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# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 30
# Folio 15v, page id 00068124:0030
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on peut conjecturer
troucerae pou dautres
qu’on. ne
resotueret generateurrs
dant toute lestendu des noubrće, quee
eur qu’an trouvera par la regle
ox desus, qui puistent former ster
rcargles, dout les2 Cosse
ayent
buite pour differenre, n u pourra
Revorers la detmonstration des
 hoses
yr
4
2
y 4 2Xy aequ. 1.  seu 4 x - y - 2Xy ago+1
ponatur = aequ. +.
seu Xaequit2b
2 = 2
Ergo 2X L1 debet esse quadr
fier 2X +1 aequ 1(4) 2bX + bX, seu 2X aequ 2b +b
Ergo vel X est 2 quo sacto y est 1. vel (+) erit 
et fier X aego 26. Hinc potest besse 2
et
ergo sumendam suus 2 + 2X +1. alter aequandum, quadrate vig.  V=X  X + 1
omnia invenori,
quadratumonnitate auctus dividi potest
poterunt
ponamusgenim X4tesse 1o  (seu X esse 3) fiet. y-
quaeramus ergo in interpis.uando quadr. unitate auctum
divisibile
X 41. aequ B0ZV
ergo eequ. 94 1. aqu. 2,5, seu 3,37, +1. aequo. 2154 seu 2+1, 2+1, + 1 aequ 25+
y + 2y +2 aqu 2y+ 2 unde poter divisi vilitas ete procedit non lagtum in 9. sed et aliu
seu quando y valet aliter  quam 3.) seu gnerolius: y 42yC +se +1 aequer
e
tantum ergo fieri (D V deber  e2 +1. aequ. l9. Ergo repesto uno quadrat
unitate auctum sit divisibile, hinc ducuntur plula: imo infinitus y
Talia illa autem  quae sim per se patent, sunt omniu quad rata
lns Iny+ 19
quore
pro arbitrio essumto
imparia
idem omnia quae terminantur in 4. seu omnia quadrata nuprerorum quaedemmnnantur in
2. Sed opus tesset omnia complecti posse unus formula
q. 2x. sed his non indigemus. sumamus 
X +1L
X+y
s
X
X+y
 = 1 aequ 2X. 6V et  vel  X Eaequ. _m yt
1 aequ. mey ALmo
so ponaus in esse puctum fier fiei y lago Fm +1 seu m +1 quod
t
uodgpo
 V S EI emposibile est. Sumamus
teg
X-1 aeqo y- X. ponatur X + 1 aqu  y4) X. du
fiet: X L1 aequ d y(+) X. Quod etiam soloeetdum in integris
fierlix 4) tix
pes
tie
m-1
in
X=1 (aequ V fiet:
CI
nam in integris ut res procedat
xC(+) hx +h. poredo grit  ponatur: n+ p aequ. 9. et
citus ita Shabetur valor ipsius dx
in integris, 
quod non difficales
sed
vel contra res protedit.
qui quaerendus
quemadindin
et per hymi vabir ipsius x. t solutum
est problema Etomnes possibiles
numeri quos Marioltus postutat fit: 9495 unde
invenientur
n-p aego r. siet np, r+p.
29
esquA  quod est impossibile
te
et rHip aeqb. seu p aego 9-
C
etne qu 2
ergo pro inip
1gr+r
np2
prbemus
+ quod apa alibr possibile, nisi si ng. rago 1, 7
2Y
 Ergo X+y. aqu.. 4 r: va triaugle dont Chypotenusa et
seu 2X +1 aequ. X 1 y + 2Xy.
pem
fiet: X p 2 ut ante, vel b aqu. 3 vel altior, quod impossibile in integris
Quando cunque ergo
solam mudo.
l, CY fier:
v
pa