234 Of the SOLIDS 



der the radius, and an arch A, fuch that cof - A = 



2 



i -f" cof<7 ~f- cof b -f- cof c - r a 1 .. A ^ J. A.' 



— —-. — 7 — ; n — ; if A be computed, the attraction 



4 coi ~ a . coi - l £ b . coi %e * 



= n . A. 



In the cafe of a circular plane, our general proportion agrees 

 with what SirlsAAC Newton has demonftrated. IfCFD(Fig. 13.) 

 be a circle, BA a line perpendicular to the plane of it from its 

 centre B j A, a particle anywhere in that line , the force with 



/ AB \ 



which A is attracted, in the direction AB, is 2 «■ ( 1 — -r-=- J *, 



in which the multiplier 2 t is fupplied, being left out in the 

 inveftigation referred to, where a quantity only proportional 



AB 

 to the attraction is required. Now ^-=- is the cofine of the 



AB 



angle BAD, and, therefore, 1 £-=- is its verfed fine ; and, 



AD 



therefore, if the arch GEK be defcribed from the centre A, 

 with the radius 1, and if the fine GH, and the chord EG be 

 drawn, HE is the verfed fine of BAD, and the attraction 

 = 2ir EH. But 2 . EH — EG a , becaufe 2 is the diameter of 

 the circle GEK ; therefore the attraction 3 «• . EG' zz the area 

 of the circle of which EG is the radius, or the fpherical furface 

 included by the' cone, which has A for its vertex, and the 

 circle CFD for its bafe. 



XXI. 



* Princip, Lib. i. Prop. 90. 



