An Elementary Treatise On the Application of the Algebraic Analysis to Geometry
An Elementary Treatise On the Application of the Algebraic Analysis to Geometry
W S B Wesley Stoker Barker Woolhouse
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ART. PAGE 115. Expression for the angle contained between any two radii vectores, when the equation of the curve involves the radius vector and the perpendicular on the tangent. - 50 116. Expressions for finding the length of any arc of a curve, and also the sectoreal area between any two radii vectores, when the equation expresses the relation be- tween the radius vector aud the perpendicular on the tangent. - - - - - 117. Expression for the radius of curvature in terras of the radius vector a...nd the perpendicular on the tangent. - 51 118. To find the equation of the evolute. . - 119. How the involute may be determined. - - 52 THE MODERN APPLICATION OF THE ALGEBRAIC ANALYSIS TO GEOMETRY. SECTION I. DEFINITIONS AND FIRST PRINCIPLES. ARTICLE 1. ^ Function is any analytical expression, containing one or more variable quantities, combined or not with constant quantities ; it is called a function of the variable quantity, or quantities, which it contains. Thus a; 2 -\- a x, \f (a 2 a; 2 ) are algebraic functions of a?; tan x, which denotes the length of the circular arc whose radius is unity and tangent a 1, is a trigonometric function of x; and a- 2 -{- y 2 - -j- x y, a x -\- by x ^ are algebraic functions of # and y.
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