CONTENTS. Page xi Resolution of Cubic and Higher Equations The Reduction of Surd Quantities The Addition and Substraction of Surd Quantities 88 The Multiplication and Division of Surd Quantities 89 On the Involution and Evolution of Surd Quantities 90 On the method of finding Multipliers which shall render Binomial Surd Quantities Rational 91 On extracting the Roots of Binomial Surds 233 -Book VI. 1:1 407 Page Theory and Arithmetic of Sines Calculation of the Tables of Sines, by Series Solution of the Cases of Plane Triangles 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- 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 V. The Quadratrix of Dinostrates VIII. The Hyperbolic or Reciprocal Spiral 435 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 OF THE INVERSE METHOD OF FLUXIONS Of Quantities Susceptible of an Exact Integration On the Integration of Rational Fractions Of the Integration of Logarithmic and Exponential On the Integration of Fluxions containing several varia- THE INVERSE METHOD OF FLUXIONS ON THE RECTIFICATION OF CURVES On the Curvilinear Surfaces of Solids of Revolution Descriptions of Instruments useful in Projections ib. PROJECTION OF A SPHERE IN PLANO STEREOGRAPHIC PROJECTION OF A SPHERE 551 GNOMONICAL PROJECTION OF THE SPHERE PRACTICAL CONSTRUCTION OF MAPS Of Measuring Irregular Surfaces and Solids 640 On the Motions of Bodies accelerated or retarded by the action of constant and uniform Forces On the Laws of Gravity, and the descent of Heavy Of the Composition and Resolution of Forces 687 On the Collision of Elastic Bodies On the Motions of Bundies on the inclined Planes 710 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. Afirmative 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 -. |