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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 29
# Folio 1v, page id 00068242:0002
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Hinc si quis a me quaerat datum Numerum
dividere in duas quadratos, ut Xx+Z aqua
seu edaego a = xx, debet esse XX a aqgy.
et fiet hac quidem methodo X numerus nihilo minor
nempe X aequ V +aaai erit tamen
vy.+
477
reguaat itaa
a
Ergo fet
uane
Ergo  a + Xx +M a -X aequ. CyX comp. + 1
fiet Ua + UX aequ yy + mma-mmX -Emyta-X
ergo debet fieri. l raequ - mn, seu M aequ L (-1 seu
posito mae baegontufiet m aequ. Y- 1. et fieit:
Ua +maequ. 0.  ergo fiet 3y aequ. 2 my sq -x
seu y, aequ 2 SX a. seu yy aequo 4X- 4a, seu
4. X aqu. 3y +4a sed hatc aequatio impossibilis posito
2
esse x mnius quam a majusquam x. Unde etiam
generalis solutio est impissibilis sed hoc obiter.
si quis quaerit ista in integris, verbigiatia.
XX A aa aqu 2Z.  scribere potent:
 N Xx - ZZ aequ aa.  facere potent
XX _ _ yy + DV
vel
7
yy-vo
24v.
a
piiore casu nempe sia a sit  par, possun ut fieri possit
sine fractione aequalis ipsi =, 2yV. et quilibet duo
factores ipsius a, possunt assumi, sin sit pro v, et yset
Sed si sit a numptus oupar fieri potert aqualis
etiam poterent inveniri .V et V, temper enim quilibet
numerus impar intelligi potest diffecentia duorum
quadratorum sola unitate differentium imo duorum
aliorum qu multis modis sed siae datus esse
deberet yy + vV aequ. a. non aeque facile exitue
ial
habetur XX + X X + 2x b + bs aequ a 
dis
seu 2XX + 2 X b H, bb aequ. a. Ergo  a - bb
Ergo a - bb aequ. CA 2x. x +b ponatur
ponatur a aequ bc. et scribetur bc = bb aequ2x X+b
et faciendo c - b aequ. aequ 2dX. fiet b aego X + b
at idem X aequi seu X aqu db - b
at idem x aequ c- b. ergo fiet db -b rego c- b
a
seu fiet: dab - db aequ c b. seu b aequ. d aequa
da-d+ 1
et X aequ 2  d C - C i restati aequatio Cc aequ dd. d +. 1)
seu de ggo dda - da + a. sed nihil hunc s +b aquae 1 bb + 1bV + v0 C N E B + v
a
ad+ d +1