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# Title: Leibniz-Handschriften zur Mathematik LH 35, 4, 1
# Folio 14r, page id 00067996:0027
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Schediasmatur
Numericis affectis
initer deptemtr. 1674)
D in Numeris  Rationalibus exequenda, 10 B. tota s
X + dX + AVX he
itque () ges H A X
 incognitarum
Aequatio quadratica Generalis duarum 
ad puras reaucendis
solutiones hatentae causa
+f.gC1F
e y
et  Cuera
+ 2deV
c
Invenienda ergo 1 talio
2dcf
Aedes Ninos.
443E
 rel,C
17 14
g. Ergo
4 it
Ergo
-f y - gl
+2dc.. +42
. Quadrato
formula ergo sive quantitas exdom ista quadato novissima quadrato  aqualis reducatur
ud eundem
quod ut t
id
pos
venominator,
partium ex quibus de componitur denominatorem,, e 2el + C7.
+ gl - d multiplicetur per _- e + . Quo facto abjiciatur
nam si et quippe quadratus, sufficierque Numeratorem
aequan quadrato et far
dep (6)
se yl
- eg
+ ed
+ Eg.
ed
c ()
e ato rades
Sive concipiendo  generalius:
+52
16dc
Eg+ t  v.. Ecq (7)
ide Quare solutio omnium problematum quadraticorum in numeris reducitur ad
solutionem hujus problematis unici. Invenire duo quad rata, quorum atteri
praescripto 8. 9. 22. explicabimus; modo cogitemus detso per data num erum multiplicate, alteriqu additum faciat numerum datum
+ cy 1.
(4) Ergo y _- f
sequationi
De Affectionibus
acy.
Quod si datus multiplicans h sive - et +C in exemplo nostro, quadratus ipse est,
facites es problema solutum est. contra, si l absit, nec h sit quadvatus
in numeris
problema impossibile est.
Qvoniam
Quoniam ergo pestulatur ut = c sit quadvatus videndum an aequatio
proposita statim ab initio
capacem reddat solutionis
in eau formani vredigi possit, quae
Id est a explicatis in cognitia
residuum
videamus an effici possit, ut disseretra intr quadrate ullulteplicatiteyX subtracto temind
sit cognitam aliquo
Miplicante alteratr  quadratiisalt
multiplicatur), sit eondratum multiplicante; sit quedratum,
Resmnta ergo Aeq. T. ponamius
ex pononop. + d 
yA4c0 atr Y. ass erit
eq cor + de qr cV + reasc + er p ers C5
X e n + 2 cd 
et GyX  enq co cur coV ren S cd +EBA CotCr I + cPs
Homogento gl. per ex cteg. 1. fei. Aeq. (10)  pC.
Ca Cpas colp caz E, ens P
2uma  pm  . f. q
Quae ordinando addito
ex ap  gr co  c us + de
2m.. von.  19.1 + re.
eris 
tum.
teneci
Enp.. + cer.
Er. dn . +ce
acue. tens.
repy. 12ep
et
Scheda hac nnihil
dictum, a quo
exitum videam
aequetas traeni
C 2el+
aequabitur Leactato P
tengle
+e5