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PREFACE
TO THIS NEW IMPROVED (THIRD) EDITION.

THE demand for this work still continuing, not willstanding the publication of other works on Arithmetick and the higher branches of the Mathematicks, is evidence of its intrinsick merit, and has induced the Proprietors of the copyright to present ihe publick with a new and improved Edition.

Application was made to the Author, requesting him to revise and improve the work for a new Edition ; but he declined on account of want of health, and the Gentleman, whom we employed, was engaged by the Author's consent, and improved and corrected the work agreeably to his dire&ions and advice.

The most important improvement in this Edition, is the introduction of exam. ples in the Federal Currency under each rule ; and while this was considered necessary, in order to extend the knowledge and use of that

currency,

it thought important not to omit examples in pounds, shillings and pence, which are, and will continue to be, the basis of many arithmetical questions ; and therefore an acquaintance with them will always be useful.

Mr. Nathanie LORD, 3d. of Ipswich, the Gentleman employed to correct and improve the work, has bestowed much attention upon it, and has received from Mr. Pike all the information and advice he desired. The manner in which Mr. Lord has executed the task entrusted to him, will, we hope, gain additional reputation for the work, and entitle him to the thanks of the publick.

THOMAS & ANDREWS. Boston, April, 1808.

was

Some errours, which escaped corre&ion, are noticed in an errata, at the end of the work.

in Federal Money

231

233

234

234
239

243

Discount

349

Use of the Barometer in Measuring Heights

353

Table of the Weight of Money

354

of Exchange

355

ditto

356

Table of the Value of sundry Pieces in the several States

357

of Commilion

358

of the net Proceeds, after the Commissions at 24 and 5 per cent. are

deducted

359

Table Thewing the number of Days from any day in one month to any day

in any other month

360

'Table of the Measure of Length of the principal places in Europe compar.

ped with the American Yard

361

Table directing how to buy and sell by the Hundred Weight

362

Comparison of the American Foot with the Feet of other Countries

365

Table to cast up Wages or Expenses for a year, at so much per day, week, or

month

364

Table to find Wages, or Expenses for a month, week or day, at so much per

year

964

A Perpetual Almanack

365

Tables reducing Troy Weight to Avoirdupois, and the contrary

966

An

ters

Page

An Account of the Gregorian Calendar, or New Style

967

Chronological Problems

367

Problem 1. To find in which Century the last year is to be Leap year, and the

contrary

367

Prob. 2. To find, with regard to any other Years, whether any Year he Leap-

Year, or not

368

3. To find the Dominical Letter according to the Julian Method 368

To find the same according to the Gregorian Method

360

5. To find the Prime, or Golden Number

970

6. To find the Julian Epact

370

7. To find the Gregorian Epact

971

To find the same forever

371

8. To calculate the Moon's Age on any given Day

372

9. To find the Times of the New and Full Moon, and first and last Quar-

378

10. Having the time of the Moon's Southing given, to find her Age 374

11. To find the time of the Moon's Southing

374

12. To find on what Day of the Week any given day in any

month

will fall

$75

13. To find the Cycle of the Sun

375

Table of the Dominical Letters according to the Cycle of the Sun

376

Prob. 14. To find the Year of the Dionyfian Period

376

15. To find the Year of Indiion

376

16. To find the Julian period

977

17. To find the Cycle of the Sun, Golden Number, and Indićtion, for

any current year

377

18. To find the Time of High Water

378

19. To find on what day Easter will happen

378

Table to find Easter from the year 1755 to 4199

380

The Use of Logarithms.

380

Plain Geometry

882

Plain Rectangular Trigonometry

986

Plain Oblique Angular Trigonometry

390

Trigonometry applied to the Mensuration of Heights and Distances 394

Mensuration of Superficies and solids

396

Section 1. Of Superficies

396

Article 1. To measure a Square

396

2. To measure a Parallelogram, or Long Square

397

3. When the Breadth of a Superficies is given to find how much in

Length will make a Square Foot, Yard, &c.

597

4. To measure a Rhombus

397

5. To measure a Rhomboides

398

6. To measure a Triangle

398

7. Another method of finding the Arca of the Triangle

400

8. To measure a Trapezium

400

9. To measure any Irregular Figure

401

10. To measure a Trapezoid

402

11. To measure any Regular Polygon

402

12. Having the Diameter of a Circle, to find the Circumference 404

13. Having the Circumference, to find the Diameter

405

14. To find the Area of a Circle

405

15. Having the Diameter, to find the Area, without the Circumference 406

16. Having the Circumference, to find the Area without the Diameter 406

17. Having the Dimensions of any of the parts of a Circle, to find

the side of a Square, equal to the Circle

406

18. Having the Area of a Circle, to find the Diameter

407

19. Having the Area, to find the Circumference

407

20. Having the side of a Square, to find the Diameter of a Circle,

which thall be equal to the Square whose side is given

408

Article 21.

B

Article 21. Having the side of a Square, to find the Circumference of a Cir-

cle equal to the given Square

408

22. Having the Diameter of a Circle, to find the Area of a Semicircle 408

23. Having the Segment of a Circle, to find the Length of the Arch Line 408

24. Having the Chord and Versed Sine of a Segment, to find the Di-

ameter of a Circle

409

25. To measure a Sector

401
26. To measure the Segment of a Circle

401

27. To measure an Ellipsis

412

Directions for applying Superficies to Surveying

413

Section 2. Of Solids

413

Article 28. To measure a Cube

413

29. To measure a Parallelopipedon

415

Having the side of a Square Solid, to find what Length will make

a Solid Foot

417

30. To measure a Cylinder

418

Having the Diameter of a Cylinder given, to find what length will

make a Solid Foot

418

To find how much a round tree, which is equally thick, from

end to end, will hew to when made Square

419

31. To measure a Prism

419

32. To measure a Pyramid or Cone

420

33. To measure the Frustum of a Pyramid or Cone

422

34. To measure a Sphere or Globe

424

35. To measure a Frustum or Segment of a Globe

425

36. To measure the middle Zone of a Globe

426

37. To measure a Spheroid

426

38. To measure' the middle Frustum of a Spheroid

426

39. To measure a Segment, or Frustum of a Spheroid

426

40. To measure a Parabolick Conoid

427

41. To measure the lower Fruftum of a Parabolick Conoid

427

42. To measure a Parabolick Spindle

427

43. To measure the middle Zone, or Frustum of a Parabolick Spindle 427

44. To measure a Cylinderoid or Prismoid

428

45. To measure a solid Ring

428

46. 'To measure the Solidity of any irregular Body whose Dimesions

cannot be taken

428

Of the five Regular Bodies

429

47. To measure a Tetraedron

429

48. To measure an Octaedron

430

49. To measure a Dodecaedron

50. To measure an Eicosiedron

430

51. To gauge a Calk

431

52. To gauge a Mash Tub

432

53. Having the Difference of Diameters, Height and Content of a

Math Tub, to find the Diameters at Top and Botton

432

54. To ullage a Caik, lying on one side, by the Gauging Rod

432

55. To find a Ship’s Tonnage

432

'The Proportions and Tonnage of Noah's Ark

434
Questions in Mensuration

434

Algebra

439

Conick Sections

471

EXPLANATION

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