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ELEMENTS OF EUCLID-Book XI. - - ...;

Book XII. - - 3.18

PLANE TRIGONOMETRY - - - - 34.5

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

SPHERICAL 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 - - - - 407

OF THE ELLIPSE - - - - - 410

OF THE HYPERBOLA - - - - 4.18

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 Dinostrate - 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 - - - 464

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 - - - - - 486

On the Integration of Fluxions containing Sines, Co-

491

sines, &c. - - - - -

627

635

Of Measuring Timber - - - 646

Miscellaneous Questions - ' - - 647

LAND SURVEYING - - - - 651

GAUGING - - - - - - 663

MECHANICS - - - - - 673

Matter, Motion, Forces, &c. - - - ib.

On the Laws of Motion - - - 677

Of Uniform Motions - - - - ib.

On the Motion of Sound - - - 679

On the Motions of Bodies accelerated or retarded by

the action of constant and uniform Forces - 680

On the Laws of Gravity, and the descent of Heavy

Bodies - - - - - 684

Of the Composition and Resolution of Forces - 687

On the Collision of Bodies - - - 691

On the Collision of Elastic Bodies - - 694

On the Mechanical Powers - - - 698

On the Wheel and Axle - - - 703

On the Pulley - - - - 704

On the Inclined Plane - - - 706

On the Wedge - - - - 707

On the Screw - - - - 709

On the Motions of Bodies on the Inclined Planes 710

On the Motions of Projectiles without resistance 713

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G L OSS ARY OF TERMS, 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, terminated at some certain point, by an ordinate to a curve. 45solute Number, in Algebra, that term or number of an equation, that is completely known. Abundant Number, in Arithmetic, a number the sum of whose aliquot 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 contiguous 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 Positive 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 without a remainder. Alternation or Permutation 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.

Approximation, 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 sign + or -.

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