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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 271r, page id 00068194:0541
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icus
summa mmum an An possint inveniti Eduo cubi aequales dato s B + 2 +3cCC (+ C) B (C)
sit b d - C, erit d= 3de d (= C3 + (3) + 3CeEp0 et ponndo. d fc, fier :
C 2se se fiat -3dc2 + 3eC2 10. sive dpe, et restabit: a rb
e3-
eC +3CC20. et foret e10. hoc ergo non proaedit, quid si sic.
sit m C+- e. fietque. d3 + 3ed d 50 sive d+ 3ed p 3C2
et pro d ponendo ed fier: Ad + 3d p 3. sive d +3d + ZB
sie d+55
2
+3
H = 3 + Y9+ 12521 quod quae hpothesis non perducie
ad numerum quia ex 21. non potest ex trahi radix. monem
A
Ergo resunta aeq. O faciamus d ( fe. fiet : fC - 3fC fc +3CeC 70  on
sve + f.3 2
DC et fiet X4E  41 +(X + aequ. 
-352   +3C c + 3e  hioi c +3
3f. +de.
1+ ytub HA
c + ge
ge
f2. 35235 4. H 733F 23f 4(2 s 2t
et habebimus. Et problema hac reducetur, ut tantum
9-  12 I1f3-3 f. 3f debeat esse quadratus. excitetur quadatus ab.
3 + g f2- 3f. 35, fer: 9 + 39F2. 3F2- 3f + gt (7 f - 3 f. 3f, qui si aequetur priori
destuncto utrobique)  fiet:  et f- 3f2. 3f pocarndo h, fiet: -12h 7 39 +g h et faciendo
45L. Unde fiet aequatio cubica, ex qua
extrahendo radicem per regulas sardani, statum judicari poterit, an ope solius quae superest arbihar
G possit reddi S rationalis. Unde patebit usque Algebra in diophantaeis. Si tamen problemi
sint nimis simplicia, credo nihil novi ex radicibus disci, ut si quaeratur an possit ex, esse
X+V p, C dato fiet xpVe-. unde nii discimus. explicemus tamen quantum possumus faclendo.
X P7
bin + cp, et Y  dm + fp. fiet  m +2bCMB + e n2 p e ante omnique patet
+2dk.  + C2, 1
si duoquadrata aequari possea nchilo haben quaesitum sed hoc impossivnle
b+ + 26d + d+ nEp, 6c + 2b cd ft 42  ta
nt + 2bc + 2d f, b et + 2bcdf + dus
-
ta
ebet aequani quad rato. sed haec pulixiora. Ind
ractus, ut , fore
e
2= numerum
 2b4 r +C  N + b7abB C
2b + d7
erim deber
 ae
sente pagate