; v.\^«vK Prohlematis ex theoria maxmorum et mtmmoriim solutio. 



Solutionls pars altera» Restat ergo, -ut coiwlitio haee inventa in altera aequationum supra 

 inventarum substituatur, indeque ambo anguli incogniti fj, et v^ quorum jam quaedam relatio constat, 

 determinentur: hoc autem modp in calculos nimis intricatos delaberemur, quam ut inde solutio 

 commoda derivari posset. Expediet ergo novam resolutionem huic conditioni^ quod punctum quae- 

 situm certo in recta CJ lincam datam AB bisecante reperitur, superstruere. 



Fig. 49. In hac ergo recta CJ sit punctum quaesitum. Ex A e% /^ in eam demittantur * 

 perpendicula AF et BG, atque ob AJ=BJ erit tam AF=BG quam JF=JG. In calculum 

 igitur introducamus has quantitates cognitas : C/= e, AF= BG = f, JF= JG = g et altitudinem 

 CV=h. Tum vero sit intervailum quaesitum JO = z, erit CO = e — z. Hinc ob OF = z-\-g 

 et OG = z — y habebitur 



■ AO=V{ff^{z-^g?) et BO = V{if-^{z-^g?) 



simulaue perpendicula ex C in rectas^O et BO demissa sic facile obtineutur .. 



AO:AF=CO:CP et BO : BG = CO: CQ, ut sit 



^^ ~~ AO ^^ ^^ sQ »j lijjt^, t9 IflKiJp Ui 



unde fit AO.FP = V{hh.AO^-i-ff{e — z)^)=^V{ffhh-^hh{z-h-gf-^ff{e — z)^) 

 BO.rQ=V{hh.BO^-^ff{e — z)^)=V{ffhh-*-hh{z — g)^-^ff{e — z)^) 

 quorum productorum summa debet esse minima. .\;^\» — oo=3?i.ilk i'> 



Ad caiculum contrahendum statuamus 



ffhh-\-qqhh-^eeff=E. ff-^hh = F. 



eff-ghh=G, eff-^ghh = H,^^^ ;,e i^boup ..iugcielDoi 



ut haec expres^^. ?ainiraa sit efficienda . ,. = ^ — ^d 



V{E — ^Gz-h- Fzz) -H V{E — 2 ^z -H Fzz),^:-^^. .^^^3 eiJauboiioi axjaiup 

 unde differentiando colligimus ^:±f . 'l^^O^ 



Fz — g Fz — H 



= :i.''.i')?,Ga Dfliil iiitl^i zdlqjjQ 



y(£ — 2G«-f-F«2) -/(E — ^iHz-t-Fzz) 



et irrationSlitate sublata -^ o 



quae evoluta praebet .. 'ifHaittim raciia' msl.r . ;;. . «Bl-^t' ^^ - ^l ciaoi ai nii/tonjj.j 



EGG—2GGHz-^FGGzz "- " ■ HlzoGup fni ' EHH-^^GHHz-^FHHzz ' ' " '■^'>«"P «» 



^2EFGz-t-kFGHzZ'^2FFGz''' - \= ^2EFHz-*-kFGHzz—2FFHz^ - '-^^^ 



-f-£:FFzz — aFFflz^H-F^z*) -i-£:FFzz — ^FFGz^-i- F^z* 



et contrahitur in banc formam 



E^GG—HH^ — ^iGGH-i-EFG—GHH — EFffjz-i-F^GG — HH^zz^O.i^^^^^^^ 

 Facta divisione per G — H nanciscimur .iuv » 0^\^ giij§.o/aT) odiii« 



