CONTENTS. On the method of finding Multipliers which shall render Binomial Surd Quantities Rational Page ELEMENTS OF EUCLID-Book XI. - - ...; 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- Application of the preceding Principles and Pro- Example of Right-Angled Spherical Triangles - 383 Examples of the cases of Oblique-Angled Spherical Origin and General Equation of the Conic Sections 404 OF SEVERAL OTHER CURVES - - - 426 I. The Conchoid of Nicomedes - ib. II. The Cissoid of Diocles - - 428 III. The Logarithmic Curve - - 429 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 Rules for finding the Fluxions of any Proposed Of Logarithmic and Exponential Fluxions - 443 Of the Fluxions of Sines, Cosines, &c. and other 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 sines, &c. - - - - - THE INVERSE METHOD OF FLUXIONS - 502* ON THE QUADRATURE OF CURVES - - ib. ON THE RECTIFICATION OF CURVES - - 508” ON THE CUBATURE OF SOLIDS - - 512° On the Curvilinear Surfaces of Solids of Revolution - 514* Descriptions of Instruments useful in Projections ib. PERSPECTIVE Part I. - - - - 519 PROJECTION OF A SPHERE IN PLANO - 347 STEREOGRAPHIC PROJECTION OF A SPHERE 551 GNOMONICAL PROJECTION OF THE SPHERE 561 627 635 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 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 -. |