co.vrjr.vra 



.ation of a normal to a given dreie . 147 



b6. Lengths of tangenta and normals. Subuugenu and sub- 



normal - . . l ; 



87. Tangent and normal lengths, subtangent and subnormal, for 



88. To find the length of a tangent from a given external pmnt 



to a given circle . 



80. 1 . jHMut ouuide of a circle two tangents to the circle 



can be drawn 



00. Chord of contact 



01. Poles and polara ... .156 



03. Fundamental theorem 



04. Geometrical construction for the polar of a given point, and 



fr the pole of a given lin\ ith regard to a given circle 



05. Circles through the intersections of two given circles . . 160 



06. Com . 160 



07. Radical axis; radical center . . . 161 



08. The equation of a circle : polar coordinates .... 162 

 00. i of a circle referred to oblique axes .... 168 



100. The angle for . intersecting curves . ... 164 



(H \ITI.I: vin 



^ECTIOKS 



101. Recapitulation ......... I7 ft 



I. 7V Ptinthola 



Special I of Second Degree 



Ax* + 2 ' / + C = 0, or By* + 2 CiVr + 2 A> + C 



. 170 



t standard form of the f the parabola . - 171 



To trace the parabola y = 4 j,r . 17* 



105. Lain* rtt tun: . 17J 



106. Geometric property of the parabola. Second standard equa- 



. 



107. Every equation of th<> f 



Ax* + 2 Gx 4- 2 Fy + C * 0, or Rf + 2 Gr 4- 2 Fy -I- C = 0, 

 represents a parabola whose axis is parallel to one of the 



nte axes . 175 



108. Reduction of the equation of a parabola to a standard form . 177 



