OHAP HI 



HIGHER PLANE CTJRYB8 



184. Definitions. A curve, in ( urteian coordinates, whose 

 equa to n tinite number of terms, each i n \.-l\- 

 ing only posit i\- integer powers of the coordinate*, is called 

 tin algebraic curve ; all : ves are called transcendental 

 curves. 



Hebraic curve* tl..- l.-^roe of whose equations exceeds 

 two, and all transcendental curves, are (if they lie wholly in 



me) called higher plane curves. On account of t 

 great historical interest, and because of their fr.-.ju.-nt use 

 in tho ('ah -nltis, a few of these curves will be examined in 

 the present < 



I \! 1 BRAIC CURVES 



185. The cissoid of Diodes.* 'Die cissoid may be defined 

 as follows : 1 1 K be a fixed circle of radius a, OA A 



his curve was invented, by a Greek mathematician named Diodes, for 



the purpose of solving the celebrated problem of the Insertion of two mean 



proportionals between two given straight lines. The solution of this prohlem 



carries with it the solution of the even more famous Delian problem of con- 



< whose volume shall be equal to two time* the volume of a 



t a be the edge of the given cube ; construct the two 



mean proportionals z and y between a and 2 a ; then y : : :?c, 



whmce * = 2 <H, *.<.. JT i* the edge of the required cube. If a = 1, then 



v 2, hence the insertion of two 



tract a line equal to the cube root of *. The cissoid may also be employed 

 to construct a line equal to the cube root of any given number (see Klein, 

 ElemcnurgcometrU', S. 36, or the English translation by Professors flasiM 



It b not positively known Just when Diodes lived ; h Is very probable, 

 however, that it was in the last half of the second century .c. 



