Page images
PDF
EPUB

Fromthe logarithm of the dividend, viz. 1425=3,15381 Take the logarithm of the divisor, viz. 57 = 1,75587

And the remainder is the loga

rithm of the quotient, viz.

}

3. IN THE RULE OF THREE.

25-1,3979

Three numbers given to find a fourth, in direct proportion. RULE. From the tables take the logarithms of each of the proposed numbers, then add the logarithms of the fecond and third together, and from the sum take the logarithm of the first and the remainder will be the logarithm of the fourth number.

Let the three proposed numbers be 18, 24 and 33, and the operation will stand thus :

1,38021 the logarithm of 24, the 2d. term. 1,51851 the logarithm of 33, the 3d. term. 2,89872 the logarithm of their product. -1,25527 the logarithm of the 1st term 18.

1,64345 the logarithm of the 4th term required, which, by the Table answers to the natural number 44, the 4th proportional to the three proposed numbers.

4. IN INVOLUTION, OR RAISING POWERS. To find any power of any proposed number, or to involve any number to any proposed power, by logarithms. RULE. Multiply the logarithm of the given root by the power, viz. by 2 for the square, by 3 for the cube,&c. and the product is the logarithm of the power fought. Required to find the cube of 12? 1,07918=the logarithm of 12.

X3=the third power, or cube.

A

3,23754-1728 the cube of 12.
5. IN EVOLUTION, OR EXTRACTING ROOTS.

To Extract any root of any proposed number. RULE. Divide the logarithm of the proposed number by the index of the required root, viz. by 2 for the square, by 3 for the cube, &c. and the quotient will be the logarithm of the root required. Required

Required to find the cube root of 1728 ? 3,23754 the logarithm of 1728, and 3,237543=1,07918 is the logarithm of the cube root of 1728,

Viz. 12.

6. IN COMPOUND INTEREST.

To find the amount of any fum for any time, and at any rate at compound interest.

RULE. Multiply the logarithm of the ratio (i. e. the amount of 11. for 1 year) by the number of years, and to the product add the logarithm of the principal; the fum will be the logarithm of the amount.

What will 451. amount to forborne 12 years, at 6 per cent. per annum, compound interest ? Log. of 1,06, the ratio, is,02533 Multiply by the time

12

,30396

Add Log. of 45, the principal 1,65321

The fum is 1,95717 which is the logarithm of 90,7-190 145. Anf.

7. IN DISCOUNT AT COMPOUND INTEREST. To find the present worth of any sum of money, due any time hence, at any rate, at compound interest.

RULE. From the logarithm of the fum to be dif counted, fubtract the logarithm of the rate multiplied by the time; and the remainder is the logarithm of the present worth.

What prefent money will pay a debt of gol. 145. due 12 years hence, discounting at the rate of 6 per cent. per annum ?

From the logarithm of 901. 14=1,95717

Sub. product of the Log. of the

ratio X by the time.

}

=

30396

The remainder 1,65421 is the

logarithm of 451. Anf. N. Ham.

[merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small]

2 10 0 1

31502

11 18 35
68

52 10 2 28 70

6

40013,33 568 5003 50016,666134650 31793 87 10 7 10 0 4 13 4 105

60020,00

1

8

00

70023,333 968815 0 58108 122 10 80 026,663 10 13 4 10

[blocks in formation]

006453140

[blocks in formation]

100033,33 1368 12 10 0 7 15 68 175

Federal

[merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][subsumed][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small]

50,001500

181501113 4

165 10

20 00

A TABLE

[blocks in formation]

347

A TABLE, directing how to buy and sell by the

d. . s. d. s. d.

○○○○○○○○

141234

24

48

666688

141234

Hundred.

[blocks in formation]

3 17 0

I

3 194

I

42 7 140이

318

I

44

7164

4 40

I

1

1

94 4.11 0

I

10

55536

7 18 8

54

14123

[blocks in formation]

34

[blocks in formation]
[blocks in formation]

6

880

[blocks in formation]
[blocks in formation]

I

34

[blocks in formation]

I

58

104

[blocks in formation]

I

80

11

[blocks in formation]

1 10 4 II

1 12 8

11

34

1150

II

141234

[blocks in formation]
[merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small]

5120

514

5 16

05190

1

48

[blocks in formation]

677778888

74

2

89

[blocks in formation]
[blocks in formation]
[blocks in formation]
[blocks in formation]

2 11 4

2 13 8

[blocks in formation]

14123-4

[blocks in formation]

648104

68 128

68150

8 17 4

819 8

I 7호 9

[ocr errors]

20

74944

84990

I 81

1

914

9 130 9160

949 18 4

9 10 08

94 10

896

[blocks in formation]

3억

[blocks in formation]
[blocks in formation]

6

141234

141234

[blocks in formation]

2 18 4

[blocks in formation]

63

08 I 2

[blocks in formation]

141234

613 0

6154

[blocks in formation]

6 17 8

3

4

1 10 10 12

[blocks in formation]
[ocr errors][merged small]
[blocks in formation]

74 3 12 4 3 14 8

1

141234

[merged small][merged small][merged small][merged small][ocr errors]

34 770

[ocr errors]

141-23-4

[blocks in formation]
[ocr errors][merged small][merged small][merged small]
[blocks in formation]
« PreviousContinue »