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# Title: Leibniz-Handschriften zur Mathematik LH 35, 4, 1
# Folio 7v, page id 00067996:0014
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Efficiendm jam est, ut quadratum de 2egr + cnr. adento er
: In teqrenque
en + eq + cnq1
relinquat quadratum ducatur 2e q + En, in 4 ta +eq 4 enq
fier requln + 2Cr a regrenque pe, producta si adimatur
2E quadratum a a regr + cnr quadrate relinqui debet
(0 vaso
quadratum, fer ergo. = In et ( Prq ecin qtaeq+4Cqtc)
y
e
duaspeses  et et vel
tert ia deforis asumt
ubitiariam
duaum priom inventa selvet pure, habemus. aesideratum, quem in finer
 (Cn) + a cn BI + B. 1- lne (- eenq) + 3 et
imo et aliter, sipunctur Pa  esfit enim
x2 ponamus
Deqen cn
quod  effici potest, si modo detur numerus quadatus, qui subtractus
iniset a Z. 3. relinquat quadratum. Seu modo ternalius possit esse
potest, si sit duorum quadratorum summa.
aequationis
aliter hoc solvi
Rostat ergo Omnia ergo rediere
BN et, adaesolutionem hujus pablematis. X + Z2 p 3l. seu quaerendi sunt
fiet aequatii duo quadrati, qui simul sumti faciunt a, fiat X + 2XZ + Z2
5, 3V + 2xZ
nunc Tantum ergo apus est 3l + ZXZ aquari quadrato V, fier ergo X p, V 3
 ponatur
 et X +Z 1 D at ZH 2X y, erit 31 A4 X 7
s.
x1
vy
12H
male
Z
sine raxa
e
tco
et 3( p. 4xyco + eo. D. rum X +Z + 2Xy + co. Ergo pro
in unas
Xg substituendo ejus mutirem sive Xl+ 2XY  2Xy+ col. D.
XC + exco Y
Ex aeq0.
co +AXVI + +Xy B 3V + 4X5., quae aequatio
t
i
facile exitum nmmeris reperit. altera aequatio D sic resolvetur.
y. axy
poratur colxx n go
3 fier 2Xy +X C XY SECX-X
et c + 2Xy F  31 + aex y. Ergo c
Ergo co   CO , XF SicOX CX A BI
sive co - X +. YrcoX. N p L3V + COX (X S. con. x (x
 HX, fiet Jam ut Radix extrahi possit ex 2X - X
ponatuo 2CoX. X  X X 6v2
et cer 
21
10+ 
fiei 2e0 X B x
et X Y 2co l erit P2CX X arcola
et fiet 10 = 2cod + 2colov
videa
e
1160
31+ 20010
 17
4co l0
l40V
V+ 21504
ga
 
Videamus
an 3H =  316 26120 1to 4V + 2co ( + 2Co l6V apo lo possit.
L2
sine (co= C0) c videamus  414 13l a Co 14 (1 2C 15ota
i
ppyrit esse quadcalum, pet eruta L + 3L0  4co  gba fiet
H 1I a2 cot+
aequai quadrato. sed sa vix habebitur exitus.
su
est data
D
de