ij02 M?\ WlLDBORF, OH 
a : c :: ft CBQ : ft ABQ. Moreover, ft SOB : radius :: ft SB 
; ft BO :: ft AQ : ft. AO. Through C and O draw the great 
circle COR; then, as f. AO : radius :: ft. OAR : f. OR :: ft. 
OAQ : ft OQ, or f. OR : ft OQj: ft OAR : f. OAQ :: c : ^ 
and for alike reafon, f. OR : f. OS :: f. OBR : 1. OBS :: c : a, 
that is, f. OR : c :: f. OQ : b :: ft GS : or ft OQ : f. OS :: 
b : * ; but f. OQ : f. OS :: f. OCQ^= ft AR : f. OCSzzft BR, 
or f. AR : f. BR Now, be is ultimately perpendicular 
to AC in d , lo the triangle CJc being right-angled at d , the fum 
of the angles C cd, cCd muft be = a right one, and their lines are 
in the ratio of Cd : cd , or of b : a ; but the fum of the angles OCQ, 
OCS, is alfo a right one, and their lines alfo have been proved 
to he in the fame ratio of b : a, confequently the angle OCQj= 
Co/, and OCS = cCd, to GCS and cCd add the common angle 
OCQ, and the angle OCc muft be= BCQ a right one ; confe- 
quently OC is perpendicular to Cc the track of the point C, as 
OA is, by hypothefis, to A a, and OB to The fines of SO, 
QO, and RO, areas a, b , andc, alfo f. S 0 2 + ft QO' + f. RO 
by trigonometry = the fquare of radius = i ; hence f. SO -f- 
f. Qp 2 = i -ft R0 2 :rft CO 2 ; f. SO 2 q- f. RO^ftBO 2 , f. QO z 
+ f. RO 2 ^ f. AO 2 ; confequently, f. AO 2 , ft BO 2 and ft CO 2 are 
as ^ 2 + £% *r + c 2 , and a + b z , or as A a, B b z 9 and Cc 2 ; where- 
fore the velocities s/b z + c z , \/V + c 2 , and of the 
points A, B, C, are in directions perpendicular to AO, BO, 
and CO, and in the ratio of the fines of the arches AO, BO, 
and CO, that is of the diftances of the points A, B, and C, 
from the axis whofe pole is O, the tracks of thefe points are 
therefore circles of the fphere whofe radii are thole diftances. 
And fo long as the velocities a, b, and c, are invariable, the 
paints Q, R, and S, which are always at the fame diftances 
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