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# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 30
# Folio 38r, page id 00068124:0075
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prollema ab bsanna propositum
rouver par une voye scientifique et demonstrative un
hiangle rectangle tet que la somme des Cubes de ses trois costés
soit un labe. C’est 3. 4.5.
X-y. _2xy. Xts
2X6 + 6X y  + 8Xy ago 33
2X +6Xryt aequ Z3 - 8 x3y3
X (3XY 3Xy (y) +8X. +X (3Xy 43XyF y). aequ. 93
2X 16Xy, e
Ekt 
aequq
a
+exy ago
fiet
Abstinendo a destructionibus  erit duorum
Cuborum summa aequalis ductum Tuborum differentiae
+ m aequ n - p. fiat l + M aequ h n - p.
lest
 +
Vam-im
+ (3 Hmi-em
et ponatur l’aego gn + f. fiet: lgn + 29nf + f, et fier: (m 3 dni m
-6x +16er7
9XX
V oynatugns + L
m= gum-fm aequ gp + Jon. et n aego m = fm -9. et
enor lid calculo onusi f
 d ponendo  p aequ e m. fiet:
(CX yHt Bxyr+o seu y aego 3,2. 6X  vv. seu LD sit vago 3p 82 et Map lper
gm gp
naequ ma-f - gem
Adu 33(t Z r) aequ. 4 X9)  ) fi V otsec +23- 6p r . p q aequ 3Ppr 9 p94 aequ.  p r 
at supra
9 +920
n aequ l + em-gem. quos duos valores aequabdo
seu G 2p r- 3ppq aequ 24 pr QHa caeguatio
e
mnltiplicetur per P fiet: 33 p6- 2p 2b q rqu. 29b 3ae 92 sit Zp aego h praego X oppaequs, et fes
- 2f = 3sa asfo 2a X25 P. set felicissime habetur p rationali te Noletur vene reductiolite rar Enor in calgulo vide pagi seg.
ret
aequ gm- f9- gem em19 em-gemtgem
+
sit jam Habebimus, ergo quommodo summa trium caborum
aquetur cubo solutione indefinita quidem non
amen universali genperfecta, quia  posuimus quadratum
pomamus jam  Z vio locum - M2
et vel x- y vel X+y. vel 2xy in locum - p.
reliqua duo rst ex his tribus referent l et n.
Jam M est aequ P seu aequ = 2xy fiet Zaequ + 2Xy
quae quantitas ubique substituatur in locum ipsius s=m
et loco n scibatur x + G. loco sumbatur y
addatur in unum n er l, seu fiat: l + n
habebimus hinc: 2X, illinc. posito 9 aequ + 1. habebitur
quantitas in qua destructa f restat solum M, seu 2Xy.
ergo quia hinc tantum X illinc tantum exi poterit utrobius
dividi per X et fier: X aequ:. y. Qua quantitat
es
ubique in valore ipsius n substituta prodibit nova aequatio
in qua solum supererit . et f omnes tomini afficientur
per poiy. vilf. Ponendo ergo f etiam affici per y.
seu f aequ. dy. dividi poterunt omnia per y et
habebitur varor ipsius y. adeoque et X. quaesitus
atque ita solutum est problema, et quia e manet
quantitas inter indeterminata pariter ac d, patet
problema modis infinitis solvi posso
est univertalis
Aolutio tamen non
stran quod omnes casus comprehendat
imo est enor