*5* 



IN FIGVRIS RECTILINEIS. 



dicalibus, deuenitur ad hanc: r^—^^^T^—^rz^^ 

 et denique fubftitutis valoribus ipfarum AD- et Al> et 

 diuidendo per a z e z ad iftam 



V(g c-f-ftg)(a6-4-c e ) (ae-4- lfi) 



y(0+i + c-Olfl + i-c + O(a-64-c + e)(-a + 64.c4-e) ; ' > 



quae dat pro quadrati infcripti iatere rVa, vt notum 

 eft. 



Problema 2. 



Ddtf/j tribus hteribus , AB, AC, CD, m» #«£«- 

 /0 A vel C inuenire quartum latus BD, te ^ area fiat 

 maxima. 



Solutio. 



Sint ABzz* , ACzz£, CDzz^, BDzzj, fin. ang. Rgu» * 

 Azz/#, finusque anguli Dzzr. Ducla perinde ac in 

 praedenti Problemate DiagonaliBC, fiat quadrilateri area. 

 *bm+c yx^ con ft ans ex areis triangulorum ABC et CDB, 

 fecundum lemma prius expreftis, maxima , ita eius dif- 

 ferentiale c J dx -^ cx y euadet aequalis nihilo, proindeque 

 dxzzi "* dy . In aequatione vero BC 2 — a 2 -\-b 2 ~- 2ab 

 V{i—nP)=<?-^y*~2l;yV.(x--xx) ex pofteriori lem- 

 mate orta, eaque difTerentiata , nempe ydy — cdyV(i — 



tf#H~vtrzr^^o^ valor ipfius dx mox inuentus fubfti- 

 tuendus eft ; quo fadlo tandem - obcinetur czzzy Vt i — xx). 

 Cum autem Diagonalis BC fit deterrninata , propter la- 

 tera BA,AC et finum anguli BAC data , y quoque da- 



tur et quidem erit hypotheuufa in triangulo B C D j nam 

 y:c~i:V(i-xx).. $h 



