Page:Œuvres de Fermat, Tannery, tome 1, 1891.djvu/232

Revocetur rursum ad analogiam duplicata ista iequalitas: erit itaque

Zs. in D - Ac. in D ad Nq. in Eq. - B in A in Eq. - Zs. in E - Ac. in E ul Nq.-BinA ad Eq.- +DinE.

Quum itaque factum sub extremis equabitur facto sub mediis, tanquam ipsi æquale, omnia homogenea poterunt dividi per E, ut supra demonstratum est: erit nempe

Zs. in Eq. 4- Zs. in D q. in E - Ac. in D in Eq. - Ac. in Dq. in E æquale Nqq. inEq.- Nq. in B in A inEq. - Nq. inZs. in E - Nq. inAc. inE - B inin Nq. inEq. - Bq. inAq. inEq. 4- B inZs. in A in E - B inAqq. inE,

et, omnibus abs E divisis, fiet tandem

Zs. in DinE + 7Zs. inDq. - Ac. inD inE -- Ac. inDq. æquale Nqq. inE - Nq. inB in A i E - Nq. in Zs. - Nq. in Ac. -B in AinNq. inE-+-Bq. inAq. inE -+B in Zs.iin A AB inAqq.

Quo peracto, nova hæc æquatio unius adhuc gradus depressionem (quoad secundam radicem) lucrata est, ut hic patet: quum enim homogenea sub E adfecta in unam equationis partem transierint, fiet

Zs. inDq. - Ac. in Dq.4- Nq. inZs. - Nq. inAc. - B inZs. in A +-B in Aqq. sequale Nqq. inE -Nq. inB in A inE - B in A in Nq. in E - B q. in Aq. inE -Zs. inD inE 4- Ac. in D in E.

Neque ulterius progrediendum, quum jam secunda radix sub latere tantum appareat, ideoque, solo applicationis beneficio, ipsius E relatio ad primam radicem manifestabitur: ut hic

${\frac {Zs.inDq.-Ac.inDq.-Nq.inZs.-N.inAc.-BinZs.inA4-Pinlq.}{Nqq.-Nq.inBinA--Nq.inBinA--Bq.inAq.-Zs.iin)+Ac.in)}}$ æquabitur E,

quo tendendum erat.

Ut igitur duæ primum propositse radices in unam transeant, resu