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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 304v, page id 00068201:0608
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AB sit X. BC sit y. Quantitatis indeterminate. determinutae vero a. b. c. d. e. f. aequalio celationem exptcen
potest
generalissima seu plenissimique ves foositot
5
ac
latem has, explica et ad quodcunque exemplum possunt applicari, pro varia explicatione literari
quae et aihito aequales ponentur cum aliqui termini desunt; e Quantitati negilivae quole
non adduntur sed auferuntur Jam ex methodo. langentiam Auidenus vel Slusus
posita CT tangente, et DC vocata h. eriit 7 aequ.. 2ax + cy + d
2by+ cx + C.
ope habemus ergo un duas aequationes nunam datam quae contiges
duas indeterminatas X et y. alteram, qucventam quae continet
hes 9. X. y. quae ritur _ ex his alia in qua nulla sit V. sed tantum duae hlerae
X. et 7. sive nquaritur relatio ipsius Z sive
Ut ergo collatur), consideratur
 =ax - dX - f
ex aequalyne priore habebjo y aequ.
positi p aequ.
by+cx+0
MoB ad salani X sid 1AB
BC pe compend.
p
ex posteriore y sine 3 aego
bx +9
=ax - X - f et 9 uegi CX + e.) fiet ex 2da aequatione fier G ax + d = CxZ - eZ
ee
seu posit a raequ. 2aX +d = cxZ = ez.
et
e)
aequ. 8b 60 fiet y 
10 r 3bZ-C
ergo aequando aeg. Y et 10 fiet PS. aequ. bry + q0. et y aque psqu quam aequaationem
jungendo aequationi 10, fier ps grs aequ. br
aequ. + 4b2gr- 4bcZ+ c2
= ax - dx = F
-4bfZ 44bcfZ -f0
= 4bd7 + +bcd ZY - e d X
4ab 23 + 4abez  ac A
p2
Jesi
CX +O
26Z- c
=cx = e
rerbax tibeh
ag seu 2bc
qu aequ
Yaeqe. ~C
X Y 2be7
ey
+ 2bcd2 2bde Z
dx
+4 abcZX + 4abeZX - 2acK -2aCCX
nn
=2bC CEX - 1b eqZ 4 rbesX
2bcr X - 2b cet
X +OZX +CC
tce
a
aequ. 4aX + 4 adX - 4 ac ZX - 4 a CZX, + d = 2rZ C 2 deZ, 4 CXZ + 2CO AZ
=bce X
 +4bd
e
n
 -IZ abcZ X + 4a bX f3bC272 -4aber. XZ + 4abdX - 9bde Z+ bdi at0
Unde ordinando habebrinus:
3bc X
22
e
e
+3ac + 4bF
abcdt 2acc. = co2
13c
 cde 
+2Ca. 24bcf
4fC
ubi notabilia: idem semper iumerus liberarm cognitarum in termino quolitet totius aequationes bio
4ab
articulo
adem signa in quolibet membro eundemque eadem signa artict humerureque articuloum a quolibet in quolio
cirtento ejusdem memori Denique bines articulos cucilibet altiorum mem brocum, ternos un feliorum
A
cC
X
C
2a
t 
e