CO= = ( (I +/-if + (g- r ) s ; 

 D0 2 =(x-/7 + (g- r f. 

 Summa igitur horum quadratorum erit 



4X 2 H-4J 2 -4(rt+/)x-4gr- + - 2 ( ft2 - i -/ 2 - h § 2H - a 7) 

 quae , quia debet effe minima , differentietur , prodibitquc 

 Jhaec aequatio: 



dx[S x — 4(«+/)] + 5y (8/ — 4g) = °> 



cui fatisfaciunt valores x — \ (a -f-/) et y — \ g, Erit igi- 

 turOP-^DG, ergo EP-[AGz:^ hinc A E ~ A P 

 — EP— Ja=z|AB. 



Corollarium 3. 



§. 3 T - Pro trapezio ABCD, rjife&o latere A B in Tab.IV, 

 E, tJu&aque refta EC, ii in ea capiatur CFz=§CE; tum Fig, 3. 

 vero, ducla recla FD, fi in ea eapiatur DO fDF, pun&um 

 O erit interfe&io reftarum latera oppofita bifecantium. Pro- 

 ducfa enim recla D O usque in L , ob triangula E F L et 

 C F D fimiiia et E F zzz § C F , erit FLzr^DF et EL~ 

 | C D, hinc FL + OF = |DF + OF, hoc %il OL = OD. 

 Demiffis igitur ex D et O in AB perpendiculis DGetOP* 

 duftaqtie per O refta MN ipfi AB parallela, erit OPziDI, 

 nec non OP = IG, ideoque D I zzz I G. Tum vero pn> 

 dufta EO usque in R, erit DR = EL; at E L zzz \ C D, 

 ergo DRz^CD. Sit O punftuin quaefitum, et A~0 2 -+- 

 B0 2 -fC0 2 + D0 2 Minimum, ponaturque AB = a, AG=b, 

 B II zzz c, D G — C H — g, AP — x, P O zzz r , erit 



A O 2 zzz x x -h y y\ 



B0 2 zzz(a — x) 2 -f-jj; 



H h 2 C O 



