An Elementary Treatise On the Application of the Algebraic Analysis to Geometry

Cover 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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