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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 4
# Folio 38r, page id 00068217:0077
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 37v); this page is its right half.
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 78 lines, status machine
# Lines: 78 recognised, mean confidence 0.81
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
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# After the first blank line: the recognised lines in reading order, one per line.

Ervo per 4.5 fier.
laqua
Eodem modo si AV equ. a.
X
ee.
Laqu. b X aequ.
aequ
v - ay + b2(6) y)
yrpers. X aequ. a - y per 1
iec seay + b2 aequo
Xy aequ. b. fiet.  - a)  + baqu. 0.
ye ay +b aequi0.
Condemus ergo Nabulam:
X + y aequ. a. Xy aequ. b. fiers 4 - ay + b aequ. 0.
X +y aequ. a. xy aequ. b. fier y - ay + b aequ. 0
X+y
X +
s
de
. y - ay + b aequ. 0.
.. yd = ay + b aequ. 0
a 
X +y + Z. aequ. a. Xy +XZ + yZ aqu. b.
Ve - ay + b aequ. 0
C.
XyZ aequ. c.
(6)
per 3 fiet : X aqu.   et per 2. fei Xaequ. b-72. quae aequando fer: 3+ ZC aqu. byqe - qu
y+
seu ordinando secundum y, fiet: Z - b7 V + cZ aegb. 0.
+
am aequationum 4 et 7. que tollantur X. et y. in aequ. 1. Et primum
ope aequationis 4. tullatur in ea X fieri: C + y + Z aequ. a. seu  +Zy + C aqu. 0.
(()
vel multiplicando per Z. fir: Z 3 + 33y + cZ aequ. 0.
a
vaz
quam aequando aequatione f. fet tollentur utrobique Z2i, et CZ. et residui, divises
na
per y. prodilit:  et invicem aequatis fiet: y3 - aZ + bZ - c aequ. 0
 prioris
si aequatio 1. fuisset X + y + gt aequ. a. tunc habuissemus laco aequ. 8. sequentem habuissenus.
 + y +Z aqu. a seu E 3 Z4y +c qu. 0 et aqu. y multi plicando per y, habra
20)
a.
habebsimus. Zy- b2 2 + cZ y aquo. quam aequando aequationi 19 tolletur utrotique ius
et residua aequando fiet: -bZ y3- ZY y- et aequ. 0.
C2)
Ergo Y aequ. 
+c
+ a3
+c
3+ C∞ (262) et ex aequa far y ryu (62)y = c200 t
+ck
Unde aequan o) duos ipsius
+
compendiicausa
y. valores fiet:
aequ. +8cez y = cZ2 vel n
Eumque et pus e vel ut comurae aequare possimus
aequationi q multiplicardom sa aequationem 14 per Z
et aequ. 7. per Z0- a ZY + cZ + et. et fiet:
= c
S per compend.
+c6 et fiet: + c eZ3 y. - c
et
cequ
+fe
X (+ v aqu. a.
Nay
eu
a
+ ce
C compen i causp.
 b.1
gen
X qua 4y aequ. b XyZ lqu. c.
Z aequ. 0.