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# Title: Leibniz-Handschriften zur Mathematik LH 35, 4, 1
# Folio 7r, page id 00067996:0013
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(4
Aequatio Quadratica duarum incognitarum conglata
in Numeris exequenda:
X + dx TE yX + e y + f9 + gl. p0.
X + d X + d H ~ C y 1fy - gl
+ 1dy
+cgre
e
+2cd.. + q2
unde fiet:
(seu 
Invenienda ergo Y talis, ut - e  ∞ fy y -gl sit que uadratus.
re
+c.. +2cd.. + aV
a
1
nde ab Aequatione quadratica completa aem traduximus ad incompletam
Jam efficiamus ut  multiplus iptus y ascendat ad quadratum
Huus aequationis
y (- f Y (= ob 0. tollamus terminum secundum
+2cd . 7+ duact
12
1- f y
+ned
E 
∞e+
(+ 52
-4cdf
+4cd
C
l
+8 - 2ec c4
1 13 1
e
t
Asgrationum 
Re solunio ergo omnium robematumvadraticaum in Numeris,
Resolutio ergo omnium Z0 eorum Constorum sive quadraticorum
in numeris huc redit ad resolutionem hujus laequationis:
-et y -el gl +f12
a
+c gl
+ et qr
e
-4cdf1
(9)C4
Sive invene generalius.
v2
hy mt v.
c
si m l’ absit, necesse est h, esse quadratum, alioqui problema est impossitile
si h sit quadratus, problena solutum est, etiumsi ul adsit
Artiq ergo fuerit saltem ab initio statim ita formare aquationem
propositam ut hl sive et + ci, fiat quadratus. Quod an commode
fieri possit videmus. Si c2 le
si C2 = l sit quadratus, tunc enim inverso modo progrediemur incipiendo
ab y; ati num incepimus ab X. Nunc ut appareat quid fieri possit,
ponamus X p _ B n Z n co + p.
eat 2it
1
e
C0 + En CP + p2
= + drs p, e2
et fiet acquaitio talis. co
1
, et y H 20 + 1p +5
et ey p C4 co + 29rco   29 seco tY
l
Et CyX Cnqco + cnr CoV + ens co+ cp 9co E Es
12
1
+er  X ahr C0 B, 29 se C + cpr V
n 1s
nx
enpt
1c4
i
+57..
2es.
12 C
es 0
d - 2 + f= 4cd 5+ed
+ cxs 1
e
opl
lita
sive faciamus. 1y