quantiplex RS ipfius G eft: unde 2 VÖ == RS. Ea- 
dem ratione demonftratur, esfc UV = ZIT, NO ss 
RT,&Ur = Z<p, 
Quia jam NO, NF, NjJ), Tunt ipfarum AI, 
AF, AK xque multiplices \ erit NF > NO, fed 
NF < NQ\ hoc eft, erit NP > PS, fed NF < 
PT. Sed, quando NP > PS, eft (5. Def. L. V.) 
UX > ZIT, &, quando NP < PT, eft (5. Def. 
L. V.) GAT <J Z(ß: ergo, in cafu præfenti, eft 
ffeapfe UX > Zn, fed UX < Z$. Ergo, eft et» 
jam UX > GF, fed GX < Ur Sed CL, CL, 
CM hint ipfarum GF, GAf, GF fimiles (esêdem) 
partes j ergo, eft C£ > CL, fed CE < CM. £. L. Z>. 
THEOREMA X. 
5'i (Tab. X, Fig, 5 & 6) quatuor magnitudinum AF, 
B , CL, D, dua confequentes B & D in œque mul- 
tas partes quotcunque, utrinque feorfam œquales , 
dividantur , quarum unaquaque in B fit = G, 
unaquaque in D fit = H, adeo ut G & H ipfas 
B & D aqualiter metiantur ; atque auferatur deinde 
G ex AF, quoties pot eft, donec vel nihil, vel Je 
minorem relinquat; pariterque H ex CE: ponatur - 
que H in CE toties femper contineri, quoties G in 
AF, idque utrinque fimiliter, vel fine, vel cum refi - 
duo; quantumvis parva fumantur partes G & H : 
dico, esfe AF : B : : CE : D. 
Dem. Caf. i. Ponatur primo fubtraÖio illa fie- 
ri posfe fine refiduo, adeo, ut ( Fig . 5) G & H 
©tjam ipfas AF & CE sequaliter metiantur. 
Sint NF & UX ipfarum AF & CE seque 
multiplices quaecunque 9 & RS & Zn ipfarum B 
& D. 
