I 



GEOMETRY 53 



2.457 Parabolic spiral: 



r 2 = a 2 6. 



2.458 Logarithmic or equiangular spiral: 



r = ae" 9 , 



n = cot a = const., 



a = angle tangent to curve makes with the radius vector. 



2.459 Lituus: 



rVO = a. 



2.460 Neoid: 



r = a + bB. 



2.461 Cissoid: 



(a + f)x = 2ay*, 



r = 20, tan 6 sin 0. 



2.462 Cassinoid: 



(*2 + / + 02)2 = 4 ^2 + ^ 



r 4 2aV 2 cos 20 = 6 4 a 4 . 



2.463 Lemniscate (6 = a in Cassinoid): 



(^ + /)2 =2fl2(: ,2_ :y 2 )) 

 r 2 = 2o 2 cos 26. 



2.464 Conchoid: 



x y = (b + ;v)2( a 2 _ yj). 



2.465 Witch of Agnesi: 



ofy = 4a 2 (2a - y). 



2.466 Tractrix: 



SOLID GEOMETRY 



2.600 The Plane. The general equation of the plane is: 



Ax + By + Cz + D = o. 



2.601 /, m, n are the direction cosines of the normal to the plane and p is the 

 perpendicular distance from the origin upon the plane. 



A, B, C 



p = Ix + my + 

 D 

 P= ~ 



