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Prop. 3. The centripetal varying as the « — i power of the 

 diftance to determine the orbit defcribed when it has two 

 apfldes. 



Solution. Let S A = i +tf and S B = 

 I — e. Any diftance S P = jf, S Y =/> and 

 the L AS P = A. Let alfo Z A be the 

 fpace thro' which a body muft fall to 

 acquire the velocity at A, and let Z S = ar 



Then (40 Prop. Cor. 2. and 1 Prop. Cor. i. Prin. Newtoni) 



5;» — T+?" : 2" — 1 — f^" :: i — e * : \l~e * 



or compon. 2" — i^f^" : i , «]" — i — e " :: i — e * : T+7* — 



i—e* 



Whence Z" — 



■4e 



— f- — c -f- 



2 2. 2. ■; 



tt+2.ti+i.n.n—J.n—2 ^^ g^^^ 

 2.2.3.4. 5. 



and becaufe z" — x" : z" — T~fi " :: Tp^» : p^ 



wc 



