( ) 
IV. De motu JSferVi tenfi. (Per Brook Taylor Armig. 
Regal. Societal , SodaL 
Lemma I. 
Sint ADFB, 
A a $ B Cnrvee 
dute^quarum re- 
latio inte fe h<ec 
eft , ut, duff is ad 
libitum ordinatisC aD,E$ F tfttC a : C D : : E $ : E F. , 
Turn ordinatis in infinitum immimitis , adeo ut coincidant 
Curv£ cum axe A B , dico quod fit ultima ratio curvature 
in a ad cuvvaturam in D, ut C a ad C D, 
D Emonftn Due ordinatam c .J' d ipfi C D proximam 5 
8c ad D & A due tangentes Dc 8c a a, ordinate 
c d occurrences in t 8c a. Turn ob c </i : c d : : C a • C D 
(per Hypothefin) tangentes produ&a? fibi invicem 8c axi 
occurrent in eodern puntto P. Unde ob triangula fimilia 
G DP 8c c t P, C a P 8c c a P, erit c 0 : c t : : C A : C D 
(::Cc/i; c d, per Hyp) :: J'0(=c0-c^)ad d t (= c t-cd*) 
Atqui funt curvature in a 8c D, ut anguli conta&us 0a JV 
SctDd; Sc ob ^ a 8 c d D coincidentes cum c C, anguli 
sfti funt ut eorum fubtenfse 8c d t, hoc eft (per ana- 
logiam fupra inventatn) ut Ca & CD. Quare, &c, 
Q. E. D. 
Lemma 
