# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068199:0227
# Permalink to this reading: https://leibnizlegible.com/page/00068199:0227?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2c
# Folio 114r, page id 00068199:0227
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 115v); this page is its right half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068199&page=227
# Source image: https://digitale-sammlungen.gwlb.de/content/00068199/jpgs/default/00000227.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 106 lines, status machine
# Lines: 106 recognised, mean confidence 0.84
# 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.

d
- 100 + 111H + 112 des + 121V + 122du + 131 8 + 132d2
0 = 2 = 200 + 211y + 312 dy +231 y + 222 du + 23+Z + 232 dZ
unse incognita varians
percnamluaria
B  100. 311 F 11I. 311y + 112. 3Iidy + 121. 3uV + 122,31 dv + 131.311Z + 132. 31 dz
0 = 200. 311 +31. 31yt 21. 31 dy +721. 3HV +222.31idy Y231. 3117 + 232. 311d2
112 d 32V F 112. d35) + 112. 32Idv + 112. 331de Et, 200. 311 4211. 221 V ∞ 211. 3312
inde explicando (b 100. 311 + 111. 321V + 111. 3717 + H2. 32
slieret
07
+212d32V + 212d3317+ 21232) dv + 2n. 331 dz
121. 3I1V. + 131. 3u1Z + 123. 311d∞ + 132. 311d2) +221. 31V 4231.3112 222311d vi 232. 31d
F EIII. 331 F 112. d331 F 131 311 = 211. 331 F212 d 331 + 231. 31 res non procederet, quid  1 et 4u ssantes 
iatC
212. 331 + 232.311
fact he bit, B - 31y + 31 W et Z = +11y + 4412 G et prodibit
112. 331 4 132.311
rober
pedeundo ad aeqqe
ado
0= 100 + 19 4 112 dy + 12l. 3 411o  122. 34 du
4 121. 311y 122. H dy
131. 41Y 132. 4u dy
122 deq. W
131. 441W + 132. 441 oW
132 d441W
et rususo = ut ante tantem primam
notami mulando in 2
et fiat 121. 341 + 52t 122 d341 + 131. 241 + 12d441 ( 221. 341 + 222 4341 + 271. 491+ 23 =d441
222. 341+ 232 441
qud sed hic diviesio institui uva potest, ut numeritor numeralori, et denomi
122. 341 + 132. 441
nator denominatori aequetur
An ergo sic.
126341 221421 seu 3IF 132. 441, 13  222 341 + 232
122. 341 + 132. 14F
228. 34 123044 B
231 44
121. GA 121
L et d441 = de. 341 + ed341, et ex aequ. 11 fiet
231
121. 391 + 122 d341 F 131 C. 341 + 132 de 341 + 132C d341 221. 341 + 22 d341 + 231 C 34112) 2de 341127
12. 2. 4 132e
222 + 232C
121. 222 + 13 2x I 1tC. = B31. in + 132. 822 Ae1391 1122 122d + 12432C 1 d 3a1
127. 232l + 131. 23288 + (132. 232ede
aequ.
+22. 22 + 122. 234 + 122. 232de 1 391
132. 221e 4 132 231ee + (13223 2 ede)
+122X328 + (132. 232C8)
122. 22d  F 122. 272e  d3a1
XBC + (1m2. 232 e0)
Ita tanden res reducta erit ad (d341: 341 per meas cognitas vel arbitrarias
sit aequalio dy .dp = Xx =+ gy: aa
vy
sit y = (E s dy = v I B dilus = dex B + vP s. erc
Ergo  omnis aquatio differentialis simplex unius literae sicareat
termino absolute deni potest attolii ad altictem
s ntumus sit 1044G+ (2 dy + 13ddy = 0 sume 20+21 y = 0 fit  420 f 21d) + 21
et dd 20 + dd21 y +2421 dY + 2) ddy =0 componantur in unum, etf
uic adunur
Pdd2o+ padrius Crpdidus Dp 2ddys Vtio +tu yAt2 du + +13 day
9420 +9d21y + 421 dy
Y 20 + Y21 G
fit + = 1 21p: 13
unde 2p d2j + 921  1. 21 p: 13 et 9- P, F- 2 det
et Y. = dd21 + d21 - 2 det d21 1 Et p dd2c L. p d21 - 2p d21d21 + r21 = 11, 21 p; 13
21
1321
21 13 = 10. 21 - d20 + 2. 201d2 = dd28, sed hoi perplexiys
13.20
21
1.1
21. 20
20
10+ 112) + 12 dy + 13ddy = sit aequalio data. Asjumatur alia arbitraria
20431 9 + 22 dy +. 23ddy =0 et fiet +13. 20 + 1321y + 13. 22 dy =0. Et differentiando fet
peedir 30 +3 2t 33 di
= 10. 23 = H. 239 12. 23 dy Hinc 
a(t d8B + d31y + 31 dys +32 ddy 0 quam aequationem conimmendi print t
+dyEdy
conferando equationes a et 6
fit
fit 13, 31. 31 , t 13, 31d3 2  1731. 32
aqu 13. 32d31 = 11. 38. 32
pur
fiet B dao + 13d3, y (4 13. 31dy (+ 13. 32 d1y
1
+ (3432dy
= 10. 32 - 11. 32y - 12. 34 dy = 13. 32 ddyes
fiat 32 = X 31Y et d32 = 31dr + rd31 Ergo ex ag. 7. fiet
13. 31. 31 + 13. 31. 31 dr ( 13. 31Y 431 = 12. 31.31Y =31Y d 31)- 11. = 31. 31YY, et divisis ommbus
per 31 prodit 17 si 13(1+ dr) 31 sublatoque utrodius d3t, sit aequario ordinaria
quod mirum nempe (13 (1+ dr)  - 12Y) _  11. 3C 7Y = 0 sed ita evanescit 31, et dificitter abetuit
134 13132 = 12 32 = 13 34431 = 11 32. 32
Sed si 32:31 = 1 fiet aequatio quam dui
Numatur 20. + 217+ 22 dy F23actu + et d d7
510qy+ su L 13daq 3 diberenti et D sut dio _ud L  dy F1 2ddy + 13dddque tonantur simal daus et obu quod talile
c1o. a uus in p. E dy Cot titrenem Ad E  qbd2
A 2, 33, 24  = 13d17
Sit 311y = 321B + 3812
assumaturque 3U ut constans
et muttiplilentur 499. 1 et 2 per 311
exde fiat explicatio
filatur