xii \T8 



CIIAITI.K VI 



TKANSF" ' . I'lN 



ACTtTL* 



7a Inuoductory ......... 



I. ' 



7 1 . Change of origin, new axes parallel respectively to the origi nul 



axes ........ . ... 12! 



Tran ^format ion from one system of n otangular axes to 

 another system, also rectangular, and having the same ori- 

 gin ; change of direction of axes ..... l-'i 



Transformation from rectangular to oblique axes, origin un- 

 changed ........... 127 



7 1. Transformation from one set of oblique axes to another, origin 



hanged ........ . li'S 



75. The degree of an equation in Cartesian coordinates is not 



changed by transformation to other axes . . . .129 



II. Polar Coordinate 



76. Transformations between polar and rectangular systems . . Liu 



CHAPTF.II vn 



THE CIRCLE 

 Special Equation of the Second Degree 



77. Introductory .......... 135 



78. '1 definition and equation ..... 



79. lu rectangular coordinates every equation of the form z* 4- $* 



+ 2 fix + 2 Fy + C = represents a circle . . . 1 ,7 



80. Equation of a circle through three given points . . .138 



inUtj Tangent*, and Normal* 



81. Definitions of secanU, tangents, and normals . . . .140 



83. Tangent*: Illustrative examples ...... Ill 



88. Equation of tangent to the circle r 1 + y 1 = r* in terms of its 



;- ........... 142 



84. Equation of tangent to the circle in terms of the coordinates 



of the point of contact : the secant method . . . .144 



