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[blocks in formation]

or 45610, 1000, and 893

893

43.

47094144
78522048
4842315713782
353336701338908 to 49.

46.

10000000•

19.

22.

9407757-494

8. 99912350214

25.

28.

1.

4. 7398981889800 5.
7. 87846125

10. 2768884-85187 II. 103080207
13. 71625861494 14. 128721301414200

31.

34.

37.

40.

16.

14. 27201490438560034-10
187157296759729-46
18. 14964459409277-63
20. 4031632208110056-69
34045491087172-1

22.

4. 1899328910 8. 5159176101 12. 11019283848 16. 8918232255 770930181732 16261578

13503780000
61286228934
263960779972
6295813800
38114062

20146968
33201610691092
121932631112635269
32228449759163

24. 6897234900

26. 740630987644-33203

28. 48435530-477265

5. 073, 0197, 000001, 00261, and '0001001.

6. 1'54, 24,079, 315.008005, 0011, and '00903.

4. 59648952 8. 274473675 12. 4953087934-4

30. 90000900009-1
32. 1654772

34. 139066-29316950
36. 8485852-43614
38. 4144081-7839494

EXAMPLES, page 20.

3. 2808846363

6. 100100100

NOTATION OF DECIMALS page 23.

I. 3, 03, 003, and 3'3; also '7, 117, 33, and 1'015. 2. 01, 0021, 0117, and '0000003.

3. 7'06, 43°2143, 9'07823457, 1'000001, and 35'721341.

32

4. 10, 150, 1000, 1006000, 18, 183, or 3135, 4, or 321, 198975, $4882,

100

9. 1000622528890200 12. 1202609

15. 607862510254-15696883

7. Two hundred and eighty-three thousandths. Five thousand three hundred and twenty-one ten thousandths, Seventy-four thousand eight hundred and ninety-five hundred thousandths. Eight hundred and twenty-one thounsand and fifty-six millionths. Twenty-seven, and eight thousand three hundred and fifty-four ten thousandths. Thirty-four, and nine ten thousandths. Forty-three, and one hundred and one thousand and seven millionths.

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7.

0000000125; 1250; 125.

8. '00000125; '00001; 2'02.

9.

11900000; 163 the quotient, 036 the divisor, and 005868 the dividend.

10. 8810891; 908.8376804; 1108754; 01745329.

11. 77492-809; 007396 7393'9; 39723.6.

REDUCTION OF DECIMALS, page 31.

I. 4375; 73; 2142857; 34375; 1875; 076923; 0112; 275

2. 5384615; 6470588; 6315789; 185; 7167235; 3183098; 4683544; 0104895.

788260449735. 29'530588194.

1. 2833; 4833; 7; 4166; 8; ·9666

2.

3.

4.

12.175 hours; 00138

IN.M=1'15202 1.M.; 1 I.M.=86804 N.M., 11515, 868421.

5.

6.

997269560 day.

7. 12-5925; 29d-716493055; 15d74229166; 1194.221701388.

8. 8°1875; 19°67916; 104°26875; 82°.325.

9. 37°305; sum 78°755 or 78° 45′ 18′′.

10.

1 Kilomètre

I.

15 cwt, 2 qrs. 4 lbs. 032.

4.

4 cwt. 2 qrs.

7. 0° 17' 44" 8062.

page 34.

1. 0.698970

5. 4'000000

or 6.000000 9. 0380211

13. 1'973128

17. I 397940

or 9'397940 21. 2.380211 or 8.380211

621382 miles; 1 mile 1609315 kilomètres.

I. 3'000000

5. 1'415974

9. 0.890812

page 35.

2.

5.

8.

2. O'954243

6. 1*146128

IO. 1.380211

14. 1698970

or 9.698970 18. 2'954243 or 8.954243 22. 5'544068 or 5'544068

7° 51′ 15′′ 3.

7 cwt. I qr.

3 cwt. I qr. 7 lbs.

LOGARITHMS OF NATURAL NUMBERS, page 40.

3. 3'954243
or 7'954243
7. 1612784

4. 2.000000
or 8.000000

11. T.380211

or 9'380211 15. T.875061

or 9.875061 19. 3.959041

or 7'959041 23. 5'755875 or 5'755875

2. 3'091315

6. 0'415974

10. 2'994581

3.

6.

LOGARITHMS OF NATURAL NUMBERS,

I.

4. 2'557507

2'000000 2. 2.161368 3. 0'468347 6. 2.899820 7. 2'99211I 8. 0681241 9. 0952308 11. T 167317 12. I'954725 13. 2.167317 or 9-167317 or 9'954725 or 8.167317

9.

3. 1'409087

7. 2004751
or 8.004751
2.835247
or 8.835247

II.

64° 22' 57".

10° 52′ 21′′.

12h 44m 28.86.

[blocks in formation]

LOGARITHMS OF NATURAL NUMBERS, page 41.

4. 3'734960 8. 1'977129

I'397940

24. 4·698970 or 6.698970

page 41.

5. 2'828015 10. 0167317 14. 2.627366 15. 5.651278

or 5.651278

12. 3:444669 or 7'444669

1. 4'585179 2. 2.585179

LOGARITHMS OF NATURAL NUMBERS, page 42.

16. 5'562474 17. 2998755

18. 3'507732

19. 5651278

20. 3.000003

3. 4'091491 4. 2'734968 5. 4823904

I.

2.

3.

4.

I.

2.

5.

6.

7.

NATURAL NUMBERS OF LOGARITHMS, page 45.

5760

669000

400000

I'I

20

9'4

14'5

6.49

5. 53 1329 6. 93.8689 456780

7.

NATURAL NUMBERS

1. 853'522

2.

4220'30

3. 71105'9

4.

23000'I

6. 2.639088

7. 1895445
8. 0*343508
9. 1'705864

10. 4'000000

204

4753

8. 586

9. 2:48

10.

9

50

I

100

7. 366.855

3659 9. 418:557

1234

II.

7916

12. 345.6

13. 24.83

14. 7000

10.

II.

12.

13.

8. 543210

666660

9.

10.

98765

II.

843210

12.

123456

13. 342'945

14. 5555'54

NATURAL NUMBERS

3.673 6.004

588-172

594500

14. 264000

15.

1000

16, 2480000

17. 26.0420 18. 15'438

15.

16.

19.

20.

21.

22.

23.

24.

11. 5'301030
12. 7·749845

13.

3'993714

14. 5·808742

15. 3052717

25.

26.

27.

[blocks in formation]

17. 4'000000 18. 4.681241 19. 3'958124 20. 4.763428 2'554755

21.

19.

20.

21.

LOGARITHMS OF NATURAL NUMBERS, page 47.

1.

0'903090 8. 1802774 15. '964240 22. I'972043 29. 4'477134 2. T'000000 9. 3.805501 16. 2953760 3. 0.690196 10. I'165244 4. 1'579784 11. 0.588160 5. 2*579784 12. 3.829561 6. 2'000000 13. 2942504 7. 2.462398 14.

23. 4722552 30. 4000039 24. 4'698970 31. 5774152 25. 5.845154 32. 7'947385 26. 5'421604 33. 2'458852 27. 5.606388 34. 3551938 28. 5699759 35. 4'932847

539954

50000

52790

*5547

*09 '0091

50800

2.606

1'7

16.5137

*009653

I *009

'052

[blocks in formation]

34.

451070 35. 2.71828 36.

27.

28.

page 46.

22. *0002909

23. 0174533

24.

00331098

25. 997270 26. 785398

OF LOGARITHMS, page 47.

28.

29.

30.

3T.

32.

33.

27. 0008567

28. 00003681

404007 37. 763888 100000 38. 4220.30 0762 39. 53°1329 *147 40. 042404 00000075 41. 0048553 1'00043

42. 2'51520

8859000
0918504
5.80693

43. 100591
44. 0002097
75

45.

I.

=

7663.

MULTIPLICATION BY LOGARITHMS, page 50. 3'7745175950; 3'000000 = 1000; 3'0224291053; 3.884399 2'971331936′12; 4·03414710818; 3'494850 = 3125; 3045714=1III. 3. 3.839603 : 6912; 5532375 = 340703; 5908534 810091; 5237543= 172800; 5786113611100.

2.

4. 4586678=38608; 4·677607 = 47600;

2731378538738; 3519872 =

3310 35.

5. 3'971387 = 9362·4; 2993736 = 985.68; 4'659678 = 45674′9; 2·892873 = 7814; 3'4454252788.85.

6. 31002491259'64; 2°511391 = 324'631; 2'935576 = 862·137; 5'000000 =

100000.

7. 5'599311= 397476; 3.590806 = 3897.68; 2.706547 = 508.8; 4'523226 = 33360; 8.825336066886.

8. 5045979111168;

2 6409784375; 2411417257.88;

6.080006

1202283.

9. 2'953494898·45; 1*595937 = 39'44; 2·864036731°2; 9′252805=17898. 10, 179875762'9154; ·260964018237; T·559971 = ·363054.

II.

2'000000 = '01; 5'00000000001; I'000000='1; 5'000000= 100000. 12. 5755418 = '00005694; 46221100004189; 347336800297419; 2629523004261.

DIVISION BY LOGARITHMS, page 53.

I. 191907883; 2.778875601; 1924279 = 84; 2'096910 = 125.

2. 498668096979⋅6; 2'698970 = 500; 1982985 96158; 1775257 = 59.6015.

3. 165321245; 1278754 = 19; 0·857333 = 7·2; 1·822584 = 66·4636.

4. 2462138289·827; 2°525020=334′982; 2°045813=111*125; 1·361728=23 5. 183275268038; 0.561751364545; 030734107333; 3'509203= 3230.

6. 1'000000= 10; 7'425115·266143; 2'376859 = 238155; 2'000000=100. 7. 2264818184; 2'380753=240'3; 3'9466518844'04; 2'797960628. 8. 1'940506 = 87.1978; 179787 = *0151282; 0·176670 — 1°502; 0·833525= 6.81592.

=

9. 5421422263889; 1'421442 = 26·3889; 0'421422 = 2·63889; 3'421422 = 2638 89.

14.6584; 1003528=

10. 405710100011405; 2°537395 = 344663; 1166086

10:0816.

II. 3'339894 = 2187 23; 30047511011; 1172049 = '14861; 3028878 = 1068.76.

12.

= 10000.

0'0000001; 1'000000= 10; 3·000000001; 3.000000 1000; 4'000000

13. 3077427 = 1195*16; 3°112507 = 1295'71.

14. The result of the division is 103275, and the product is identical with it, as far as the sixth decimal figure.

NATURAL SINES AND COSINES, page 55.

Natural Sines.

I. 570774
2. 867085

DDD

3. 947463
4. 370382

5. 723895
6. 974228

7. 800000

8. 997630

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