4i8 MEDltJTIOSES DE OJJKTlTJTIBrS 



Deniqiie 4) S\ ihcnt x'-±{2V-a' -a^x"-', 2 aV-a"-]-(i*) 

 Af-+-/7*— o , adcoqiie i).v=r-[-^; 2)1-—^^^ — «*; 

 ^}x—^-V—a*: \alentibiis fignis iiifcrioiibiis liabctiir acqiia- 

 tio cum fiiis radicibiis pro Cubo ^. ? t \ fin nutem tigna 

 fuperiora adhibcntur,proCubo oppofito ^.PT(§. XXXXl). 

 §.51. Q.iodfi paiilio attcntius confidcicmus od^o 

 illos Cubos (§. XXXXII. XXXXIII.) ad idcni pun- 

 <flum P coniugatos , cc ablblutc confidcrando intcr (c ac- 

 qualcs :, apparcbit , intcr cos tantum dari duos , ncmpe 

 Cubum a.PT ct y . P/ , eiUs conditionis , \t eorum 

 omnes tres radices , ctiam quoad formam exprefllouis , 

 inter fe acquales fint ( quo in ca(u , fccundo Tcimino in 

 ne]uatione dcfinicntc fublato , tota acquatio trnnb(brmata , 

 ly' * * * — o , nuUcfcit) , rcliquos \cro 6 Cubos eius condi- 

 tionis c(re,\t dnae filtcm radices,fcu dimcnfiones,ctiam quo- 

 ad formam cxpre^Tionis, intcr (c acqualcs cxiftant (quo in ca- 

 (u , tcrminum (ecundum in aequatione dcfinicntc tollcndo,in 

 acquationc transfbrmata folus Terminus fecundus dcficit, et in 

 Formnla pro i ) v valor partis irratioualis -^^ >^(Q* + P^) fit 

 — o) (§. XXXXVill. XXXXIX). Qiiod(i crgo Cu- 

 bus dcriuatiuus per acquationcm dcfinicntcm pi-opofitus , ta- 

 lis fuerit , \t trium radicum , aut dimcnfionnm ( re \cra 

 aequalium ) uulla altcri , quoad formam expreffionis , ac- 

 qualis fit , tum nec cflc potcrit pars irrationalis 

 ljiy(Q' H-P*) — o , fcd cubus propofitus acquc bcnc 

 ad duos Cubos ex illis O(flo in §. XXXXII. ct XXXXIII. 

 dcfcriptis , rcduci potcrit , c g. \el ad Cubum y.P/, 

 vel ad Cubum a . P; , quorum (cilicet {()!ac bafcs intcr (c 

 oppofirac fiint. E. gr. fit acquatio biquadratica piira 

 x*^** — a*^o , fcu (.v'-«') (.vM-<7'J — o , cuius 



adco 



