# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068199:0385
# Permalink to this reading: https://leibnizlegible.com/page/00068199:0385?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2c
# Folio 193r, page id 00068199:0385
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 194v); this page is its right half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068199&page=385
# Source image: https://digitale-sammlungen.gwlb.de/content/00068199/jpgs/default/00000385.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 65 lines, status machine
# Lines: 65 recognised, mean confidence 0.89
# 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.

dy: dx = xx + gy,: aa Assumatur g 34y + 33y3 + 32yy + 31y + 30 =0
fiet -dy = d30 + d3iyt d3ryy + d33y + d34y: 317 2. 31943. 339y + 4. 34y  = Xx + gy,: aa
1.31 XX + 2.3F pyy + 3. 33 Xx yy + 4. 34 Xx y3
+ 1. 31 yy +2. 32 y + 3. 33y + 4. 34y = 0 ~ 30 m + 31 my + 32 myy + 34  + 34 mys
3ony + 31 nyy1 317 131 1y t 31 py
= d30 - d31y - d32 yy - d33 y = d34y e Fiet n = 4. ex summo
2 sit m supersunt aequationes 5, et incognitae 5, nempe 34, 33, 32, 31,30, cum constrnte 
arbitiaria (3= hom + d30 fit 3. 33 +30m + 1g0 d31= 32m t 3. 30m + 9d30 
3(33 = = 434 - 3 34m. Hinc 31 et 33 tollendo in y7, fiet
-3de rx 1 3. 3+M X + 30m + d30 - d32 = 32m   H X = a35 1  4 L.5C
- 3 d34 pp - 3. 34mXX - d32 = 32m + 30m + d30
supersunt y et y
in y fit 2. 32 = d31 + 31m + 4. 30
it 4. (34 - 30) =  a (31 + 33) m + d (31 +33)
Er
Ey y fit 4. 34 = d33+ 33m
+ d31 + 31m + 4. 30
sed nihil ex his, nisi prius investigemus modum ex divensis literis simpli aequationibus
differentialibus simplicitus inve compositis investigandi pluriliteris, in vestigandi uniliter
sit  aequatu sint binae aequationes dta differentiales simplices biliterae
datae, iIt y + 112dy + 121Z + 122d7 + 100 = 0 et 211y +212dy + 2218 + 222d7 + 200
c(
Ossumantur binae tale, 32Z + 322 dZ + 300 =0 et 4uy+ 412 dy + 421Z+ 422 dz +400 =0
quaesitae.
videatur an ex his duabus componi possint priores duae. Ope a44. daturum
Follatur dzue siet + 111. 2229+ 1h2. 222 dy + 121. 222 Z (t 122 222 d7) + 100. 222-8 = 0
= 172. 211 y - 122. 212 dy - 122. 2417( Frr. 222 d,3 - 122. 200)
Espari modo ex duabus posterioribus tollatur aZ, fiet t
+ 321, 472Z + 392. 422 dy  + 300. 4227
- 922. 411y - 312. 412dy 322. 42178322. 422 d3 - 322.400)
6 = 0
Et aequationes 5 et b coincidentiandofiet 4+= 1m 222+ 122. 2H: 32.
400 = - 100. 222 F122. 200 4 300. 422,
et 411 = - 118. 222 + 122. 214,: 322
41Z = - 112. 222 + 122. 211,: 322
421 = - 121. 222 + 122. 221 4 321, 4227: 322
dollatur jam q iterum bis, et fiet:
et ex cognitis fet + 11. 22y f 12. 22) d9s   121. 221Z) + 122. 211 dZ + 100. 2217
quaesitis seu
ilemque ex incognitis
= 141. 2ug - 121. 212 dy R. 121. 2417- 121. 222 clZ - 121. 200)
(+ 321. 421 3(+ 322. 421 dz +300. 121 2 - 9-0
32. 411Y - 321.912 dy = 311. 421 7-321. 422 dz - 321. 400)
Et aequationes _7 et 8 coincidentiando fiet
400 = = 100. 221 + 141. 200 7 300. 421, : 321
41 = - 111. 2217 121. 211, : 321
412 = - 112. 2U F 121. 212, : 321
421 = + 122. 221 - 121. 222 4 321. 4227: 322
ope quatuor aequationum, 1, 2, 3, + pestunt bis haberi aequatio, in qua absit Z et d3
adsuntque y, dy et y, quae reddentur, identicae, faciendo ut y, du, et y evanescant, quod siet
ope aaquationum sex, cum tamen habeamus arbitrarias 8
per aeq. 3 tollatur dZ ex aeq. 1.
et et ex orq. 2, habebuntur binae aeo binae aequationes se in quibus supererit Z, quarum
ope tollendo Z, fiet aequatio in qua extant y, dy, et y
Eodem modo per aequ. 1,2,4
habebitur talis aequatio, harum aequationum quaevis tollatur reddatur identica, et habebitur
si tres dentur aequationes assumentur aliae tres, literarum arbitrarium
tilitorae
una quaevis 7 sunt literae 21; et brua literurum arbitrnriarum septem poterunt reduci
videndum annoue earum unius gliterae affectione, ita res ilut redacta ad casum priorem
desideratum.
in nostro casu 131-d30= 3om  2. 32 - d31 = 31m  tn 4. 30 et 3. 33 +1. 31 - d32 = 32m + 4. 31 ubi patat
Et non posse omnino tolli d31, quia occunit semel tantum sed solamus 31, fit 31 = jom + dec = 4 92 - = a32 = = 32M
sed Assumantur binae biliterae, (quippe jam solute), et una tulitera, habemus arbitr literas 10+12 = 22
um meritum eo aem quca ateru sett  pu pert eisur ite