t»HYSICAL ANU LITERARY. 14^1 



point A, fo let the area of the el-; 

 lipfe be to the fedlor ACB ; join 

 SB, and draw CD parallel to SB on 

 the fame fide of AP that SB is ; 

 and let CD be equal to CA ; join 

 SD; let CD, SD, meet the ellipfe in 

 E, F : the true place of the planet 

 IS between the points E, F; that 

 is, the planet is paffed the point . 

 E, but not come to the point F. 



Let G be the place of the planet ; join 

 SG, and join BD meeting AP in H, and 

 join KB ; draw SL parallel to KB meeting 

 BD in L. Becaufe CD is parallel to SB, 

 CD will be to SB as CH to HS > therefore, 

 twice CD will be to SB as twice CH to HS.. 

 But, becaufd twice CD is equal to AP, that 

 is, equal to KB together with BS, and twice 

 CH is equal to KH together with HSj there- 

 fore KB together with BS will be to BS as 

 KH together with HS is to HS ; and there- 

 fore KB will be to BS as KH to HS, that is, 

 as KB to SLj therefore BS, SL are equal: 

 therefore the angle SBL is equal to the angle 



SLB,. 



