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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 92r, page id 00068201:0183
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quadrati aequales numero dato
Maji 1675
E V +X  ab. Aequatio resolvenda in numeris rationalibus, , ita ut datis a. b. c.
quaerantur y. et X.
Certum est aequationem non semper in numeris rationalibus resolvi posse.
xi potest radix hoc modo:
X p,  ab - c y
Ut reapse extrahamus radicem forte rectius relenta aequatione ita procedemus.
1Veq
et stabit.
1
+
2c
aV YX
a
c
a a 2 1t
= ab
Hind jam apparet  si extermno 1 + cAV
V
Ergo XN nisi ponamus X. contineri
in y.
2
Itaque proa ponamus aZ + =ZX+X
pommus y, Z+ Q X. unde
+ 237X + dX
a
a2+ cd2
a3
ex aequatione nam u extahi possit ex aequatione, quomodocunque d, et Z explicentur necessees est tamen
N ingreti radicem, et quidem nulla irrationcli affectam, quod non potest obtiner, inisi ex 1+ Ed2
radio exhari possit, quid non obtinebitur aliu X in radue quae hanc destrud inationali affectarm
nisi forte velimus iterum explicare Z per X + erc sed hoc inutile jam enim conietur in priori
explicatione ipsius y. ab initio, quotrescunque enim ponamus N esse in y, hoc exprintur per d.
Itaque finstra Z puosus per X. explicatum, ipsam autem d per X explicanido tunc in y. valor ipsi us X
asseiget ultra quadralum: Et vero tunc necesse est radicem cubicam vel quadrato. Quadratiam
extrahi posse, ex aquatione ubi omnia multo difficiliora.
20
cende a + rachd + ae, po sive d = a ae Ergo rap,- a- a + 2a0
sive rari ae - a. ergo d
Ergo
2aC
heorx
43
a
zac
2 atx
+
e
+ee
ac
l
cr
art ab
arbitrarium, un cere videtur
an
ab
e
reoque
raen
a + 2aC+ a  ca
4ae
pky
b
1Ia
h1
 
2ac
=a2 e3 H, ae h 9
e= a2, ∞,
eotr
quod si jam ponamus  esse
FtC
AZ
pa
a
DA
ect
Unde jum aequatio
povesum
deta rac
d ejus resolatio non minus dicir