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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 133v, page id 00068200:0268
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quibus positis videamus au liceat a sumere pro artituo, seu Y - p  g +
eit 2al  L Hgr + gp + Xpr = fP, quod utique fieri potest, cum p et alius
praeterea ex his dubbus Y, et g. pro arbitrio sumi possit. Sumto ergo p pro artituo
oquia a datur ponamus determinari , ,. jamque r, et p deter minatis
in aequatione. = + 3gY + 29β_0, de finietur g.
Quo genere calculi, nescu
an aliquid fingi queat subtilius. Exequatuur tameu, sumtis ergo a, et, , fiet
Y  ab + 2gp + pV  g  al - pr + p2
2gP
sulstituto fiet - 3
non
= 2g- 2p
quo valore in altera aequatione
+ 3alr 3pr +3pr. + alp - p r + p3 0., reductaque aequatione
2Y= 2p.
patet g minime ascendere ad arlitium quadratum, ideoque assumtis, a. Y. p
pro arbitrio, determinari g. neque quicquam solutionit prorsus indefinitae obstare
Si calculus recte processit patet p. +r3 + pr + 3alX-Xpr 17 pY + alp- pr +p
fiet: r  al +29p +p quod multo minus procedit.
=29 + p
An sic, aequalio umelliplicetur per 2, dividatur per - Y, fiei Y 6g - 2 gp al O
aequatio D dividatur per +Y, fiet - 2g - 29P + p = p, juectisque aequationibus
Y - 4gr  al g pr + pr  or, quae d’addatur ipsi D fiet
r=ral - 6gr - rgso  r
an  non extractione quadam compendium, haberi possit, esto Y, quadratus
et -29 + P e f, etiam quadntus E g 
assumtis ergo g numeo quadrato eh
1I Or A 4p
fiet ergo 2al p - 2 h3 Sonltapl- 2sp + p. hs or tp  - p  id est
Y. a, h. P assignatis pu arbitiio, et posito  6rleplbrlt9
et 6rl + qu
5 4 + 295 + s fiet 6rl  295 +q, et Serl-qu
et radix S6rl+ 2pL, ert g + Erl - qu
2al F- 2h 6rlaqu
qa  2h p= + ph  6rl - qu-
  ponendes
q
atque ita al assumi potest pro arbitrio cum ipso assimta supersit alius 
determinandus
Y.
gu
Hl a
in qua de aequatione ut aliam praeter a, radicem simplicem obtineamus difficile
factu est. Ergo videamus quid fiat, si pro r, substituamus ejus valorem,
a
Ne dostima desistamus tamen videamusque
e
2
eritque
e
una idat indu et
1
.
so