( ii \ri LI; vn 



THE CIRCLE 

 Special Equation of the Second Degree 



77. It must U' kept eleurly itt miinl that one of tin? rhirf 



aim* of an element. i -e in Analytic Geometry is to 



teach a new mil A0</ for the *t u 1 \ i ^...UMiri' H of 



vea and surfaces. Power and facility in the use of Mi.-h 



a new method are best acquired by applying it first to those 



whose properties are already best understood. A nnl 



y, the straight line having already been studied in 



ter \', tin- i-in-li- \\ill ii.-xt be examined. 

 It \\ ill .ij.pear later tit. it tlie circle is only a special case of 

 onic sections already referred to in . ami might, 



fore, be advantageously stu 10 general \ 



of those curves had been examined ; the present oni< r 

 adopted, however, because the student is already famili.ir 

 with tin- rhief properties of the circle. 



In solving the exercises of this chapter the student should 

 the analytic methods, even when purely geometric methods 

 might suffice, he is learning to use a new instrument <>f 

 stigation, and is not merely Mu<l\ing the properties of 

 le. 



?a The circle : its definition, and equation. The circle may 

 be defined as the path tnu ! l,\ ;i point which moves in such 

 a way as to be always at a constant distance from a giv n 

 point. This tixed point is the center, and the constant 



.idius, <>f the ircle. 

 136 



