17-2 ŒUVRES DK FERMAT.- 1- PARTIE. 



(|ii;ulialiiin vcro rccla' 01 t'i'it 



N'/.+ Ef/.-h AinEhis : 

 orgo reotangulum sub V.O in .l/crit in iisdem terminis 



/(iti/s (jtiad. ( J/f/. in Nq. + M<i. ia Eq. — Mq. in /> in E l^is) ; 

 roclangnliini V(M'0 siili 10 in />' crit 



Idtii.'i qi/iii/.(/lq. in V(7. + Bq. in /fy. -[- AV/. In A \n E bis). 



Ha^c duo rcctangula debout, ex pra'ccptis artiy, adicquari duobus rec- 

 fangulis 3/ in .V et B\ii N. 



Ducantur omnia quadratice, ut (;olIatiii" asymmetria; deinde, ablatis 

 coninniiillms cl k-rniino asymmetro ex una parte collocato, tiat novus 

 ductus quadraliciis. Quo peracto, demptis communibus et reliquis 

 |)ei' E divisis, ar tandem elisis bomogeneis ab E afTectis, juxta prse- 

 ocpta niclbodi qna' dudum omnibus innotuit, et facto parabolismo, 

 fit tandem simplicissinia anjuatio inter A et M : boc est, a primo ad 

 ultimuni abruptis omnibus asymmctriarum obicibus, recta DH in figura 

 fit lequalis rectse M. 



Unde patet punctum diaclasticuni ita inveniri si, ductis rectis CD 



et CF, fiât ut resistentia medii densioris ad resistentiam mcdii rarioris, 



sivc 



i:l // nn M, ita recla FI) ad reclam UI[, 



et a puncto H excitetur recta HI ad diametrum perpendicularis et cir- 

 culo occurrens in puncto I, quo ref'ractio verget : ideoque radius a 

 mcdio raro ad densum pertingens frangetur versus perpendicuhireni, 

 quod congruit omnino et generaliter invente tbeoremati Carlesiano, 

 cujus accuratissimam demonstrationem a principio nostro dorivatam 

 exhibet superior analysis. 



