220 MEOnATIONES DE Ql^ANTITATIBrS 



di fit pcr altitudinem deoifiim fiimtnm P / j ex his iri- 

 bus dimenfionibus niri^natis oiictiir in priorc calii Cubus 

 •y . ?t~-i-a^.-a — — a , in poitcriore autcm cafu 

 Cubus a. P f — ~{- a* . ~ a =. — a^. Exameii radicis 

 fecundae et terti.ie ficilc inllituitur. E(l enim x* 

 H-^.v* -+- a\v -^ a' ={ ^ V ~ a^)* -\-a . - <z'-ha". 

 1f V - a" -^- a' — ±^ a" V - a' ~ a' -\- a V -a 

 -t- «* — c>. 



f. 52. Tandcm confidcrcmus ciusmodi acqu-.itionem 

 cubicam , in qui trcs cubi rcrpondeutes ncc quoud formam 

 expreirioois , hec abfolute confiderati inter le aequales Iiint: 

 manifelUim eft , eam continere debcre trcs radices , et 

 quoad formam cxprelUonis , et ablolutc confidcratas , in- 

 ter le inaequales , et harum primani valcre dcbcrc pro fin- 

 gulis tribus dimenfionibus Cubi primi , fccundam pro le- 

 cundi , tcrtiam pro tertii fingulis tribus dimenfionibus. E. gr. 

 fit propofita aequatio 1;'*— 71;— 6;— o ,. quae cum perti- 

 ncat ad Cafum I. ex §. XXXIII ct XXXIV „ compa- 

 randn erit cum hac 1;* * — 3 P 1; — 2 Q^n: o. Habetur 

 erga P-J ; Q.— 3 , eritquc i ) 1; — [Q^- V(Q_'-P';]'= ' 

 -4-[Q-y(Q;-K)]' • ':i:[3-f-V(3S';)J'- M[3'V(3.'-,^')]" ••' 

 =^[3-h*/V-3T" '-f-[3-^/V-3]'^'-.^H-iV-a, -^\-iy 

 ^3 ( §,• XXXVII. ) =: -h 3 i ct hinc z)v ~ (=^-^* 



a-+-iV-3)4- ^^-^^ (?-iV-3^ = - 1 -t- \v-2 , -: 



-SV-3=-*-, et 3)^.=:tzi=V'=:L)(j+.y_3y^.(rr!d-ti) 



(;-lV-3)=r-i-|V-3 , -•-+-IV-3 =-!• Ex^quo ap- 

 paret, elTe 3 ^-'^-3 :r:(J-f-iV-3/ =:(-J-|-jV-3)' 

 — ( i-hi^^-s)*' id qiiod, examine £i(flo , facile com- 

 probatur. 



