D I O P K A N T E V M. 4$ 



Denominator D — (a a -h a ct) (^^-f-S6) (cc-^-yy) 



(a 6 c -f-tt &c — aVy ^ a € 7)* 



D 



t> 



(a 6e -4- a gc — qg^v-fi. «67)* 



D 

 (067.4. «67 — ogc-^.a5c)' 

 D 



(n g 7 -^ a & 7 .4- g fe c — g 6 c)* 



D 

 (agc-4-ffi&c- f .o&7 — ag^)* 



D 

 ( a 6 7 -f. a g 7 -f. g c ~ at 5 c )^ 



D 

 (e 6 c ^-.age-^qgY^ jt fc^y)» 

 D 



35. Girca ordinem fecundum annqtafle luua- 

 bit , effe r' 



D " ^* D D 



(g& — a 6)^ 1 (a6 -h a g)' _> t 4_ aabb-i-aa^^—aais—eiahb 



•V D *" D — ■• D , ,~?r* 



Deinde in ordine tertio, fi quatuor partes prioris 

 columnae inuicem addantur , fumma erit 



. ' .- V ' i " ■ ■ < 



\J, f' \{a a — aa) i g c 7 ' ' I£i r^ f 



(a H- a ano 6 -t- e g) (c c -H 7 7) 



Hinc non contemnenda fubfidia peti poterunt pro 

 qunuis numerorum quaefitorum multitudine,, dum, 

 fi folutio in genere tentatetur , infignes difficultates 

 occurrerent. Quoniam igitur cafns duorum numero- 

 rum per fe eft perrpicuus , a cafu trinm exordiar 

 inde ad quatuor progrefiTurus. 



Cafus triiim iltimeror. 



3<J. Ponamus pro tribus numeris quaefitis has 

 fra<2:iones : 



[ab — a g)* . (fl g — a J)» 



aa-*-aa' (a a -(- a a)(6 6 -f-g g) ' (a -+- a aj(6 6-+. g g) 



quarum fumma eft 



F 2 Tnde 



