PHYSICAL anv LITERARY. 157 
join KB; draw SL parallel to KB meeting 
* BDin 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, becaufe twice CD is equal to AP, that 
is, equal to KB together with BS, and 
twice CH is equal to KH together with 
HS; therefore KB together with BS will > 
be to KS as KH together with HS is'to 
HS ; ; aad therefore KB will be to BS as 
KH to HS, that is, as KB to SL; there- 
fore BS, SL are equal: Therefore the an: 
gle SBL is equal to the angle SLB, that is, 
equal to the angle KBD ; and therefore, 
froin a known property of the ellipfe, BD 
is a tangent to the ellipfe at the point B; 
and therefore | Prop. 2.) the fector ACB 
| is greater than the fector ASE, and lefs 
| than the fector ASF: But, becaufe Gi is the 
place of the planet, the area of the ellipfe 
will be to the feétor ASG as the periodic 
time of the planet round the fun is to the 
time clapfed fince the planet paffed thro’ 
the point A, that is, as the area of the el- 
lipfe to the fector ACB ; therefore the fec- 
tor ASG is equal to the fe@or ACB; and 
aa therefore 
