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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 30
# Folio 9r, page id 00068243:0017
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Insigne calculi compendium in diopeanters
a
X - y p b. X + Z et
(
2
2
X - y p a b
x- Z d
e
X= ZH cd Y. 27e52
Si ultimae tres aequationes efficiantur, et sint X. y. Z. primi inter se
necessario effectae erunt priores omnes.
jungantur 7 et 9. fiet: 
2C11
X H aT+y  Cd +7. Ergo y H Cd + Z - a b, H c5 +Z per 9.
(10)
(12)
Ergo fiet: Cdi a6 + e 
2
(4)
163) Css est + yt Ergo ZH ( Ca b F (X Cd
VH Xab H
2
seu cd
(15)
5+CS ut ante: sit cd p + ab(4) ef + g
(13
fiet cd (ab + cf+ g + +(F) rabes  F 2abg (4) 2efg 1 (a6 + e77)
et abp 97+) 2049
=(+) 2ef =
sit ve xAhx a
X ab + (X 2xh+ h
thd
Cdpi.
=1
2h
2m
ca
2
 et X cd + m ab+h
et 2m A 2h
Aim, -ne  ab +ef2
2h
fiet: ab  2hef +2hm-imiti xhers +tm
ua
2m - 2h
I Am. ph
dA
resu ( 3(Bresu(+ rgest r9
(H2etag
rh
XY CZ+ m effiet ex 8. 2+ 2Zm + m, Z+ Ca
L
n
a
retqe
A() ref =29
fier XC aeb +h. et yp, +ab  +2)ti ab- t
Ek
et Z1 Scd-m
s
-y
e
sunt hes plure sese formulae quadrato aequandae, factum
ex omnibus in se in vicem aequetur quadrato, quod si
illae omnes ponantur primae interse, necesse est
etiam
bXy + CXY + dX
6X t cy + d7
1X
X+y  b
(4 bX  CG X+y ⊓4
Y+ZB C. y- Z H f2
D
ingulas esse quadratas. idem est de Tubo
uod
si hoc aequatio
av
=X
+X y LXG
X-y
X -9V
X7- Xy = 7Z0 + yZV
2
+ et 7V
Axt -g4
XZy) xyt
V7u
solvatur, in numeris integris
strimis inter se, habebitur habentur tres numeri x. y. quaesit
X
qu +yZ2 abedtu
cy
y-
2
1
rutionalite