# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068160:0046
# Permalink to this reading: https://leibnizlegible.com/page/00068160:0046?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 10, 7
# Folio 23v, page id 00068160:0046
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 24r); this page is its left half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068160&page=46
# Source image: https://digitale-sammlungen.gwlb.de/content/00068160/jpgs/default/00000046.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 62 lines, status machine
# Lines: 62 recognised, mean confidence 0.83
# 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.

a
ex
Compendio studeatur equationibus 1 et 2 neme q, co:p =co:b ut
et b- nb= p+ p9 ducamus  earum differentiales, ubi primum
cripserimus b = p+ ap. Eexq fiet: 
2
 + cob = cd p +n p 17, A seu ex + q p qpap+ qPa ( Co p EcipapA t p 
el ln
ex 8q. lisenex
P
 = eo p .
ed prolixitatis evitandae causa utendum est aprtibus mei calculi differer
sunt cniu nostra aequationes nihit aliud quam differertiales rectre se
tialis. Nempe in og. 1. est   co: p -co:b = n - q. seu est
d c0: p = n - 9. jam d co: p (c d co v = d co. D-
=- seu (- Co Co: p - co: p+ 2p (B) = co p + Co 2plp  co p: p4
sec
seu dco: pr 2c(ap): p3 quod et alias ex nostro calculo differentiali
(7) 
constabat etae et ex aeq. 1. ad inassignabiles) reformata fit 2C0 ap). p = n - g
At 5g. 8. 2 e erat b -p patnb. seu dp = parnb, et
fiet 2p = p9 + Pn +  () sed (qun, quispe caeteris in comparabilis
10,
ortasse negligi potest. jam tollamus q et n per aequationes 3 et 4, ex aequa=
honibus 1, et 2 reformatis, seu ex op. 8 et 10. cum sit hee 
q  v. seu  per aeg 3. Glr dp et n- (dp)
(11)
ex aeg. 3 patet esse g = 1 - v. Est autem 2C18 seu  = dp
(14
(14)
itaque fiet q = dp - v. Rursus  3C2Q seu n = (d p) = se dp +ddp
2
et fiet: itaque 4 + n = (dps2dpva v (+ dp + 2dp dap + ddp
(4)
quo valore ipsius 4 n substituto in aeq. 8. et deletis -dd p, tanquam
incomparabiliter exiguii, fiet pivisisque amnibus per ap., tunc ex aequ.8.
sequitur in
fiet co. p N v+ dap Uende sequit
casu arearum aequelaense uniformiter cresceptium v + ddx
et vereor ne admisus erior, quod ap in aequ. 8. fut potius
esse radiorum
(ap) nempe et d et in 9. 8) pro (dp) ponendo dp + dap., fiet
A Co ap4: p + fco dap: p = Z sy dp dap - Z ap V. ut autem
1b,
secvetur lex homogeneorum pro eo scribatur aer, ut ( sit ipso ap
homogenea, fiet; a  qp: p - a e dap: p - ap dap = ap v. ubi
videndum abjici oporteat a ui ddx: ps quippe caeleris incomparabile. Nam feri
a
inde po Nam aliquo casu contiagere posset, ut an ap: p dp V et
ap dap haberent differentiam ipsis incomparabilem nempe asi dap: p3
quo casu aaM et dax P: ae haberent differentam dd p; d ergo
fieret sam seu tempus dapp: an = An in logaritEm p. Certe
in his valde cauas esse nos oportet praesertim cumgenentles
regulas constituimus quia fieri aliquando potest at in certis casibus ut
eriustam sese destorautlomparabilia, quo casa supersunt
ipsis incomparabilia
q- dp- v
n= dx + ddo
na q- Eipaipo. 2 d
Eo ap. P
seu a piap: pd
et dp adp