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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 133r, page id 00068200:0267
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 132v); this page is its right half.
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esto at g ei  in a H D H Z. Ponendoque a e fl, fiet
ideoque
a
item is
-29fb
+2 fn p 5 vnf enf
M
+P
f. 29b
e
s
V 2)
-fg2(a. fg bt +gg apb 1 fbl  9 gbl2, B omiseram
onamus a e s Brnus forte ad rem ita perveniemusu, aequatio inventa erat
la + n F, 2nal +nf efn
drantal foligs
fiet fb + n e, 2bn + nf - 29 f
2 b +f 229
suntisque fb abn+ns.  erit, nt - 297
1 - 2 901
vel sumta n e gh, fiet gh
2
en
d
+Ai
+sn = f 2
vel snt nterio, set  p
2b+f-29
, sive h =2g  et supra 2fb ⊓ 2bgh + 9hf
2b + f-29
26+f 29
Atque ita  f. et b, et per consequens a, primus numerorum quaesitorum, sumi possunt pro
arbitrio Nam - 4lg
Contra intentionem
2
2b+ f- 29
 2 fbl, omnes hae tres linec oscendent ad quadratum
2b9 +9f
es
Rectius ergo resumta aequatione suberiore et ubi posita n b, vel reductis
Terminis fret: 462f +2f b -4gfb, +2n b + n f -n 954bn +abnf  4bng
e
nsb + 2
 - 2nf9 = 4g 2 n X
Ex his teminis  pemus..  4gf b 1 nf  Enfg 4gn ponamus 49 p, +s  p,
fietf 2fpb...
.. 2f2b 4gfb..  + nf- infg- 4gn faciendum est ergo, ut explicatione
unus horum quadratorum alterum evanescat, quem in finem explicemus non g, sed f.
poncndoque f et 20 + P, fiet nfa e + 4gn + 4gpn + p n
sed habebimus tamen
et an + 4g b, et = 2ng et in summa stabunt, n 4gn. - 290 + 44b - +gn
quae u ut faciant 0, ponenda est 2M  Ab n (- 2b
-n
et b5
rede  care fiet fa 138 a d a3   1b 2 fF 9 Net 2t bf - 297
un
a
et ag fet ispap
nf- inf infp, +nf- infp- npt
Ergo in aequatione fb + n i Xbn + nF - 2gon
80ct 3
A
2(+f -29
2
n +f-29 reductaque equatione, n + fa egnr aeg 
C
1) =n +nf - agn, sive -7 +n F 9
- 4
ponendoque fg vel - n + fn - s
de
W _ fn - 29 + p, et f7
+f - 29
vL
4
sive  +2sn-f +fg - 2gr
n + f.29
+ sgr 10
59 -gn + 4970 Ponendoque
fg(. 29+9p. quibus valoribus
in aequatione superiore in locum  et fg, substitutis habebimus:  gn t sgp - p - gre 70
sumtisque pro arbitrio n et
2
vute
 292fV 1 ∞ + p
Ideo sive Talut+ 
C
+
1
 2gf
Ergo g et
2C +fb- 2pb
ponumus nanals
svel positas a
Xb.