 6 + 6 6 + 2 8 + 8 6 + 6 7+9 3 + 8 i 8 + 9 + 9 + 9 4+4 6 + 8 3 + 8 1 9 + 9 8 + 6 + 5 2 + 2 3 + 8 6 + 7 7+7 + 9 3 + 3 1 + 1 2 + 4 6 + 7 1 i LESSON XXIV. One load from 1 load leaves how many ? 1 fork from 2 forks leaves how many ? 1 horse from 3 horses leaves how many ? 1 cow from 4 cows leaves how many ? 1 tree from 5 trees leaves how many ? 1 sheep from 6 sheepTleaves how many ? 1 sheaf from 7 sheavQs leaves how many? 1 post from 8 posts leaves how many ? 1 bird from 9 birds leaves how many ? ^-!^^ 8UBTEACTI0N. 29, LESSON XXV. * (See Manual, Sec. I , Exercise III.) Copy, complete and read the following tables : Ex. 1. Model. (1) (2) (3) C4.) 1 6-1=5 8-1 9-1 8-1 3-1 1 7-1=6 6-1 7-1 6-1 7-1 1 IK 9-1=8 3-1 8-1 8-1 6-1 1 ^^K 7-1=6 4-1 6-1 2-1 8-1 ^^B 5-1=4 9-1 1-1 2-1 3-1 H 3-1=2 6-1 4-1 4-1 4-1 iff^. Model. (1) (2.) (3.) (4.) 3-1=2 4-1 5-1 4-1 5-1 !■ 5 + 1=6 3-1 6 + 1 3 + 1 6 + 1 ■ 6+1=7 7-1 7+1 6-1 7-1 m 3-1=2 6-1 3-1 7-1 8 + 1 3+1=4 3-1 6 + 1 4-1 0+1 5-1=4 4-1 5 + 1 4+1 4-1 Ex. 3. (1.) (2) (3.) (4) (5) (6) 4+1 4- 1 9-1 1-1 4-1 1 + 9 8+1 6+1 6-1 1 + 1 3 + 1 9-1 4-1 3+1 8-1 1 + 4+0 8 + 7 3-1 4- 1 7+1. . 1 + 8 5-0 1 + 8 6 + 1 7- 1 9-1 8-1 6 + 1 4-1 2 + 1 9- 1 3-1 3-1 9-1 9-1 * I^ote for tJie Teacher \— Illustrate ttie meaning and the use of the sign || jf subtraction (-) in the following Exercises. 3* LESSON XXVI. Two boys from 2 boys leave how many ? 2 barrels from 3 barrels leave how many ? 2 cages from 4 cages leave how many ? 2 rabbits from 5 rabbits leave how maoy ? 2 turnips from 6 turnips leave how many ? 2 chicks from 7 chicks leave how many ? 2 branches from 8 branches leave how many ? 2 birds from 9 birds leave how many ? ' 2 ears from 10 ears leave how many ? SUBTRACTION. 31 ■ LESSON XZVII vm (See Manual, Sec. I., Exercise III.) ^opy7 complete, and read the foUomng tables : Ex. 1. (1.) (2.) (3.) <4.) (5.) (6.) 3-2 4-2 4-2 4-2 4-2 4-2 6-2 6-2 6—2 6-2 6-2 8-2 H 4-2 7-2 3-2 8-2 4-2 7-2 ■ 8-2 3-2 4-2 4-2 3-2 3-2 ■ 5-2 4-2 6-2 3-2 4-2 4-2 B 6-2 4-2 6-2 6-2 5-2 Ex. 2. (1.) (2.) (3.) (4.) (5.) (6.) 2-2 4-^2 4-2 4-2 5-2 4-2 4-2 6-2 7-2 6-2 7-2 6-2 6-2 4—2 4-2 3-2 3-2 3-2 3-2 3-2 6—2 4-2 6-2 2-2 6-2 8-2 8-2 6—2 4—2 3-2 3-2 6-2 3-2 4-2 3-2 6-2 Ex. 3. (1.) (2.) (3.) (4.) («■) (6.) 2-2 6-2 4-2 9-2 6-2 9 + 2 8 + 2 8-2 7+2 7+2 8 + 2 7 + 2 7+2 4+2 4-2 8-2 2-2 10+2 4-2 7+2 8 + 2 6 + 2 7+2 11-2 6 + 2 3-2 7-2 8 + 2 11 + 2 12 + 2 1 4-2 8 + 2 6 + 2 4-2 11 + 2 7+2 1 LESSON XXIX. 3 books from 3 books leave how many ? 3 pictures from 4 pictures leave how many ? 3 globes from 5 globes leave how many ? 3 chairs from 6 chairs leave how many ? 3 books from 7 books leave how many ? 3 pictures from 8 pictures leave how many ? 3 busts from 9 busts leave how many? 3 books from 10 books leave how many ? 3 pictures from 11 pictures leave how many? 3 busts from 12 busts leave how many ? STXBTBACTION. 33 LESSON XZIX (See Manual, Sec I., Exercise IIL) Copy, complete, and read the following tables : KT. 1. (1.) (2.) (3.) (4.) (5.) (6-) 4_3 8-3 4-3 6-3 4-3 4-3 7-3 7-3 6-3 4-3 7-3 8-3 mm 8 3 4 3 7 3 8-3 6-2 4-3 ■ 4-3 5-3 8-3 7-3 8-3 7-3 H 6-3 7-3 7-2 4-8 4-3 6-3 H 4-3 4-3 4-3 3-3 4-3 9-3 Ex.2. (1.) (a) (3.) (4.) (5.) (6.) 3-2 4-3 4-3 6-3 9-6 8-3 8-2 5-3 3-3 3-3 11-3 7-3 7-3 12-3 7-3 7-3 8-3 6-3 8-3 11-3 11-3 11-3 6-3 11-3 9_3 9-3 12-3 8-3 7-4 7-3 6-8 11-3 10-3 6-3 3-3 6-3 Kl. 3. . (1.) (2.) (3.) (4.) (5.) (6.) 3+2 4-1 3+7 6 + 3 8-3 4-2 4+3 3_2 4+2 7-3 4+3 7+3 6-3 7+2 7-3 4+2 7-3 8 + 3 7-3 3+7 3+8 8-2 6 + 7 12-3 3+7 9-3 7+3 6 + 1 5-2 9 + 3 4+3 7-2 11-2 3-1 4+3 7+3 LESSON XXX. 4 houses from 4 houses leave no houses. 4 roses from 5 roses leave 1 rose. 4 gates from 6 gates leave 2 gates. 4 girls from 7 girls leave 3 girls. 4 kittens from 8 kittens leave 4 kittens. 4 dishes from 9 dishes leave 5 dishes. 4 stools from 10 stools leave 6 stools. 4 cats from 11 cats leave 7 cats. 4 bushes from 12 bushes leave 8 bushes: 4 windows from 13 windows leave 9 windows. * Problems.— There are two stools, each has 4 legs ; how many legs have both ? There are 7 little girls at a picnic, 4 of them re- turn; how many remain? There are 8 roses on the rose-bush; Henry picked 4 of them ; how many remain ? etc. * ITiese and the following problems are not for the pupils to tludy, but for the teacher to dictate to the class. 8UBTEACTI0N. 35 LESSON XXXI. (See Manual, 8eo. I., Exercise III.) . Copy, complete, and read the following tables : £x. 1. (1.) (2.) (3) (4.) <5.) (6.) 6-4 5-4 8-4 7-4 9-4 8-4 ■ 7-4 6-4 6-4 8-4 8-4 7-4 B 8-4 9-4 8-4 6-4 6-4 6-4 ■ 9-4 4-4 7_4 13_4 8-4 8-4 p 8-4 6-4 6-4 4-4 9-4 8-4 6-4 7-4 9-4 7-4 11-4 7-4 Ex. 8. (1) (2.) (3.) (4.) (5.) (6.) 4-3 8-4 8-4 7-4 13-4 11-4 8-4 7-4 11-4 6-4 10—4 13—4 7-4 11-4 12-4 8-4 8-4 10-4 9-4 9-4 13-4 4-4 11-4 9-4 1 6-4 8-4 11-4 8-4 7-4 12-4 ! 12-4 10-4 8-4 7-4 6-4 4-4 ! e:x. 3. (1.) (2.) (3.) (4.) (5.) (6.) 8+4 3+4 8+4 8-4 9+4 4-4 4-4 7+4 4-4 8+4 7+4 8 + 6 6-4 6-4 8-4 7-4 13-4 4-4 7+4 8-4 8+4 3 + 4 10-4 8+4 3+4 9+4 5+4 4+6 11-4 7+4 6 + 7 6+4 7-4 13-4 6+4 13-4 LESSOX XXXIJ. 5 saws from 5 saws leave no saws. 5 boxes from 6 boxes leave 1 box. 5 planes from 7 planes leave 2 planes. 5 hammers from 8 hammers leave 3 hammers. 5 chisels from 9 chisels leave 4 chisels. 5 boards from 10 boards leave 5 boards, 5 benches from 11 benches leave 6 benches. 5 axes from 12 axes leave 7 axes. 5 rules from 13 rules leave 8 rules. 5 cages from 14 cages leave 9 cages. Problems.— A little boy agreed to make 8 bird-cages ; he has 4 of them done; how many has he yet to make ? He had 11 chisels, but broke 3 of them ; how many had he left? He used 5 pieces of board, and has 4 left ; how many liad he at first ? He had 8 augers; he loaned three of them ; how many had he left? etc. ,' SUBTRACTION. 37 1 LESSON ZXXIII. ■ ■ (See Manual, Sec. I., Exercise III.) Copy, complete, and read the following tables ; ; Ex. 1. (1.) (2.) (3.) (4.) (6.) (6.) 6-5 4-5 10-5 8-5 14-5 14-5 ■ 7-5 6-5 8—5 7-5 9-5 6-5 1 9-5 7-5 7-5 13-5 7-5 8-5 10-5 8-5 6-5 14-5 6-5 9-5 8-5 6-5 8-5 6-5 8-6 11-5 7-5 5-5 9-5 5-5 13-5 6-5 Ex. 2. (1-) (2.) (3.) (4.) (5.) (6.) 1-5 11-5 13-5 14-5 14-5 7-5 1 7-5 7-5 6-5 7-5 8-5 6-5 ■ 6-5 11-5 8-5 8-5 6-5 7-5 9-5 12-5 8-5 8-5 8-5 9-5 8-5 13-5 7-5 13-5 7-5 9-5 13-5 14-5 6-5 6-5 8-5 7-5 Ex.3. (I-) (2.) <3.) (4.) <«•) (6.) 3 + 5 4 + 5 8 + 1 8-2 5 + 6 5-5 7+5 7-5 9 + 2 3 + 8 7+4 7-4 9-5 3 + 5 7-2 7-5 7-2 4-4 13-5 2 + 5 7 + 2 2 + 5 7+2 0-0 ! 14-5 5-2 13-4 7-2 4+2 1~0 4 5 + 3 7-5 7-4 3+4 2 + 3 1-1 38 SUBTRACTION. LESSON XXXIV. 6 tents from 6 tents leave no tents. 6 Indians from 7 In^'ians leave 1 Indian. 6 canoes from 8 canoes leave 2 canoes. 6 paddles from 9 paddles leave 3 paddles. 6 trees from 10 trees leave 4 trees. 6 bushels from 11 bushels leave 5 bushels. 6 birds from 12 birds leave 6 birds. 6 bows from 13 bows leave 7 bows. 6 arrows from 14 arrows leave 8 arrows. 6 spears from 15 spears leave 9 spears. Problems.— A party of 12 Indians went to hunt ; 6 of them re- turned ; how many were still away ? In a village there were 11 wigwams, all but 3 were blown down ; how many were blown down ? There are 8 Indians in the boats, and 1 is standing on th( shore ; how many are there in all ? etc. SUBTEACnON. 39 LESSON XXXV (See Manual, Sec. I., Exercise III.) Oopj, complete, and read the following tables : Ix. 1. a.) (2.) (3 ) (4.) (5.) (6.) 14-6 9_6 15-6 14-6 9-6 14-6 14-6 7-6 11-6 7-6 8-6 13-6 15-6 9-6 8-6 8-6 7-6 7-6 11-6 12-6 15-6 14-6 10-6 8-6 14-6 13-6 13-6 15-6 13-6 14-6 j 13-6 13-6 11-6 12—6 15-6 9-6 Sx. 2 . (1.) (2.) (3.) (4.) (S.) (6.) 5 + 6 7-6 5-3 5 + 7 15-6 8 + 6 7-6 8-6 5-3 .'-3 13—6 7+6 4+2 8 + 2 8 + 3 13 -5 14-6 7-6 m 8 + 2 7+6 6+3 15-3 8-0 5-2 3 + 1 3-2 7-2 0-0 7+3 3-1 6 + 1 3+6 6-4 7-3 5 + 3 6-6 Sx. 3. (1-) (2.) (3.) (4.) (5.) (6.) 7-6 8 + 6 9 + 6 15-6 13-6 11-6 9 + 6 13-6 11-6 9-5 7 + 5 12-6 i 8 + 6 11-6 13-6 11-6 6 + 6 13—6 i * 15-6 15-6 14-6 10-6 14-6 9+6 13-6 12-6 13-6 13-6 13-6 15-6 11-6 15-6 10-6 14-6 9 + 6 6 + 6 LESSON XXXVI. 7 turkeys from 7 turkeys leave how many ? 7 turkeys from 8 turkeys leave how many ? 7 chicks from 9 chicks leave 2 chicks. 7 doves from 10 doves leave 3 doves. 7 cows from 11 cows leave 4 cows. 7 hens from 12 hens leave 5 hens. 7 swallows from 13 swallows leave 6 swallows. 7 pails from 14 pails leave 7 pails. 7 sheds from 15 sheds leave 8 sheds. 7 barns from 16 barns leave 9 barns. Problems. — There are 6 chicks and 1 chirk in a brood; how many chicks are there? There are 13 swallows in a flock, 7 of them have flown away ; how many remain ? etc. " SUBTRACTION. 41 1 1 LESSON ZXXVII. i (See ManuaV Sec. I. Exercise III.) \ Copy, complete, and read the following tables : fix. 1. (1.) (2.) (3.) (4.) (5) (6) 10-7 11-7 14-7 14-7 7- -7 8-7 16-7 8-7 16-7 13-7 16- -7 9-7 13-7 9-7 15-7 16-7 8- -7 13-7 i 11-7 11-7 8-7 15-7 9- -7 16-7 ; 16-7 14-7 16-7 8-7 16- -7 15-7 j ! 14-7 16—7 13-7 9-7 15- -7 8-7 Ejc. 2. (1.) (2.) (3.) (4.) <5.) (6-> 7-1 74-7 13_7 15-7 10- -7 15-7 7 + 7 9 + 7 14_7 16-7 16- -7 16-7 7-3 9-7 15-7 13-7 lo- -7 11-7 '1 7+4 10 + 7 16-7 ll -7 13- -6 12-7 7 + 5 11-7 15-7 12-7 11- -7 9-7 _7-6 12-7 7+0 11-7 14- -7 7+7 Bx. 3. (1.) (2.) (3.) (4-) («•) , (6.) 7+2 13_6 8 + 3 8+3 8+7 4+5 7-1 3+6 7-2 7+1 5+9 7 + 7 8-1 4+6 8-3 5-2 6- -3 3 + 8 4-2 7+5 7-4 5 + 2 9- -7 9-7 2 + 2 5-2 6+2 9-7 13- ^7 3-1 5 + 2 5+2 4+3 6 + 6 16- -7 8-2 1 4» - % . 42 SUBTRACTION. LESSON XXXVII. Eight trees from 8 trees leave no trees. 8 ropes from 9 ropes leave 1 rope. 8 boys from 10 boys leave 2 boys. 8 girls from 11 girls leave 3 girls. 8 bouses from 12 bouses leave 4 bouses. 8 barns from 13 barns leave 6 barns. 8 caps from 14 caps leave 6 caps. 8 flowers from 15 flowers leave 7 flowers. 8 bushes from 16 bushes leave 5 bushes. 8 horses from 17 horses leave 9 horses. Problems. — John swung his little sister 5 minutes and his littie brother 7 minutes ; how many minutes did he swing both ? StTBTEACTION. 43 LESSON XXXIX. (See Manual, Sec. I., Exercise IIL) Copy, complete, and read the following tables : Ex. I. (1.) (2.) (3.) (4.) (5.) (6.) 9-8 8-8 11-8 16-8 16-8 17-8 17-8 17-8 16-8 13-8 13-8 13—8 IB 16-8 '^ 13-8 13-8 13-8 15-8 12-8 12-8 i 16-8 14-9 14-8 17-8 9-8 11-8 15-8 17-8 11—8 12-8 13-8 _17-8 12-8 18-8 13-8 13-8 17-8 ' i Bx. a. (1.) (2.) (3.) (4.) (5.) (6.) 17-8 14-8 9-8 8-2 13-8 14-8 11-8 13-8 8 + 7 8 + 1 15-8 17-8 16-8 12—8 8 + 6 8-0 16-8 16-8 15-8 10-8 8-5 11-8 13-8 11-8 14-8 11-8 8+4 13-8 11-8 12-8 13-8 8 + 8 8+3 15-8 13-8 13-8 Ex. 3. (1.) (2.) (3.) (4.) (5.) (6.) 17-8 6 + 9 5 + 8 8-8 6+8 8 + 16-8 11-8 13-8 8+8 9-8 0+8 13-8 8-8 6 + 8 3 + 8 13-8 8-8 14-8 8 + 8 14-8 13-8 17-8 8-0 17-8 10-8 4 + 6 14-8 6+8 7+8 13-8 9 + 8 5 + 7 4+7 5+8 8 + 8 LESSON XL. 9 mills from 9 mills leave no mills. 9 trees from 10 trees leave 1 tree. 9 men from 11 men leave 2 men. 9 boats from 12 boats leave 3 boats. 9 do^s from 13 dogs leave 4 dogs. 9 wheels from 14 wheels leave 5 wheels. 9 doors from 15 doors leave 6 doors. 9 bridges from 16 bridges leave 7 bridges. 9 fish-poles from 17 fish-poles leave 8 fish-poles. 9 posts from 18 posts leave 9 posts. Problems- — A man caught 8 fishes at one time and 6 at another ; how many did he catch in all ? If a mill grinds 8 bushels of corn and 12 bushels of wheat ; how much more wheat does it grind than corn ? i , STTBTEACnON. 45 X.BSSON XX.I. (See Manual, Sec. I., Exorcise III.) ; Copy, read, and complete the following tables : Ex. 1. (1.) (2.) (3.) (4.) (5.) (6.) 9-9 •9-3 15-9 13-9 14-9 15-9 9-8 9_2 18-9 14-9 13-9 16-9 9-.T 9-1 17-9 16-9 18-9 18-9 i j 9-6 9-0 16-9 18-9 16-9 13-9 1 9-5 10-9 18-9 13-9 17-9 15-9 1 9-4 11-9 17-9 10-9 9-9 18-9 Ex. 2. (1.) (2.) (3.) (4.) <5.) C6.) 8 + 7 4-3 4+6 3+7 4 + 6 4 + 6 5 + 6 9-4 3+7 8+9 13-9 8 + 6 3-2 9 + 3 18-9 3-1 14-8 9+1 : 8-4 8 + 7 17-8 + 1 7+8 3 + 1 9-3 4+3 4+7 8+0 9 + 5 5-2 7 + 6 8+7 6+9 9-3 11-9 7-2 Ex. 3. (1.) (2.) (3.) (4.) («.) (6.) ' 9 + 9 9+1 8+8 4+9 15-9 4+8 13-9 18-9 7+9 7 + 8 7+9 7 + 9 18-9 17-9 ii_9 9_8 8 + 9 6 + 9 3 + 7 13-9 8-9 17-9 17-9 13-9 7+9 6 + 9 17—9 11-9 16-9 15-9 18-9 3 + 9 13-9 13-9 13-9 17-9 1 »^ Once 2 2 times 3 times 4 times 5 times 6 times 7 times 8 times 9 times LESSON XLII. ducks are 2 ducks. 2 men are 4 men. 2 ducks "are 6 ducks. 2 dogs are 8 dogs. 2 guns are 10 guns. 2 trees are 12 trees. 2 ducks are 14 ducks. 2 islands are 16 islands. 2 logs are 18 logs. MULTIPLICATION. 47 LESSON XIiIII .* (See Manual, Sec. I., Exercise IV.) Copy, complete, and read the following tables : Ex. 1. Model. (1.) (2.) (3.) (4) : ' 4x2=^8 2x2 2x2 5x2 4x2 3x2=6 0x2 3x2 4x2 5x2 2x2=4 3x2 4x2 1x2 3x2 1x2=2 2x3 1x2 1x1 2x2 5x2=10 3x2 3x2 2x2 4x2 4x2=8 4x2 4x2 3x2 1x2 Kx. 2. Model. (1.) (2.) (3.) (4-) 3x2=6 6x2 1x2 6x2 4x2 4x2=8 7x2 7x2 7x2 3x2 5x2=10 6x2 3x2 6x2 9x2 7x2=14 7x2 6x2 3x2 6x2 2x2=4 4x2 8x2 8x2 9x2 0x2=0 4x0 3x2 1 6x2 3x2 Bx. 3. (1.) (2.) (3.) (4.) («•) (6.) 3x2 5+2 5x2 4+2 0x6 7+2 2+3 7-2 5-2 6+2 6x0 4-2 4x2 3x2 5+2 2+6 6-0 7 + 2 6-2 7x2 2+5 2x6 6 + 9-1 2x6 6-2 3+0 6x2 + 6 8-2 4-2 4+2 0+3 6-0 9x2 4-2 j * Note for the ^(gac^er.— Illustrate the meaning and tlie use of the sign J of multiplication ( x ) in the following Exercises. " ^^^^ Once 3 2 times 3 times 4 times 5 times 6 times 7 times 8 times 9 times LESSON XLIV. ladders are 3 ladders. 3 poles are 6 poles. 3 windows are 9 windows. 3 men are 12 men. 3 poles are 15 poles. 3 window^s are 18 windows. 3 hods are 21 hods. 3 timbers are 24 timbers. 3 bricks are 27 bricks. Pkoblems.— If a man carry 9 bricks in his hod at one load, how many bricks can he carry in going 3 times ? There are 9 windows in one story ; how many windows in 3 stories ? MULTIPLICATION. 49 LESSON XLV. 1 (See Manual, Sec. I., Exercise IV.) i Copy, complete, and read the following tables : Ex. 1. (1.) (2.) (3.) (4.) ca.j (6.) 5x3 1x3 2x3 4x3 6x3 3x6 I 4x3 7x3 3x3 5x3 7x3 3x2 1 3x3 5x3 0x3 4x3 8x3 3x5 2x3 2x3 5x3 1x3 5x3 5x3 4x3 4x3 8x3 0x3 7x3 4x3 5x3 2x3 6x3 3x0 6x3 2x3 Ex. 2. (1.) (2.) (3.) (4-) (5.) «5.) i 4x3 5x3 7x3 1x3 5x3 6x3 5x3 7x3 6x3 9x4 7x3 7x3 7x3 6x3 4x3 6x3 6x3 6x3 8x3 3x3 0x3 7x3 8x3 8x3 4x3 7x3 6x3 5x3 7x3 6x3 6x3 9x3 7x3 6x3 9x3 9x3 Ex.3. (1.) (2.) (3.) (4.) (5.) (6-) '' 3x3 4x3 3 + 7 + 3 4+3 4x3 4x3 4-3 + 3 3x7 3 + 3 4-3 ! 12-3 4+3 3-0 5 + 3 3-3 7+3 i 7x3 7x8 3 + 3x5 7-3 7-3 -j 7+3 7-3 3x0 6x3 11-3 3 + 3 ' 7-3 7 + 3 0x3 8x6 10-3 3-3 ,i — 50 MULTIPLICATION. 4 times 2 pigs are 8 pigs. 4 times 4 goats are 16 goats. 5 times 5 ducks are 25 ciucks. LESSON XLYI. Once 4 goats are 4 goats. 2 times 4 feet are 8 feet. 3 times 4 nests are 12 nests. 4 times 4 birds are 16 birds. 5 times 4 pigs are 20 pigs. 6 times 4 kids are 24 kids. 7 times 4 wings are 28 wings. 8 times 4 eggs are 32 eggs. 9 times 4 ears are 36 ears. '' 1 MtTLTIPLIOATION. 51 LBSSON SLVIl ^ , (Sec Manual, Sec. I., Exercise IV.) Copy, read, and complete the following tables : j !bx. 1. (1-) (2.) (3.) (4.) (a.) (6.) 3x4 6x4 6x4 3x4 6x4 4x4 2x4 2x4 7x4 2x4 3x4 6x4 0x4 7x4 3x6 4x4 7x4 3x4 1x4 9x4 8x4 0x4 3x4 7x4 8x4 3x4 2x4 3x4 6x4 6x4 3x4 2x4 7x4 3x4 2x4 3x4 Ex. 2. (1.) (2.) (3.) (4.) (6.) (S.) 3x4 5x4 8x4 6x4 8x4 5x4 4x4 3x4 7x4 5x4 6x4 7x4 7x4 7x4 8x4 7x4 8x4 8x4 9x4 5x4 0x4 3x4 9x4 3x4 6x4 8x4 9x4 6x4 7x4 7x4 1 4x4 7x4 7x4 7x4 6x4 6x4 Kt.3. (1.) (2.) (3.) (4.) (5.) C6.) 3+4 5x4 6 + 4 8-4 6x4 2+4 3x4 5-4 6-4 8-0 6 + 4 2-1 3-0 5+4 6x4 0x8 13-4 8x4 4x4 13-4 11-4 8x0 7x4 8x4 7x4 7+4 8-4 5-3 8 + 4 8+4 4x4 7-4 6+4 4x7 7+4 8x3 1 52 MULTIPLICATION. 5 times 1 horse are 5 horses. 5 times 2 cows are 10 cows. 5 times 3 pigs are 15 pigs. 5 times 4 sheep are 20 sheep. Once 5 2 times 3 times 4 times 5 times 6 times 7 times 8 times 9 times LESSON XL VIII. horses are 5 horses. 5 posts are 10 posts. 5 doors are 15 doors. 5 cows are 20 cows. 5 pigs are 25 pigs. 5 stys are 30 stys. 5 sheep are 35 sheep. 5 trees are 40 trees. 5 sheds are 45 sheds. MULTIPLICATION. 53 I.X3SSON XLIX ■ ^^^ (See Manual, Sec. I., Exercise lY.) Copy, complete, aud read the following tables : fix. 1. (1) (2) (3.) (4.) («•) (6) II 4x5 6x5 5x2 5x5 4x5 2x5 3x5 2x5 5x3 3x5 3x5 3x5 6x5 3x5 6x5 6x5 2x5 4x5 2x5 7x5 2x5 4x5 3x5 3x5 3x5 2x4 3x5 3x5 6x5 6x5 _4x5 4x5 2x5 2x5 3x5 2x5 fix. 2. a.) &■) (3.) (4.) (5.) (<5.) 3x5 6x5 8x5 9x5 9x5 3x5 4x5 7x5 9x5 7x5 7x5 5x5 7x5 3x5 7x5 8x5 4x5 9x5 3x5 0x5 6x5 5x5 8x5 7x5 6x5 7x5 7x5 7x5 9x5 6x5 7x5 6x5 8x5 8x5 7x5 3x5 fix. 3. (1.) (2.) (3.) (4.) («■) (6-) 3 + 2 7-5 7+6 7-5 8 + 3 5-0 7x3 6x5 12-5 8-5 5 + 3 5 + 6 + 3 6 + 5 13-5 7-5 5 + 8 + 5 4-2 14-5 8+5 13-5 5-2 0x5 9-5 13-5 6 + 5 5-3 7+3 5x5 9x5 12-5 5-0 5 + 3 8-5 7-5 6« ■^ I 54 MULTIPLICATION. LESSON L. Once 6 sloops are 6 sloops. 2 times 6 steamboats are 12 steamboats. 3 times 6 towers are 18 towers. 4 times 6 houses are 24 houses. 5 times 6 men are 30 men. 6 times 6 birds are 36 birds. 7 times 6 men are 42 men. 8 times 6 masts are 48 masts. 9 times 6 flags are 54 flap^s. Problems. — If a ship have 3 masts, how many masts have 6 such ships ? Thore are 12 sea-gulls in a flock; a sailor shot 5 of them; how many escaped ? MULTIPLICATION. 55 y i BSSON LI. I ^.^-^ (See Manual, Sec. I., Exercise IV.) Copy, complete, and read the following tables: £x. 1. (!■) (2.) (3) (4.) (S-) (6.) 5x6 8x6 7x6 8x6 5x6 5x6 4x6 7x6 9x6 3x6 3x6 7x6 3x6 5x6 5x6 7x6 9x6 3x6 4x6 3x6 8x6 3x6 3x6 6x0 3x6 2x6 9x6 9x6 8x6 3x6 2x6 7x2 3x6 8x6 9x5 9x6 EX» 2. (1.) .(2.) (3.) (4.) (5.) (6.) 2 + 3 4x2 4 + 6 5+3 4 + 6 13-3 6 + 4 3x6 (2.) (3.) (4.) (5.) (6.) 6-f-3 4x3 8 + 3 12^3 6-=-3 8x3 4-3 9x3 9+3 9x3 9^3 3x3 7+3 12^3 11-3 7-h3 11-3 11-3 8x3 6+3 8x3 8-3 8x3 24-^3 24^3 8—3 27^3 9-^3 9 + 3 8 + 3 7+3 11-3 7+3 8x3 7+3 3 + 9 i*-~ LESSON LXII. 4 birds are contained in 4 birds once. 4 spokes are contained in 8 spokes 2 times. 4 bags are contained in 12 bags 3 times. 4 mills are contained in 16 mills 4 times. 4 posts are contained in 20 posts 5 times. 4 houses are contained in 24 houses 6 times. 4 windows are contained in 28 windows 7 times. 4 horses are contained in 32 horses 8 times. 4 men are contained in 36 men 9 times. Problems.— One wind-mill has 4 wings, how many wings will 4 such mills have? How many loads will 16 bags of corn make if a man draws 4 bags at a load ? There are 4 windows in the house, how many windows will 6 such houses have ? There are 8 spokes in a wheel ; how many spokes in 2 wheels ? If a cart have 2 wheels, how many wheels have 4 carts ? i DIVISION. 67 LESSON LXIII . (See Manual, Sec. I. , Exercise V.) Copy, complete, and read the following 1 tables : BX. 1. (1.) (2.) (3.) (*•) (5.) (C.) 4^4 4-T-4 8^4 24^4 28-^4 32^4 8 : 4 12 : 4 12 : 4 16^4 32-^4 20^4 12H-4 16^4 16-h4 12-^4 28--4 28^4 8^4 12--4 20-^4 8^4 24^4 24^4 12-^4 8-^4 12H-4 36^4 16-h4 32^4 4-^4 16-^4 8^4 20^4 124-4 28H-4 1 Ex. 8. (1.) (2.) (3.) (4.) («•) j (6.) 32^4 4-T-4 8^4 4-V-4 28-^4 12-^4 24^4 8--4 12H-4 8^4 20-H-4 20^4 ■ 12---4 24^4 32-^4 16^4 16^4 28-^4 8^4 36H-4 36^4 24: 4 20-=-4 32-T-4 20^4 28--4 24^4 28---4 28^4 8-^4 16^-4 20-^4 12-^4 36-^4 36-^4 4--4 Ex.3. (1.) (2.) (3.) (4.) (5.) (6.) 1 24^4 32^4 6x4 8-4 5x4 4x8 ' 8x4 8x4 7—4 7x4 7-4 9+4 12-4 6-4 8x4 36-=-4 8x4 9-4 6+4 8+4 7+4 7-4 4x8 32^4 8-^4 13-4 13-4 12-4 9x4 7x4 7+4 7x4 7x4 6 + 4 36^4 6-4 68 DIVISION. LESSON LXIV. 5 barrels are once 5 barrels. 10 men are 2 times 5 men. 15 boxes are 3 times 5 boxes. 20 boats are 4 times 5 boats. 25 logs are 5 times 5 logs. 30 baskets are 6 times 5 baskets. 35 sea-gnlls are 7 times 5 sea-gulls. 40 rods are 8 times 5 rods. 45 lines are 9 times 5 lines. Problems. — There were 17 piles lying on the dock ; 9 have been driven ; how many remain ? DIVISION. 69 LSSSON LXV. (See Manual, Sec. I., Exercise V.) Copy, read, and complete the following tables : Ex. 1. (1.) (2.) (3.) (4.) (S.) (6.) 5-5 25^5 30-^5 15-^5 40^5 40^6 15-f-5 15-H-5 25--5 30^5 15--5 30--5 10^5 5^5 20-^5 35^5 25^5 45^5 20-^5 10--5 15^5 40^5 35^5 15^5 10^5 20-^5 10^5 35-^5 20-^5 25-f-5 5^5 25^5 15-^5 15^5 40-:-5 20^5 Ex. a. (1.) (2.) (3.) (4.) («.) (6.) 25-^5 15-^6 20^-5 5-V-5 IOh-5 15-=-5 30^5 lO-r-5 35-^5 15-^5 20-^5 25^5 40^5 5^5 40^5 25^5 30-=-5 30-^5 20^6 30-f-5 25^5 35^5 40^5 40^5 45^5 40-^5 30^5 45-^5 15-T-5 45^5 10-^5 45-^5 20^5 25-^5 20-^5 35-^5 Ex. 3. (1.) (2.) (3.) (4.) (5.) (6.) 25^5 30^5 7+5 45--5 6+5 4x5 4x5 7x5 8+5 7x5 12-6 11-5 ! 3+5 5-5 13-5 5x5 8 + 7 10^5 8-5 8 + 5 40-=-5 10-5 8—5 3x5 14-5 5x8 6x6 10^5 8x5 7+5 10^5 13-5 7-5 10x5 6+5 9+6 i 70 DIVISION. LESSON LXVI. 6 cliiirches are once 6 churches. 12 sheep are 2 times 6 sheep. 18 ducks are 3 times 6 ducks. 24 dogs are 4 times dogs. 30 men are 5 times 6 men. 36 boys are 6 times 6 boys. 42 saddles are 7 times 6 saddles. 48 bridles are 8 times 6 bridles. 54 horses are 9 times 6 horses. Problkms. — Willie rode 2 hours every day for a week, how many hours did he ride in all ? Divisiojsr. 71 1 LESSON LXVII. i j (See Manual, See I., Exercise V.) Copy, complete, and read the following tables : ' Ex. 1 (1.) (2.) (3.) (4.) (5) (6,) 1 G-:-6 30-r-6 30-^6 42^6 48^6 54-=-6 ; 18-^6 18-T-6 30^6 12^6 30^6 48-^6 ' 12^6 6-^6 24^6 Q^Q 36-=-6 36-r-6 | IK 24-4-6 18-^6 18^6 30-^6 48--6 42^6 6-4-6 30-4-6 12^6 42-^6 24-4-6 24-^6 1 18^6 24-4-6 6^0 18^6 18-4-6 54-^6 Ex. 2 . (1.) (2.) (3.) <4.) (5.) (6.) 42-4-6 12-4-6 24-4-6 30-4-6 42^6 18^6 48-^6 18^6 30^6 36^6 30^-6 24^6 30^6 30-=-6 42^6 42^6 36-4-6 36^6 | 12^6 42^6 48^6 54-4-6 48^6 48-=-6 54^6 54^6 18^6 6-4-6 18^6 42^6 ! 30-4-6 18^6 12-^6 18-=-6 12-4-6 54^6 £x. 3 (1.) (2.) (3.) (4.) (5.) (6.) 24-4-6 6x8 7-6 5x6 4x6 13-6 24^4 5x6 5x6 7-5 8x8 7-6 IKv 2x6 13-6 13-6 13-6 7-6 8x6 p 15-6 7-f6 15-6 7x6 7x6 4-1-6 13-6 8-f6 8-f6 12^6 14-6 8x6 8x6 48-4-6 8x6 8-6 11-6 7x6 " DIVISION. LESSON LXYin. 7 baskets are once 7 baskets. 14 hop-poles are 2 times 7 bop-poles. 21 men are 3 times 7 men. 28 girls are 4 times 7 girls. 35 hop-vines are 5 times 7 hop-vines. 42 birds are 6 times 7 birds. 49 hats are 7 times 7 hats. 56 coats are 8 times 7 coats. 63 knives are 9 times 7 knives. Problems.— There are 8 birds flying away from the hop-yard ; they are separated into 2 flocks; how many birds in each flock ? 1 DIVISION. 73 LESSON LXIX. (See Manual, Sec I., Exercise V.) ! Copy, complete, and read the following tables : Ex.1. (1.) (2) (3.) (4.) (5.) (6.) 7-^7 28^7 42-^7 49-^7 49^7 63-r-7 14-^7 21-^7 14-^7 42^7 56^7 28-=-7 ; 284-7 35^7 21-V-7 28-^7 42^7 14^7 21H-7 21^7 35-^7 49h-7 63^7 42-=-7 ' 14--7 14--7 42--7 14-v-7 56-^7 21--7 28-^7 7-4-7 14-^7 7-^7 28-=-7 56^7 i Ex. 2. (1.) (2.) (3.) (4.) (5.) (6.) 49-^7 21^7 21-^7 28-^7 28-=-7 14-=-7 42^7 14^7 7-^7 14---7 7^7 21-j-7 35--7 35--7 28--7 42--7 21--7 35-^7 | 28^7 49^7 35-^-7 49-^7 35^7 49^7 56-^7 63-f-7 56-^7 63-=-7 49-^7 63-f-7 21-^7 42--7 G3-^7 35h-7 63^7 56--7 Ex.3. (1.) (2.) (3.) (4.) (5.) (6.) 49-^7 21-^7 8-t-7 .5x7 4x7 4x7 Cx7 35-r-7 5-F7 8x7 G + 7 C-l-7 8x7 16-7 9-7 28^7 9-h7 9-h7 15-7 4x7 6x7 66-^7 9-7 8-7 6-F7 5x7 5x7 8x7 8x7 7x7 5-1-7 6-r7 63-h7 6x7 43--7 28-f-7 T 74 DIVISION. LESSON LXX. 8 cows are once 8 cows. 16 hens are 2 times 8 hens. 24 houses are 3 times 8 houses. 32 feet are 4 times 8 feet. 40 claws are 5 times 8 claws. 48 dishes are 6 times 8 dishes. 56 boards are 7 times 8 boards. 64 doors are 8 times 8 doors. 72 windows are 9 times 8 windows. Problems.— Henry found a nest containing 8 eggs; how many eggs will 2 such nests contain ? The cow gives 8 quarts of milk every night and morning ; how many quarts does she give each day? DIVISION. 75 LBSSON liZZI. See Manual, Sec. I., Exercise V.) Copy, complete, and read the following tables : Ex. 1. (1.) (2.) (3.) (4.) (5.) <6.) 32- -8 40- -8 56- -8 24- -8 48- -8 73-- 16- -8 8- -8 40- -8 32- -8 64- -8 32^ 8- -8 24- -8 32- -8 56- -8 48- -8 64^ 32- -8 32- -8 16- -8 48- -8 64- -8 48^ 24- -8 40- -8 24- -8 40- -8 56- -8 64-f- 16- ^8 24- -8 48- ^8 56- -8 40- -8 40^ £x. 2. (1.) (2.) (3.) (4.) (5.) (6.) 40- -8 48- -8 56- -8 24- -8 24- -8 48-; 48- -8 56- -8 72- -8 8- -8 56- -8 56-^ 72- -8 72- -8 56- -8 48- -8 40- -8 72^ 32- -8 24- -8 40- -8 16- -8 48- -8 24h 48- -8 64- -8 48- -8 64- -8 32- -8 8-; 32- -8 40- ^8 64- -8 24- -8 24- -8 72-= Ex. 3. (1.) (2.) (3.) (4.) (5.) (6.) 40_^8 32-^8 72-f-8 40-f-8 15-8 48-^8 6x8 4x8 64-^8 6x8 48-f-8 6 + 8 7 + 8 6x8 7x8 72^8 6x8 16-8 16-8 8x8 3x8 9-8 15-8 11-8 17_8 13-8 15-8 7 + 8 94-8 3x8 14-8 5 + 8 12-8 6x8 6 + 8 8x7 LESSON LXXIl. 9 men are once 9 men. 18 boats are 2 times 9 boats. 27 poles are 3 times 9 poles, 36 brido;es are 4 times 9 bridges. 45 trees are 5 times 9 trees. 54 rocks are 6 times 9 rocks. 63 birds are 7 times 9 birds. 72 fishes are 8 times 9 fishes. 81 fish-lines are 9 times 9 fish-lines. Pkoblems.— A man caught 4 fishes the first hour and 7 the next hour, how many did he catch in the 2 hours ? DIVISION. 77 LESSON liXXIII. (See Manual, Sec I., Exercise V.) Copy, complete, and read the following tables : fix. 1. (1.) (2.) (3.) (4.) (5) (6.) 9-f-9 45-^9 45-^9 63^9 72-^9 36-^9 18-^9 27-^9 54-r-9 27-f-9 63-9 63^9 36-T-9 45-^9 36^9 18-^9 54-^9 54^9 27-^9 36-^9 18-f-9 63-^-9 45-^-9 72-^9 18-^9 45-9 9-^9 54^9 72^9 81-^9 27-^9 36---9 27-^9 63^9 27-^9 63-f-9 Ex. 2. (1 ) (2.) (3.) (4.) (5.) (6.) 54_^9 45^9 27-f-9 18-^9 45-^9 18^9 63^9 54-T-9 36-f-9 27-^9 63-v-9 9-^9 81-^9 63-^9 634-9 9-^9 81^9 27-^9 18-^9 81-^9 81-^9 45-^-9 72-^9 63-^9 45-^9 36-T-9 63-^9 27-r-9 81h-9 36-^9 27-^9 63-T-9 54-^9 81-h9 18-^9 45-^9 Ex. 3. (1.) (2.) (3.) (4.) (5.) (6.) 6x8 5x9 6 + 9 9 + 1 45--9 63-^9 81-^9 72-f-9 17-9 9x9 5x9 4x9 8x9 63-f-9 36-^9 27-^9 45^9 9 + 9 3 + 9 18-9 8x9 10-9 5 + 8 9~9 9 + 6 9x9 6 + 9 1 + 9 13-9 8x9 17-9 7x7 17-9 10 + 8 8x8 18-^9 7* 78 FRACTIONS. FEACTIONS. LESSON LXXIV. (See Manual, Sec. I., Exercise VI.) Two halves. Three thirds. Four fourths. Five fifths. How many halves in one apple ? How many halves in one peach ? How many thirds in one pie ? How many thirds in one fish ? How many fourths in one horse? How many fourths in one loaf? How many fifths in one string ? How many fifths in one stick ? One half. One third. Two fourths. Three fifths. How many halves make one melon ? How many thirds make one pear ? How many fourths make one orange ? How many fifths make one apple ? UNITED STATES MINT. money. A mint is the place where money is made. Federal JTIoney. Federal money is the currency of the United States. LESSON LXXV. (See Manual, Sec. I., Exercise VII.) 10 mills (m.) make 1 cent. ct. 10 cents make 1 dime. d. 10 dimes make 1 dollar. $. 10 dollars make 1 ea^le. E. 80 FEDERAL MONEY. American Coins. Copper, Silver. Silver. ENGLISH MONEY. 81 i LESSON LXXVI. (See Manual, Sec. I., Exercise VII) English Money. English money is the currency of Great Britain. TABLE. 4 farthings (far.) make 1 penny. d. 12 pence make 1 shilling. s. 20 shillings make ] ^ P«™^ «/ I £. ^ I sovereign, j Far.— Copper -5 mills. Sov.— Gold— $4 84. Silver— 18 cents. JV^oie. — The franc is a French coin. 82 ENGLISH MONEY. Avoirdupois Weight. Avoirdupois weight is used for weighing all common articles. LESSON LXXVn. (See Manual, Sec. I., Exercise VII.) 16 drams (dr.) make 1 16 ounces make 1 25 pounds make 1 100 pounds or ) ^^^^ 4 quarters ) 20 hundred weight make 1 ton. ounce, pound, quarter, hundred weight oz. lb. qr. i ^''''^Z^ \ cwt. ( weight ) AVOIRDUPOIS WEIGHT. 83 LESSON LXXVIII. Avoirdupois 'Weigbt - Continued. 437i gr. 7000 gr. * jifote. — ^The exact weight of an Avoirdupois dram is I^W Troy grains. 8i TROY WEIGHT. Troy \¥eiglit, Troy weight is used in weighing gold; silver, and jewels, and in philosophical experiments. LESSON LXXIX. (See Maimal, Sec. I., Exercise VII.) 24 grains (gr.) make 1 pennyweight, pwt. 20 pennyweights make 1 ounce. oz. 12 ounces make 1 pound. lb. 3*2 grains make 1 carat. k. 24 grs. 480 grs. 576( Note.Sl grains make a carat, Diamond weight 5760 grs. apothecaries' WEIGfHT. 85 Apothecaries' Weiglit. LESSON LXXX. (See Manual, Sec. I, Exercise VII.) 20 grains (gi\) make 1 scruple, sc. or 3. 3 scruples make 1 dram. dr. or 3 . 8 drams make 1 ounce, oz. or §. 12 ounces make 1 pound, lb. or ft>. ^® 20 grs. 60 grs. 480 grs. 6760. liong Measure* Teacher. — Arthur, can you tell me how far a wile is? Arthur. — If I place 12 sticks an inch long in a row, the row will be Sifoot long. If I make a measure 8 times as long as the row of sticks, it will be a yard measure, like the one on the table. Five and a half times the yard measure will be a rod, and is just the width of the room. Forty times the width of tbe room is the distance between every other telegraph pole, or one furlong. Eight times the distance between every other tele- graph pole is the distance t o the railroad-bridge, or one mile» LONG MEASURE. 871 LESSON LXXXI. (See Manual, Sec. I., Exercise VII.) Long Measure. Long measure is used for measuring distance. TABLE. 12 inches (in.) make 1 foot. ft. 3 feet make 1 yard. yd. ?t ri"? A \ «iake 1 \ ^°^' P^f ^' I rd. 11 halt yards ) ( or pole. ) 40 rods make 1 furlong. fur. 8 furlongs make 1 mile. mi. 69i statute miles | . . . -, 277 quarter miles f "^^^^ ^ ^^S'^^* ^^S- 360 degrees make 1 circle of the earth, cir. Gniiter's Cbain Measure* Gunter's Chain Measure is used by surveyors. TABLE. 25 links (li.) make 1 rod. rd. 4 rods or 1 T -, 1 . -, 100 links \ ""^^'^ ^ ^^^^^°- . ^^- 80 chains make 1 mile. mi. iiM I I 1 Inch. Note. — A link is about 11 inches in length. SQUARE MEASURE, Square Measure. Father. — Charley, if yon wish to know the size of an acre, cut 144 pieces of pnper one inch square, and place them on the tahle; this is cnlled a square /(?o^. To make a square yard^ place 9 single squares in a square, which is just the size of the table. To make a piece of land the size of the grass-plat in the door-yard, it will require 30^^ square yards, which is called a square rod. Forty square rods is just one rood^ or a quarter of an acre of land, and is the size of the lot across the road in which you see the sheep. Four such lots contain 4 roods of land, and is called an acre. SQUARE MEASURE. 89 LESSON LXXXII. (See Manual, Sec. I., Exercise VII.) Square Measure. Square measure is used in computing the area of surfaces. TABLE. 144 square inches (in.) make 1 square foot. 9 square feet make 1 square yard. SOi square yards or ) ^^^^ ^ ^ ^^^ 121 qr. square yards ) ^ .r. 1 1 -I ( rood or quarter 40 square rods make 1 j ^^ ^,^ \^^^^ 4 I "^""^^^l^ ^""'^^ ^'^ I make 1 acre. ^.n 1 -I ( square mile or 640 acres make 1 ^ ^ , . ( section. SurTeyorjs' Square Measure. Surveyors' square measure is used in comput- ing the area or contents of portions of land. TABLE. 625 square links make 1 square rod. sq. rd. 16 square rods make 1 square chain, sq. ch. 10 square chains make 1 acre. A. 640 acres make 1 square mile. sq. mi. 36 square miles make 1 township. T. CUBIC MEASURE, Cubic Measnrc. In building the walls of a cellar, or of a building, the amount of stone or brick used is determined by cubic measure. A cubic inch is a square block 1 inch long, 1 inch wide, and 1 inch thick, thus : t l" l 'l ' I 'I 'I I '! 'l - \ ' I A row of 10 cuLk inches. A tier of 100 cubic inchcB. CUBIC MEASURE. 91 LESSON LXXXIII. (See Manual, Sec. I., Exercise VII.) Cubic Measure, Cubic measure is used to estimate the con- tents of solids. TABLE. 1728 27 40 50 16 8 128 cubic inches cubic feet cubic ft. of round timber or cubic ft. of hewn timber cubic feet cord feet or ) cubic feet ( 24| cubic feet make 1 cubic foot, make 1 cubic yard. - make 1 ton or load. make 1 cord foot. make 1 cord of wood. ( perch of make 1 •< stone or f masonry. Cubic inch. Cubic foot. Cubic yard. 92 WmE MEASURE. "Wine Measure. Wine measure is used in raeasuring liquids. LESSON XXXIX. 4 gills make 1 pint. 2 pints make 1 quart. 4 quarts make 1 gallon. 63* s>r I -*= 1 "'■""• 2 barrels or 63 pt. qt. gal. bbl. ZD 1 ffaUoir'' \ make 1 hogshead, hhd. ^1^^ ,^^^- DEY MEASURE. 93 Dry treasure. Dry measure is used in measuring vegetables and articles not fluid. LESSON LXXXV. (See Manual, Sec. I., Exercise VII.) 2 pints (pt.) make 1 quart. qt. 8 quarts make 1 peck. pk. 4 pecks make 1 bushel. bu. ! 94 MEASURE OF TIME. Ifleasure of Time. Time is the measure of duration. LESSON LXXXVI. (See Manual, Sec. I., Exercise V.) 60 seconds (sec.) make 1 minute. 60 minutes make 1 hour. 24 hours make 1 day. 7 days make 1 week. 4 weeks and 2 days or ) i ,i 30 days J make one month. 365 days make a year. yr, 52 weeks make a year. yr. 12 calendar months make a year. yr. mm. h. da. wk. mo. ■^ CIKCULA.R AND AITGULAE MEASURES. 95 LESSON LXXXVII. (See Manual, Sec. I., Exercise VI.) Circular Measure. Circular measure is used in measuring arcs of circles. TABLE. 60 seconds ('') make 1 minute. ' 60 minutes " 1 degree. ° 90 degrees " 1 quadrant. qad. 4 quadrants " 1 circumference, cir. Angular ITIeasnre. Angular measure is used for measuring differ- ence of directions. TABLE. 60 seconds (") make 1 minute. 60 minutes " 1 degree. ° 90 degrees " 1 right angle, r. a. 96 MISCELLANEOUS TABLES. Season. Winter, LESSON LXXXVIII. Miscellaneous Tables. DIVISION OF THE TEAR. Names of months. 1. January, 2. February, 3. March, 4. April, 5. May, 6. June, 7. July, 8. August, 9. September, 10. October, 11. November, 12. December, No. of days. 31 28 or 29 31 30 31 30 31 31 30 31 30 31 365 or 366 Abbreviations. Jan. Feb. Mar. Apr. Jun. ^ Aug. Sept. Oct. Nov. Dec. COUNTING. 12 units or things make 1 dozen. 12 dozen " 1 gross. 12 gross " 1 great gross. 20 units " 1 score. PAPER. 24 sheets make 1 quire. 20 quires 2 reams 5 bundles " 1 ream. " 1 bundle. " 1 bale. SEASONS. {March, ( June, April, Summer < July, May. I August. I September, i December, October, Winters January, November. ( February, Thirty days hath September, I February hath twenty-eight,* April, June, and November, | And thirty-one the others rate. * Every leap-year, February has twenty-nine days. 98 BOM AN NOTATION. LESSON LXXXIX. Table of Roman Notation. I denotes II III IV " y YI VII VIII " IX X XI XII XIII " XIV " XV XVI « XVII " XVIII " XIX " XX XXI " XXII " XXII " XXIV « one. two. three. four. five. seven, eight, nine. ten. eleven. twelve. thi/teeh. fourteen. fifteen. sixteen. seventeen. eighteen. nineteen. twenty. twenty-one. twenty-two. twenty-three. twenty-four. XXX denotes thirty. ; XL " forty. I L " fifty. ! LX " sixty. LXX " seventy. ; LXXX "eighty. | XC "ninety. C " one hundred. 1 CC " two hundred. CCC " three hundred. CCCC " four hundred. D " five hundred. DC " six hundred. DCC " seven hundred. DCCC " eight hundred. DCCCC " nine hundred. M " one thousand. MD "fifteen hundred MM " two thousand. X " ten thousand. XI " eleven th'sand. M " one million. ; MM " two millions, j FINIS. 5 'ff sai^^