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(T. S.) The following Tables furnish 741 questions, formed by Multiplication, Division, and the Square and Cube Roots, with answers to each operation,

For example. I will take the Number 36 in the first column, and require that number to be multiplied by 36, and the answer is 1296, in the same line. Again, 1296 x 36=16656 Ans, and 46656;-1996=36 and 46656436=1296. require the square root of 36, and in the same line you find the answer, 6.000000. Require the Cube Root of 36. Ans. 3.301927. Number. Square. Cube. Square Root. Cube Root. 1 1

1 1.0000000 1.000000 4

8 1:4142136 1.259921 9

27 1.7320508 1.442250 16

64 2:0000000 1:587401 25

125 2:2360680 1.709976 6 36

216 2:4494897 1.817121 7 49

343 2.6457513 1.912933 64

512 2.8284271 2'000000 81

729 3:0000000 2'080084 10

1000 3 1622777 2:154435

1331 33166248 2:223980 12

1728 3:4641016 2:289428 13 169 2197

36055513 2-351335 14

2744 37416574 2 410142 15

225 3375 3.8729833 2 466212 16 256 4096 4'0000000 2'519812 17 289 4913 4:1231056 2571282 18 324 5832 42426407 2620741 19 361

6859 4:3588989 2 668402 20 400 8000

4.4721360 2.714418 21 441

9261 4-5825757 2.758.923 22

484 10648 4 6904158 2*802039 23

529 12167 4.7958315 2 843867

576 13824 4 8989795 2*884499 25

625 15625 5:0000000 2924018 26 676 17576 5.0990195 2.962496 27

19683 5.1961524 3.000000 28

784 21952 5.2915026 3.036589 841 24389

5.3851648 3:072917 30 900 2.000

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132 A Table of Squares, Cubes, and Roots.

39

Number. Square.

36 1296
37 1369
38 1444

1521 40 1600 41 1681 42 1764 43 1819 44 1936 45 2025 46 2116 47 2209 48 2304 49 2401 50 2500 51 2601 52 2704 53 2809 51 2916 55 3025 56 3136

3249 58 3364 59 3181 60 3600 61 3721 62 3844 63 3969 64 4096 65 4225 66 4356 67 4489

4624 69

4761 70

4900 71

5041 72 5184 73 5329 74 5476 75 5625 76 5776 77 5929 78 6084 79 6241

6400

57

Cube. 46656 50653 54872 59319 64000 68921 74088 79507 85184 91125 97336 103823 1 10592 117649 1 25000 132651 140608 148877 157464 166375 175616 185193 195112 205379 216000 226981 238328 250047 262144 274625 287496 300763 314432 328509 343000 357911 373248 389017 405224 421875 438976 456533 474552 493039 512000

Square Koot.

6•0000000 6-0827625 6.1644140 6.2449980 6:3245553 6.4081242 6.4807407 6.5574385 6-6332496 6.7082039 6 7823300 6.8556546 6.9282032 7.0000000 7.0710678 7.1414281 7.2111026 7.2801099 7:3484692 704161985 7.4833148 705198344 76157731 7.6811457 77459667 78102497 708740079 7.9372539 8:0000000 8:0622577 8.1240384 8:1853528 8.2462113 8:3066239 8:3666003 8:4261498 8.4852814 8.5440037 8.6023253 8.6602540 8.7177979 8.7749644 8.8317609 8.8881944 8*9442719

Cube Root. 3:301927 3:332222 3.361975 3:391211 3:419952 3:448217 3:4760:27 3 503398 3.530348 3.556893 3:583048 3.6088:26 3.634241 3.659306 3.68 1031 3708130 3732511 3:756286 3779763 3.802953 3.825862 3848501 3870877 3-892996 3.914867 3936497 3.957892 3979057 4.000000 4'020726 4041240 4'061548 4'081656 4:101566 4'121285 4:140818 4'160168 4:179339 4.198336 4'217163 4.235824 4.254321 4.272659 4.290841 4:308870

68

80

81.

91

Number. Square.

6561 82 6724 83 6889 84 7056 85 7225 86 7396 87 7569 88 7744 --89 7921 90 8100

8281 92

8464 93 8649 94

8836 95 9025 96 9216 97 9109 98 9604 99 9801 100

10000 101 10201 102

10104 1 103 10600 104

10816 105 11025 106 11236 107 11419 108 11664 109 11881

12100 Ill

12321 112 12544 113 12769

12996 115

13225

13456 117

13689.

13924 119 14161 120 14400 121 14641 , 122 14884 123 15129 124 15376 125 15025

Cube. 531441 551368 571787 592701 614125 636056 658503 681472 704969 729000 753571 778688 804357 830584 857375 884736 912673 941192 970299 1000000 1030301 1061208 1092727 1124864 1157625 1191016 1225043 1259712 1295029 1331000 1367631 1404928 1442897 1481544 1520875 1560896 1601613 1643032 1685159 1728000 1771561 1815848 1860867 1906624 1953125

Square Root.

9.0000000 9.0553851 9:1104336 9:1651514 9.2195445 9.2736185 9:3273791 9.3808315 9.4339811 9*4868330 9:539392) 9'5916630 9'6436508 9'6953597 9°7467913 9:7979590 9'8188578 9'8994949 9'9198744 10'0000000 10'0498756 10'0995049 10*1188916 10'1980390 10'2469508 10'2956301 10'3440804 10'3923048 10'4403065 10*4880885 10 5356538 10'5830052 10'6301458 10'6770783 10*7238053 10 7703296 10'8166538 10'8627805 10'9087121 10'9544512 11'0000000 1'0453610 11'0905365 11'1355287 11'1803399

Cube Root. 4:326749 4:344481 4:362011 4.379519 4.396830 4.414005 4.431017 4.417960 4.461745 4.481405, 4.497942 4.514337 4.530655 4.546836. 4 562903 4.578857 4 594701 4.610436 4.626065 4 641589 4.657010 4 672330 4.687548 4.702669 4.717694 4.732624 4:747459 4.762203 4776856 4.791420 4.8 7.820284 4.831588 4.848808 4.862944 4.876999 4.890973 4.904868 4 918685 4.932424 4.916088 4.959675 4.973190 4 986631 5.000000

110

114

116

118

THI

SIMPLE INTEREST. NHERE are five letters to be observed in Simple Interest, viz.

P the Principal.
T the Time.
R the Ratio, or rate per cent.
I the Interest.
A the Amount
A TABLE OF RATIOS.

8

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3 .03

54

,055 34 ,,035

6
,06

8 ,085
.04

61
,065

,09
,045

7
,07

91 ,095
,05

75 ,075 10 ,1 Note. The Ratio is the Simple Interest of £1. for one year, at the rate per cent. proposed, and is found thus :

£. £. £.
As 100: 3::1:,03.

As 100 : 3,5 ::1:,035. When the Principal, Time, and Rate per cent. are given to find the

Interest.
Rule*. Multiply the principal, time, and rate together, and
It will give the interest required.

Note. The proposition and rule are better erpressed thus :
I. When P, R, T, are given to find I.
ROLE. prt=1.

Note. When two or more letters are put together like a word, they are to be multiplied one into another.

EXAMPLES.

1. What is the interest of £945...10...0 for three years, at 3 per cent per annum?

Ans. £945,5 X ,05X3=141,825, or £141...16. .6. -2. What is the interest of £547...14...0 at 4, per cent. per annum, for 6 years ?

Ans. £131...8...11. 2 qrs. ,08. 3. What is the interest of £796... 15...0 at 45 per cent. per annum, for 5 years ?

Ans. £179...5...4. 2 grs. 4. What is the interest of £397...9...5 for 2 years and d, at 32 per cent. per annum ?

Ans. £34...15...6. 3,55 qrs. 5. What is the interest of £554...17...6 for 3 years 8 months, at 45 per cent. per annum

Ans. £91...ll..... 2 qro.

See the demonstration of this and the following rules in the Algebraist's Assistant.

.

0. What is the interest of £236... 18...8 for 3 years 8 months, at 5. per cent. per annuin ?

Ans. £47...15...7,203. When the Interest is for any Number of Days only. Rule. Multiply the interest of £l. for a day, at the given rate, by the principal and number of days, it will give the answer

INTEREST of £1. FOR ONE DAY
Per Cent. Decimals.

Per Cent. Decimals.
3
,000082 9178

6} 00017809219
3
,0000.7589041

7

,00019178082 ,000 10958904

72 ,00020547915 ,00012328767

,00021917818 ,00013695630

81 ,00023287671 5 ,00015068193

,00024657534 6 ,00016138356

9} ,00026027597 Note. The above Table is thus found ;

As 365 : ,03 :: 1 :,00008219178. And as 365 : ,035 :: 1: .00009589011, &c.

ZXAMPLES. 7. What is the interest of £240 for 120 days, at 4 per eent. per annum ?

Ans, 00030958904 x 240 x 120=£3. .3...11.

х 8. What is the interest of £361...18 ..0 for 154 days, at per cent. per annum ?

Ans. £7... 13...11 y. What is the interest of £725...15...0 for 74 days, at 4 per cent per annum. ?

Ans. £5... 17...S4. 10. 'What is the interest of £ 100 from the 1st of June 1755, to the 9ih of March following, at 5 per cent. per annum ?

Ans. £3...16..JI. ll. When P, R, T, are given to find A. RULE. prt +p=A.

EXAMPLES.

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11. What will £279... 12 ..0 amount to in 7 years, at 4 per cent per annum?

Ans. £367...13...5, 3,04 qr's.

279,6 x ,015 ~ 7 + 279,6=367,674. 12. What will $320...17. .O amount to in 5 years, at 3. per cent. per annum ?

Ans. £376... 19... 1.2,8 qrs. When there is any odd time giren with the whole years, reduce the odd time into days, and work with the decimal parts of a year which are equal to ihose days.

13. What will £926.. 12.. O amount to in 5 years £, at 4 per cont. per annum. ?

Ans. £1130 ..9.... 1,92 qrs. 14. What will € 273...19.0 amount to in 4 years, 175 days, at 3 per cent. per annum ? Ans. £310...14...13,38480064 qrs

Ill. When A, R, T, are girer, to find P.

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RULE

*P.

at + 1

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