PROBLEMATVM. 107 



dfltiir , ibi hoc latus a circiilo tangetur , vnde pun- 

 dum C ab ifto puncflo diftabit interuallo za-c-{-x, 

 quod cum ex circuli natura illi b — x fit ae- 

 quale,erit xzz ''^ _^~~'', Qiiare hoc pundum G re- 

 fpcdu bafis AB ita definitur vt fit : 



AR := '^--^ et RG = .-3;^^^. 



IV. Pro centro clrcuU circumfcripti H. Tab. Ii. 



p. Hic quidem ftatim eft ex conftrudione 

 AS=:|r. Tum vero ex A in BC dudlo perpen- 

 diculo AM, erit AMzz^^ et CM=:^^r^. 

 lunda autem redla AH ex natura circuli liquet 

 fore angulum AHS aequalem angulo ACB , ideo- 

 que triangulum AHS fimile erit triangulo ACM 

 vnde fit , 



AM:CM=:AS:HS 



icque colligitur HS = -^^ — —,1 . 



Qiiare fitus pundli H refpedu bafis AB ita defini- 

 tur vt fit : 



AS = i^ et SHzr^-^t4^-. 

 10. Hinc iam definire poterimus diftantias in- 

 ter haec quaterna punfta , fi quidem in eadem fi- 

 gura exprimerentur , erit enim \ 



EF'- (AP--AQ)'-4-(PE-QF)' 

 EG^zr: (AP- AR )' _}-(PE-RG)* 

 EH'::;(AP-AS/-{-(PE-SH/ 



O s FG" 



