i~ 



202 DE INVENTIONE MEDIARVM 



I-Il izzV-Qz ,. q-zKz 

 II-III ozzq-^Rs V — i^Kzz 



vnde fit 



III. o — R(i -:i;)-PA;~Qrrz:R(i -X"XZ-xzz)-x 



idsoque R —z — -£ , , at eft x — 5-=-^. 



Ergo R zz — ^^ — -—-^ — ^^^ ficque prodit 



p r ■— z z . /^ — z z — z . D % — r 



^ — r — z^ » ^ — r — z' ' *^ j^^^r^J 



quarum formarum cum denominntor fit 



r- I — 3 (^— ^')^-' oir— if x^ — {r—iyx' 



feu (r-i)(i-3.r— sC^— i)-^'' — (^— i)'-^';) 



perfplcuum eft noftras tres progrefTiones efle recur- 

 rentes fcala relationis exiftente 3,3(^—1), (^^— i)% 

 ita vt iit 



Kunc pro terminis generalibus harum progreffjo- 

 num fradiones P, Q, R in fimplices refolui opor- 

 tet : quoniam autem denominatoris fador fimplex 



eft Vr—z fimul vicem binorum reliquorum gerens, 



fiquidem V r tres inuoluit valores diuerfos , fufRcit 

 hunc vnicum fadorem confideraffe. Sit ergo ex 

 fra(^ione K fradio fimplex oriunda — -^ — , et nu- 



3 



yr — » 



mera- 



