*5 2

Astronomy.

in most of them, so extremely small, ^ .be almost insensible; and therefore 1

m l ° n

11 0

the End of the second Part of Time the Body a ycrallel to DK. Now because CS = CH, V P’S E = E I; and because the Angle HPZy th 6

(per Conies') and HI parallel to PR, therefo sealternate Angle P HI = PIH, and soPI — EH»

sequently E P = ?- = A C, from the

Gei* 6 '

H6

of an Ellipsis. Let the Lctus ReElum of the Ellipl* 5- A B C 2 . , zllS

E == n, (because 2AC:2BC-"^^-fl^

Qj; intersect P S in *. Then because Q_R - P *?

,d

_ -... -— - ft vr"

the Triangle P x v similar to the Triangle Ph-lc :have P r : P :: P E (= AC) :PC; therefore ChjjP v ::A C : P C :: L X QR : L X P w. (TheoryAgain, LXP*:GwXuP::L:Gt/.

Also, GtiX7iP:Q.9 i ::PC I :DC 1 , Qvr b“ £1 Theorem III. Again, Qjr 1 : Q_T 2 : : PE 1 :when the Points P and Q_coincide, it is Q_jP ^ r A*and P E 2 — C A'; wherefore then Qjp: Q_T* If spef

~ ' "'nd la

: P F 2 . Now because PFXCDciACXB 1

Conies) therefore PF‘X CD^AC 1 X BC

an 1

:CL'

r

A C 1 : P F 2 :: C D J : BC 2 ; consequently Qjv:: C D 2 : C Bv (‘Theorem IV.) . vl ,_

2Z. These four Theorems set separately as b e ■Theorem I. L X QR : L X P -0 :: AC : P v ‘

II. L X P -v : G v X v? :: L : G%,

III. Gt;XnP:Q_'n 1 ::PC 2 :CN-

IV. Qjj* -. Q_T 2 :: C D 2 : C B 2 - qR

It is evident, by joining all the Ratios we have L ^ j} !:Q.T 2 ::ACXLXPC 2 XCP 2 :PCXG^

X C B 2 ; but because AC XL — 2 B C 2 , we hav c0 ,QR : QfT 2 :: 2 P C : G v. Now when P --nd ^incide, 2 PC — Ov, and then L X Q_R = Q-.

g pi ySP '

multiplying each Side by we shall have La