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# Catalogue record: 24367 — [De aequatione genrali ad curvam ordinariam deque generali modo tollendi literam]
# Incipit: Sit aequatio generalis ad curvam ordinariam
# Date: 1692
# Other printings: Knobloch: Beginn der Determinantentheorie, 1980, S. 244-246
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=24367&katnr=56689
# Work: https://leibnizlegible.com/work/00068201
# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folios: Bl. 193 (from the shelfmark LH 35, 14, 1 Bl. 193): 2 pages, canvases 385–386, page ids 00068201:0385 to 00068201:0386
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068201&page=385
# Lines: 99 recognised on 2 of 2 pages, mean confidence 0.86
# Catalogue: Leibniz-Katalog / Arbeitskatalog der Leibniz-Edition (https://leibniz-katalog.bbaw.de/), ed. Arbeitsstelle Potsdam I der Berlin-Brandenburgischen Akademie der Wissenschaften, CC BY 4.0.
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## Folio 193r — 00068201:0385
# Source image: https://digitale-sammlungen.gwlb.de/content/00068201/jpgs/default/00000385.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 98 lines, status machine
1
eda Y+ B2B FioC
Sit aequatio generalis ad curvam ettic ordinariam
+10 +2
= +ux + x
+12X
+ 22
ete aede
V + 321) + 33y
s
2ax
3
5
fiat dy: dx = v et fiet - v(
data
et C. vel spendio s L100 +. 101y 4 102y + 1037710 4y erc 
Aequationis 2 differentialis est: d100 sx + d 101. y Lx + d 102 y dx + d 1031) dx
d100 + dioi y + dio2 yy = d3 p etc  1. 101 dy + 2. 10 2yly +3, 03 dy
1. 101 + 2. 1027 + 3, 103yy et
sit jam ulia aequatio (6 200 + 201, 202VB + 203V2 ete. quaeritur aequatio 2. Necesse est autem
aequationem 2 et B esse ejusdem gradus quod patet ex aequ. 5. quia v datur ex y rationaliter
Res jam eo redit, ut per aequationes jam A si per aequationes 5 et _ tollamus y. prodibit aequatio7
in qua supererit v, quae non assurget ultra gradum  quem habet y in aeg. 2. Et aeg. 7. comparando
erit cum aeq. 6. Aliter: per aeg. 5. tollatur V ex aeg. 6. et prodibit aequatiob quae debet coincidere cum
ceg. 2. vel saltem habere cum ea communem divisorem. ta  id est si ope aequationum
8 et 2. tollatur y residuum debet aequari nihilo. Patet ergo utroque modo  desiderari 
teo uut calculus inveniendi communem divisorem, seu tollendi literam duabus aequationibus communem
possumus tamen et alio modo uti
illud notandum est fieri etiam posse
quo etiam obtinebimus, ut non sit opus calculo generali oro quovis gradu, sed ut omnia fiant per
inveniatur.
culculum generalem. Nempe aeq. 2. multiplicetur per formulam generalem prodibit aequatio us
quae comparanda est cum aeq. 8. Verurtamen res omnis tandem eodem redibit, quare utile erit
t
ptimum erit pro d100, divi ec. scribere 360, 301, et C
2102, ete scribere 401, 402,
parar multiflicare
10 + 1y 20 20+ Ery = 0, multiplicando priorem aequationem per 2x posteriorem per 11. fille opar
12
et duns a se invicem pubtrahendo producta, fiet: 10.21 = 11. 20 =0
10- _ H + 1 Gy=  20 + 21gt aryy 20 multiplicando illam per 22 hanc per 20. fiet
et subtrahendo producta fit +H 22y + 10c 
16
(et.)
20
20+ 219+2297 = 0 multiplicetur aeq. 4 per 229 et 49. 5 per 11
2. 30
-12 21
et  E0 1. 20 + 11. 21.y (F 11. 2299
aleta a
(20
jam aequationes 4 et  6 conferantur
cum aequ. 1, et 2. firt
fiet aequ. comparanda aequitioni , nempe -10. (24) + 1.(20) = 0 da est (20) = 11. 20 (
A. 11. 20 = 10. 11. 21 = 10.10.2220 (y+
= 10. 22. - 11. 22 y9
ind (21) =. 11. 21 = 10. 22, uud alo caeir aut 7 per 8, hend -10 11. 21 (10 40 22 + H. H. 20 -
Rolonta aeg. 1 vel 4. sit 20 + 21y + 229y + 239 =0 multiplicetur aequ. 1. per ∞23 yy
et aqu. 10 per 11.  et hc ab hoc producto subtrahatur illud, fiet
11. 20 + 1. 21, 9 + 11. 22yy(F 11. 231 =0 et res reducta est ad terminos aequationum I et 5
habetrze  - 10. 11. (21) + 10. 10. (22)f 11. 11. (20)0. p.
10. 23 9y = 11. 2393)
unde fit quid 3 (20) = 11. 20 et (21) = 11. 21. et (27 = 11. 22, = 10. 23 idei ex 69. 12 per 1 fiet
11.111. 20 - 10, 11. 11. 21 + 10. 10. 11. 22 = 10. 10. +0-23 40 Unde conferendo aequationes 3, qa
habetur progressus in infinitum, ut perpere non sit necesse pro hac serie
jam aequationem 10 + 19 + 129y 0 confera conjungamus cum aliis, et quidem
primum cum 20 + 21 y 0 quod idem est a Ergo res reductu est ad aq ubi idem est calcrlus
qui ex aequationibus 5 et 4. unde exx aeg. 9, pro 10, 11, 20, 21, 22, substituendo 20, 2, 10, 1, 12, id est
verbo 2.. pro 1. et contra fiet 12. 20.20 - 11. 20. 21 + 10. 21. 21 =0
Aursus aequationem 15. conjungamus cum 20 + 2y + 22 qy d et multiplicando hanc per 12
illano per 22. fit 20 +12. 20 F1. 2 y(= 12. 22y9 20 et res redut ad terminos aeque. 15 et 16.
- 10. 22 - 11. 22y = 12. 22 9y et ex aey. 17. pro 20, 21, , ponendot 12. 20 eft12. 21
10. 22
=p1. 22
t fiet.  1. 12, 12, 20. 20 B 2C1O2. 10. 12 12. 20, 22 + 10. 10. 12. 22. 22
= 11. 12. 12. 2021 (+, 1D. 11. 12. 21.22 + 11. 11, 12.20. 22.  10. 11. 11. 22.29
 10. 11. 11. 24. 2D = (2) 10. 11. 12. 21. 22+10. 12. 12. 21. 21
et dioisut omnibus per 12 atque ordinando secundum 20, 21, 22, fiet aequatio
+ 12. 12. 20. 20 - 11.12. 20. 21 +10. 13, 21. 21 + H. 1
...-
(2110
+ 10. 10. 22. 22 = 10. 11. 21. 22
Y sc aequatid
secundum artem compinatoriam expressa, ita determinatur quod, tam 10, 11, 12, quam
20, 21, 22 per se sigillatim servant leges homogeneorum, et  po qualibet non
ascenditur a 2dum gradum  qu nec fachunt nisi biniones, seu non insurgunt iltra
adum gradum et eodem modo se habent tam illae quantitates quam hae; et
in quovis termino est binio ex una serie in binionem ex alia unde ascendit aequalio
praeteren 10 et 12
adeoque uetiam 20, et 22 se habent eodem modo
minus ducitur in seipsam, et signo- in
o affectus est signo +, in quo aliqua erm
2 ad qualtum gradun.
Crm
quo nulla.
venique is binarius praefixus est, ubi ed concurrunt utraeque convenientiae
 Regutioni 17 inest aeq. 21
sugno et coeficiente observul ut dictum esse

## Folio 193v — 00068201:0386
# Source image: https://digitale-sammlungen.gwlb.de/content/00068201/jpgs/default/00000386.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 1 line, status machine
Noletum et via redmendi via ad meros literas sumplices, ia faculius cut locu  regaleis cobinationuim, et immediaas