132 ESSAYS anv OBSERVATIONS 
fector BCF as p is tog; therefore the fe- 
micircle is to the fector BDE as p is to gq. 
QE. D. 
KFpLer firft of all difcovered that the 
planets revolved in ellipfes round the fun 
placed in one of the /ocz, and that they de- 
-fcribed equal areas in equal times round. 
the fun. Let the femi-ellipfe, | Fig. 6.] 
whofe greater axzs is AP, focus S, and cen- 
tre C, reprefent half the orbit of a planet 
round the fun in S; and fuppofe the pla- . 
net at the point K in its orbit; join SK: 
Half the periodic time of the planet round 
the jun, is to the time the planet moves 
from A to P, as the area of the femi-el- 
lipfe'to the area ASK; and therefore, to. 
find the place of the planet at any given 
time, it is neceflary to find’the poftion 
of the right line SK, which fhall cut off 
the area ASK proportional to the time, 
that is, To draw the line SK fo that the 
area of the femi-ellipfe may be to the area 
ASK, as half the periodic time of the pla- 
net round the fun to the given time. 
From K let fall KH perpendicular to 
AP, meeting the femicircle defcribed up- 
on 
—a oS 
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