# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068196:0588
# Permalink to this reading: https://leibnizlegible.com/page/00068196:0588?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 296v, page id 00068196:0588
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 297r); this page is its left half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068196&page=588
# Source image: https://digitale-sammlungen.gwlb.de/content/00068196/jpgs/default/00000588.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 94 lines, status machine
# Lines: 94 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.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line: the recognised lines in reading order, one per line.

Si sit proposita Aequatio
dx ity = 1BX +2By + 12], : 3Ox + quy + C41
fiat X = 50Z + 501 + 51, et y = 60 Z +60v + 6) fet dx 50 d7 + Solv ptys 6oty r
et ex aeq. 1. fiet 50dZ + 50 dv, :, 60 d2 +60dv = 20 56  206. 8
et fiet: + 3050.50
+ q0. (. 50
= 10. 50. 60
- 20. 60.60
+ 40. 60 50
10.50 60
= 20. 60 60
122+ E vV +YZ + +30. 51. 50 3+V
+40. 61.50
+ 341. 50
= 10, 51, 60
= 20.61. 60
= 121 60
40. 64v
=O
erum jam video cur talis methodus non procedat.
e
cer simalie
40.6190
1349. 50
omnem ota liceat reducere ad homoeoptota, nam ita res
in effectu reducitur ad unam a indeterminam, naeque
quoniam fe  ponendo Z+ V = K, feret X = 50K + 51 et y 60k +61
quod absurdum est. Ergo minium oportet assurgere ad gradum
secundum, itaque siat  dx: du = 10X 420y + 121,: 30x + 40y + 341
vaz
vdv vdz de
= 10. 502 ete (ut in 2) + 20. 6077 et (ut in 3) + 121 :, 30. 50  ese (ut i 2) + 40. 6027ete (aln.) + 3u 2. 3050.502 d + 16240 50803 vd 1 2 341 50. l 810 50. 802 d
releunit. et ex ag. 1. fiet: 2. 50 Zd3 et (ut 1ia): 2.60 2 12 (x te (ut in 5)   saX  t al i 1) + 206011
vdu
Et multiplicatione istibuta per crucem, ex aequ. 6 fet fiet
2. 30. 505222 dZ + 2. 30. 50.50Z7vdv + g. 30. 50.
3050
2. 30. 50.70
30.50. 70
qvaque + 2. 30. 50. 51 474 3 Y 2. 30. 50. 51 Z vdv
30 50.51
L 30 70.51
30, 70.51
+350. 70Z. dv + 30. 7051 2Zdv + 30. 70. 72 Zd  + 30. 51. 72d3
30. 51. 51
30. 50. 51 222
plicatione per exucem in aeq. 6.  coefficiens ipsius ZVdZue est. 3070 51 + 3051. 7D
 2 4 30, 70. 51 + 30. 51. 2.50+30. 51.70 +40. 80.51 +40. 61. 2.50+ 40.61.70
 10, 70. 61 = 10, 51, 2. 60 - 10, 51. 80= 20. 80.61-20. 61. 2. 60 -20. 61. 80
coefficiens ipsius Z  Z7aV ess, 30. 50.51, + 30.51. 2. 50 + 30. 51. 70 + 40. 60. 51 140. 61. 2. 50 4061 70
10.50,30-20, 60. 8
et qqu dque Habet coefficiculer (. 10. 450 4 30. 70. 2.50+ 30 18. 70 + 40. 60. 2. 50  40 80 2.50 + 40. 90.70 
et debet esse 9= 26 calculi autem contrahendi causa, licebit quodam quosdam terminos
ponere aequales Tnihilo, in assumlis, non tamen simul hovet 60 nisi velimus facere  et e -0 ut s
eec
1050.83- 10. 78. 2. 60- 20. b0. 1. 29 802 b0
E
+3050.70 +40. b0.40
=10n 50 2.60 10. 70. 2. 60-10. 70. 80 - 20 60. 260- 20 80. 2.60- 2. ∞. 80 1
O2 10.50.61 - 10, 51. 2. 60 + 10. 51.80-29. 60. 61-2061. 2. 6 20 61.80
Rursus 23   habl aefsicientem 3050 250 +40. 60. 250 
delevant. Erquet 70, 56, 51, 72, 82 sint . uexo
quos certam inter se relationem debere fine paginae praecedentis costendimus e
nempe ut colfficienss ZVdZ sit duplus coefficientis Zq dv; et ut coefficens
jam facta multi
a
1a50. 2. 60 - 60, 2, 664 330 5or0Y 1B  3. Gorobonorto da tis
 52150, 20. 707  (a 2+ +40.
ede
Multiniatio instituenda esset per crucem in aeg. 6. ad procleecendam aeg. 7.
Sed sufficit nos praevidere quae deb esse quomodo se habeant illi coefficiente,
ipsie
ipsius ZZV dqu sit triplus coefficientis 23 de
debet esse d = 20.
a
et X= 177 + 850 V _ et X = 50ZZ + 70ZV +  51 Z + 72. et y =60 21 190 ZV1 69 + 31
do
et dx= 2.502dZ + 70Zav + si dq et du = 2. 60ZdZ + Z dp + 61 az .
vdo
+3. 30. 50. 72 ZdZ
30 51. 51
seie
d
.
2061
121 60
6.51. 60
12, 82
poterant
ilti
nam n
calculo
sequante
non