7^ Mémoires de l'AcademIe Royale 



Lemma il 



'Circumfcriptum vero ^aralklogram- 

 '/niim C D majus erit quàm aliud fa- 

 raUelogrammum FE , <jiiod tiempe cir- 

 ciimfcriftumjit figura genitrici. Nam 

 diiBà tangente ferO, & comfletâ fi- 

 gura , erit CD aejuale ipft FM. Ergo 

 CD majus efl cjuàm FE. ^(od erat 

 dcmnftrandum. 



THEOREMAr 



Sumatur i°. alloua pars figura definiu , fiità ABCDE ; Die» 

 '^qualem ejfe figura B C G. 



^liàs major effet vel minor. 



Sit primo major ; fecetur^tie BK femper hifariam donec HE mU 

 iius fit exceffu : thm infcribatur in figura mixtà BCE, alia figura, 

 conflans ex parallelogrammis xquè altis RD , LM , &c. tjuorum ul- 

 timumfit 1 ; Eritcjue infcripta figura ob conftruclionem adbuc ma: 

 jorfpatio BG C. ^wd efl contra Lemma vrimum, 



Sit deinde minor ; fefio^ue B K femper bifariam , repertumfit HE 

 minus defeElu : thm circnmfcribatur figura BCE alia figura conflans 

 ex parallelogrammis éiijuè altis s & erit circumfcripta figura adhuc 

 mnor figura BCE. Quod effe non porefl. Nam eadem figura circum- 

 fcripta trilineo BCE major efl cjuim alia cju^dam figura circum' 

 fcripta ipfl BGC , per fecundum Lemma. Patet ergo (\md demonf- 

 trandum. 



jibcat jam in infinitiim ( quamquam haÛtms di^a fuffice/e deèc 

 rent. ) Dico xquales effe figuras , crc, 

 Aliis altéra ipfariim major erit. 



