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ELEMENTS OF EUCLID_Book XI.

283

-Book XII.

318

PLANE TRIGONOMETRY

345

Theory and Arithmetic of Sines

ib.

Calculation of the Tables of Sines, by Series

340*

Solution of the Cases of Plane Triangles

348

Triigonometry applied to Heights and Distances 361

SPHERICĂL TRIGONOMETRY

361

Miscellaneous Examples on Heights and Distances 367

Principles and Proportions for the Solution of Sphe-

rical Triangles

375

Application of the preceding Principles and Pro-

portions

379

Example of Right-Angled Spherical Triangles 383

Examples of the cases of Oblique-Angled Spherical

Triangles

393

CONIC SECTIONS

397

Origin and General Equation of the Conic Sections 404

OF THE PARABOLA

OF THE ELLIPSE

410

OF THE HYPERBOLA

418

OF SEVERAL OTHER CURVES

426

I. The Conchoid of Nicomedes

ib.

II. The Cissoid of Diocles

428

III. The Logarithmic Curve

429

IV. The Cycloid

430

V. The Quadratrix of Dinostrates

431

VI. The Spiral of Archimedes

433

VII. The Parabolic Spiral

434

VIII. The Hyperbolic or Reciprocal Spiral 435

IX. The Logarithmic Spiral

436

FLUXIONS

437

Rules for finding the Fluxions of any Proposed

Functions

440

Of Logarithmic and Exponential Fluxions - 443

Of the Fluxions of Sines, Cosines, &c. and other

Circular Functions-

445

Application of Fluxions to the Theory of Curves 447

Of Involute and Evolute Curves

452

Of Vanishing Fractions

OF THE INVERSE METHOD OF FLUXIONS

467

Of Quantities Susceptible of an Exact Integration

ib.

On the Integration of Rational Fractions

474

Of the Integration of Logarithmic and Exponential

Fluxions

On the Integration of Fluxions containing Sines, Co-

sines, &c.

491

USED IN THE MATHEMATICAL SCIENCES.

Abbreviation, in Arithmetic, &c. the reducing of Fractions to lower

terms. Aberration, in Astronomy, an apparent motion of the celestial bodies. Absciss, or Abscissa, is a part or segment cut off from a line, ter

minated at some certain point, by an ordinate to a curve. Absolute Number, in Algebra, that term or number of an equation,

that is completely known. Abundant Number, in Arithmetic, a number the sum of whose ali.

quot parts is greater than the number itself. Accelerated Motion, that which receives fresh accessions of velocity,

either uniform or variable. Adjacent angle, in Geometry, an angle which is immediately conti

guous to another, so that they have one common side. Affected or Adfected Equation, in Algebra, one which contains two,

or more several powers of the unknown quantity. Affirmative or Posilive quantity; one, which is to be added, or taken

effectively. Algebra, a method of performing the calculations of all kinds of

quantities by means of general signs or characters. Aliquot part, such a part of a number as will exactly divide it with

out a remainder. Alternation or Permulation of quantities, the varying or changing

the order or position of them. Analysis, the method of resolving problems by reducing them to

equations. Angle in geometry, the mutual inclination of two lines, or two

planes. Approrimation, a continual approach, nearer and nearer to a root or

any quantity sought. Apses or Apsides, are the two points in the orbits of planets, when they are at their greatest and least distance from the sun or the

earth, and the line which joins them is called the sign of Apsides. Asymptote, properly a right line which approaches nearer and nearer

to some curve, or it may be considered as a tangent to the curve,

when conceived to be infinitely produced. Ariom, a self-evident truth, or a proposition immediately asserted

to, when the terms of it are properly understood. Azis, in Geometry, the straight line in a plain figure, about which

it revolves, to generate a solid. Binomial, a quantity consisting of two terms or members connected

by the sigi. + or -.

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