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COURSE

M A THE MATICS;

- For THE . . Use of ACADEMIES . - As WELL AS /

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THE FIFTH AMERI&h.N, FROM THE NINTH
IONBox EDFTION,
with MANY coroctions. And IMPRovements.
RY OLINTHUS GREGORY, LL.D.

*Corresponding Associate of the Academy of Dijon, Honorary Member of the Lite and Philosophical Society of New-York, of the New-York. Historical Society, of the Liter and Philosophical, and the Antiquarian Societies of Newcastle upon Tyne, of the Cambridge j Society, of the Institution of Civil Engineers, &c. &c. Secretary to the Astronomical Society of London, and Professor of Mathematics is

the Royal Military Academy.

WITH THE ADDITIONS
or

ROBERT ADRAIN, LL.D. F.A.P.S. F.A.A.S., &c.
And Professor of Mathematics and Natural Philosophy.

THE WHOLE

Corrected AND IMPRoved,

WOL. I.

NEW.YORK: . 7. E. D.E.A.JY, PRI.W TER."

t. AND J. SWORDs; T. A. RONALDs; Collins AND Co.; collins AND HANNay; G. AND C. AND H. CARVILL; white, GALLAHER, AND white; O. A. ROORBACH; AND M'ELRATH AND BANGs.

1831.

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southern patrict of New-York, to wit: BE IT REMEMBERED, That on the 22d day of February, Anno Domini 1881, W. E. DeAN, of the said district, hath deposited in this office the title of a book, the title

of which is in the words following, to wit:

... A course of Mathematics; for the use of Academies as well as private tuition. In Two Volumes. By Charles Hutton, LL.D. F.R.S., late Professor of Mathematics in the Royal Military Academy. The Fifth American from the Ninth London Edition, with many corrections and improvements. By Olinthus Gregory, LL.D. Corresponding Associate of the Academy of Dijon, Honorary Member of the Literary and Philosophical Society of New-York, of the New-York Historical Society, of the Literary and Philosophical, and the Antiquarian Societies of Newcastle upon Tyne, of the Cambridge Philosophical Society, of the Institution of Civil Engineers, &c. &c. Secretary to the Astronomical Society of London, and Professor of Mathematics in the Royal Military Academy, with the Additions of Robert Adrain, LL.D. F.A.P.S.F.A. A.S., &c, and Professor of Mathematics and Natural Philosophy. The whole corrected and improved.” - - -

the right whereof he claims as proprietor. In conformity with an Act of Congress, entitled “An Act to amend the several Acts respecting copy-rights.”

FRED. J. BETTS,
Clerk of the Southern District of Wew-York. .

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The present American edition is in part a reprint of the Ninth English edition by Dr. Olinthus Gregony, with most of the improvements introduced into former American editions by Dr. AdRAIN, together with such modifications of the English editions as appeared calculated to in-, crease the general usefulness of the work. At the same time two or three Chapters, devoted to subjects of no great value at present to the American student, have been omitted, to leave room for matter of more interest and importance.

of
WOI. I.

Gangnal Preliminary Principles Pa. } | Involution by Logarithms Pa. 159

Arith METIC. Evolution by Logarithms 100

Notation and Numeration 4 ALGEBRA.

o outon . . . . . : Definitions and Notation - . 162,

Subtraction - - 11 so - - 15;

Multiplication - - 13|R. - - - 1:0

Division - - - 18 ultiplication - - 172

Reduction - - - 23 Division - - .* - 175

Compound Addition - 32 fo. - - - 179

Commissioned Officers' Regimen- É. usion - - !.

tal Pay - - - 35 soon - - - 192

Compound Subtraction - 37 . ‘....' - . . - 196

— Multiplication . ..., Arithmetical Proportion and Pro-

——- Division - - 42 , Kresso - - - 203

Golden Rule, or Rule of Three - 45 Piles of Shot and Shells - 207

Compound Proporticn - ; Geometrical Proportion and Pro-

Vulgar Fractions - - ? | Ins gression . . . . - 212

Reduction of Vulgar Fractions g;|Infinite Series, and their Summa-

Addition of Vulgar Fractions - 61 so E - - - - 214

Subtraction of Vulgar Fractions 63 o e Equations - - #

Multiplication of Vuig at Fractions. ib. { o: : Equations ... - :

Division of Vulgar Fractions . .64}'s...}. Higher Equations - 2 ;

Rule of Three in Yulgar Fractions 65 ë. Interest - - - 26

Decimal Fractions '''“...;|Compound Interest - - 267

Addition of Decimals - . . .# Anguties - - - . 270

Subtraction of Decimals. . . . . . . . $3

Multiplication of Decimals. ... ib. . . . . GEOMETRY.

Division of Decimals. . . . . 2.76. Thefinitions and Remarks - - 275

Reduction of Decimald ... • , , o, . Axjqms - - - 281

Rule of Three in Decimals . 76 . Theorems - - - ib.

Duodecimals - - 37 || Of Ratios and Proportions—Defi-

Involution - - - 78 nitions - - - . 318

Evolution - - - 80 Theorems - - - 320

To extract the Square Root - 81 Q: Planes and Solids—Definitions 338

To extract the Cube Root - 85 Theorems - - - 340

*To extract any Root whatever - 88 Problems - - - 355

Table of Powers and Roots - 91 | Application of Algebra to Geome-

Ratios, Proportions, and Progres- try - - - - 371

sions - - - - Problems - - - 372

Arithmetical Proportion - 112|Plane Trigonometry - . 378

Geometrical Proportion - - 116|Trigonometrical Formulae - 393

Harmonical Proportion - 121 | Heights and Distances : - 396

Fellowskip, or Partnership - 122|Mensuration of Planes or Areas 405

Single Fellowship - - ib. Mensuration of Solids - • 420

Double Fellowship - - 125 | Land Surveying - - 430

Simple Interest - - . 127 |Artificers.Works - - 459

Compound Interest - - 130|Timber Measuring - - 468

Alligation Medial - - 132|Qonic Sections - -- - 472

Alligation Alternate - - 133 Of the Ellipse - - 476

Single Position - - 136|Qs the Hyperbola - - 494

Double Position - - 138 . Of the Parabola - - 518.

Practical Questions - 141 É. o: Sections - §

quations of the Curve -

LOGArithms S, Elements of Isoperimetry - - 539

Definition and Properties of Loga- Surfaces - - - 541

rithms - - - - 146 | Solids - - - - 551

To compute Logarithms - 149 |Practical Questions in Mensuration 562

Description and Use of Logarithms 153 Logarithms of Numbers.- - 571

Multiplication by Logarithms - 157|Table of Logarithmic Sines, and

Division by Logarithms - 158 | Tangents - - 590

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