__ &b ) o ( as _ 2 f 3 
Ex conftru£fcione patet Tr. BCA , CDA, DEA , 
&c. feriem efîe Triangulorum fimilium; id, quod 
pariter valet de Tr. BHA, PIKA &c. Et, cum 
BC , BH fint in fitu proximo, erit Tr. PC// oo & 
= Tr. BHA., & fie porro, ad fubfequentia CD A, 
HKA & c. pergendo. Simili ratione perfequi licet 
Triangulorum OSD , OS/T, PTE, PTL &c. fimili- 
tudinem , & mutuam , & cum prioribus fingulis in¬ 
tercedentem. Ultra, jungantur BO , OP, P.Ô , 0 /^> 
& fuper PO defcriptus intelligatur femicirculus'; 
tranfibit hic per puncta H, C, ob re£tos OHB , 
OCP, Trapeziique OHCB duo anguli BOH - 4- PC// 
erunt = (duobus Re£tis =) BCH 4 - BCA , & abla¬ 
to communi BCH , POP/ = BCA ; fed eft etiam 
BHO=BAC ; ergo Tr. BCA 00 BOH ( BOC ). Eo¬ 
dem pa£to oftenditur Tr. QDP, PEQ^&c. (pede 
ede eadem, quæ ilngula ante enumerata Triangu¬ 
la. Hinc 
5- I- 
Determinatur Curva AO. 
BA : <dC : : PC : CD 
: : PC : CO 
: : 2PC : OD 
: : 2BA : OS > 
Ergo OS = 2 r 4 C, & igitur SD — 2 AD — 2 ÆS, 
hoc eft, erit fubtangens abfciftæ dupla; quæ fola 
proprietas, vel reliquis nondum excuffis, curvam 
efie Parabolam Aoollonianam evincit. Sed &, ci- ' 
tra problematis ad illud theorema redudionem, 
prodit direfte hoc pa£to æquatio ad curvam qux- 
fitain : 
BA . AS — {BA. AD —) AC* 
4 BA.AS— (4 AC* = ) OS *; 
quo 
