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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 2
# Folio 197v, page id 00068195:0394
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talis solutio non fulura sit recpoca
ita ut extra eam alia no esse non possit
erit tamen vera, si 4a +8a + 4 censentur aequale = ff. Cto.
et  a2 + 243+ 4a + 1 o censeatur  qub = gg B
aequatio ergo est: 4a2 + 8 a + 4) = ff
a +2a +2 = H - 2
a at2 = q s4
Nota si a sumatur 1. tuperior quidem
terminus est quadratum sed non inferior
si tamen ei adjiciatur 1. est ipse
tum 9. Iovertatur rasio, et loco
dd + +a +8a +4
ar+ 2a3F ∞a+1
duatur, a+ 2a+ a +I
ded qapea +t
addatur supeion 1. erit ex ipse utum sumo
sito quod a sit 1. et acedet toti
= a 12a 740 +2 sed ita
qa e8a +4
Omna perturbabuntu
Alia ergo alia ratio investrganda est
Qua ex duo divisione numeri dati per
datum fit Quadratum. A= cc. Ergo non posserior.
L =c. Similiter ergo ut rod utistium
Casum redeamus, si 4a + 8a +4 = f dd.
Sd tra +4a f2.
Ego 4a +9a +4 it cut = d.
a2 +2a3+4a f2
Ergo
4 a +8a +4 -  d
ard + 2a d + 4 2d
4a+8a
= d+ 4
a3 + 2ad + adF 2d aa + 2a + 4ad f 2d
4u
a trrad aadted
Si Numerus qui per alium divisus producit qua
dratum, est numerus 8 f4
purso
est numerus qui quadralum multiplicanis, producit
dividendum ergo
4 a +2a + 4a +23d- 4a +6a +4.
16 110re 1 
B
4a + ba
13d ga
4∞ + 8a + 41 + 1
2a
a evel
24 Aat utu
14
144)
Exhhac duitone spatet, ut eatsas 
it quadratum 2a
4a +
Aa+ _ + 4
xa harca
+c
 a
seu 30 7(=4a.
3a
sErgo aC).
3a+4+1 = 4a +3
3a +2 = fa) 3a +a
Ergo 3a + 4 = 4a +3.
Ergo 3a + 3a + 10
si jam a. sipponatur esse 2. tunc 4
4a + 8a + 4 + 1 erit tunc prorz quide
terminus 4a+8a
.C. verit quadralis sed
64
+ 8a + 5
1 1
4a + aHt
A∞ + X + +
Ex hoc
Calculo se qui
4a +8a +5 sit
Numers quadratus qualiscunque suppo–
natur a, quia scilicet, orretur
aequatio inter 4 et = 2+1. seu .
quod est impossibile. Notamdus est hit
modus satis elesans probandi an aliqud
possit exprim calculo 
sed vereor ut sit planie sufficiens
luo est, cum subtenis a quo subtra
hendum subtrahendo major
elud dum minor, tunc enim mutam
sipotus radto
6d1 16+16+5
a A 
e p