PH^SICAt'A& LITERARY. Hi 



Kepler firft of all difcovered that the pla- 

 hets revolved in ellipfes round the fun placed 

 in one of the foci, and that they defcribed 

 equal areas in equal times round the fun. Let 

 the femi-ellipfe, [Fig. 6.] whofe greater a^s 

 is AP, Jocus S, and centre C, reprefent half 

 the orbit of a planet round the fun in S; and 

 fuppofe the planet at the point K in its orbit i 

 join SK : half the periodic time of the planet 

 found the fun, is to the titne the planet moves 

 from A to P, as the area of the femi-ellipfe 

 to the area ASK j and therefore to find the 

 place of the planet at any given time, it i9 

 fteceifary to find the pofition of the right 

 line SK, v^^hich lliall cut off the area ASi£ 

 proportional to the time, that is, To draw th^ 

 line SK fo that the area of the femi-ellipfe 

 may be to the area ASK, as half the periodic 

 time of the planet round the fun to the 

 given tirhe. 



From K let fall KH perpendicular to APj 

 meeting the femicircle defcribed upon AP in 

 G, and join SG : it is evident, from the na- 

 ture of the ellipfe and circle, that the ferrii- 

 cif cle is to the fedlor ASG as the femi-ellipfe 

 to the fedor ASKj therefore the femicircle is 

 to the feftor ASG as half the periodic time bt 

 Vol. 11. Q, ti5^ 



