# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068196:0483
# Permalink to this reading: https://leibnizlegible.com/page/00068196:0483?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 244r, page id 00068196:0483
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 243v); this page is its right half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068196&page=483
# Source image: https://digitale-sammlungen.gwlb.de/content/00068196/jpgs/default/00000483.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 120 lines, status machine
# Lines: 120 recognised, mean confidence 0.80
# 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.

Ria et y: a,
ilatio
Hinc jam sumamus aequationem differentialem hujus parabolae, et quasi ignoraremus
undenam ducta sit haec parabola ea aequatio, quaeramque lineam ei convenientem methodo
nostra paulo ante explicata. Nempe differentiando aequationem 22, fit adu= 4Xx
Exattanda aq Quadienda aeq. 12. fit aayus = 4XY. seu 4X = aagy: x, quem valorem substituendo in
dissimulato, applicemus ei Methodum nostram novam. Complebemius tamen prius aequa
dx
aa
jam d C,  r, bbiore  VIbbCCdio. A et dx- Cduo a
jam du 22Cdeo, bb + 2cc0: a dx = cdco: a Ergo dy: dx = 2 bb + 2cco: aa. Ergo ex aeg. 26. Per 20,21, 29
fiet  B3(. bb + 2cco. 2, bb + icco = . bb +rcco. quae aequatio identica est, adeoque calculus succedit.
4a
jam in aequ. 2b substituendo valores ex aeq2, 29 et 4. fiet 
aa
aa
de du ado
dque daz
ex ddv dz
do Sydtyalo-av a
destinctis destmendis doddque = dz ddv - d0ddzue, seu 2 dv ddzue  dzddx, quod ut comprobemus
substituatur valores ex 14, 16, 12, 19. etfint (d, (bo rrcco dus n cdu = bb +rco do, Cc deo borrtao, quod succedit
jam ex aeq. 30 fit _ 2 log. dZ = log. B e loeet + tog.Mo fiet  log. naed posito n esse numerum,
aa
Ct
fiet aZ = Pn dodco quod verum esse docet aeq. 11. ubi n - 2 Sed hoc dissicmntato, videauns
en inde inveniri possit relatio inter x et y et al. fit Z sed lvideo nos ex aeq. 32 nil discere
2aVd atq- tax novi, nam si sit  velimus tollere do per aeq. 5. redit, aeq. 30  ifficit 
dxdd v:, dz ddqe = y: a C. Ergo adx: dd Z = (y: a: X: a =) y: X
(4) Ex assumtis, pert et 4
vursus ex 30 est alv: ddque = 2 dv: dqe = EX. a 2 d: dque. Ergo per 1fit lav. d4 = E X: a, quam
du
nam do: du 2 x: a
aeq. jungendo cum aeq. 33. fit ag = 2XX et habetur aeq. quae sita
Calculum ergo jam resumamus ni dissicuntando omnia cognita
dus  yq faciamus X
a3 dx
dx
a2
 ex 2 fit dx ) dz dax- avdaz et du
y (3) duddo et sit dz
=dque ddz
16) da
valores ex ag4. 2, 7, 3, substituendo in aeq. 1 fiet:
tan  constanti deo,
dus () du adu
dx= AZ dz ddo - dv adi
du au dau C
(3
133. dzddz ddv-dv dd
(4)
unde destructis destruendis fit: dv ddzu = dqe ddv- dvadque seu 2 dxdd = dzue adv. Uende
i ex aegq. 2, 3, 9 tollendo dv:dque et ddv: ddz, habebitur relatio inter X: a et y: a
Nempe, ex aeq. 3 est adv: ddque = y: X. Ergo ex 9 per e et 10 fit 2X: a  y.X, adeoque
2XX  ay, quod an verum probemus, fit 4Xdx ady. seu dy: dx 4X: a,
quem valorem substituendo in aeq. 1. fint, 4 4X: atyg: aa seu 2XX = ay ut
erat assumtu Itaque invenimus quaesitum sed non video quomodo haec methodus
ccnuentuo
semper succedere possit, quia nimium praestat
sit  sit aliud exemplum, quod non praeinvenimus
sit data 8 + 4
L 7
+
dx
fit
aq
dv +
4z
dz dav
dy dazuli  dua
aq. 9 per 2 et 4 fit: Y + Z. F 
Repetamus equ. pripes usque ad _7.
du dde
 daque
a  et fit 2.
= 2
gya
Ergo ex
a3 Xay -x 7 X3
a xy - x + yya = a xy - axy. videamus an sucedat
4 (10)
+a xydx + ax dus -6X dx +2a ydus  a Xy dy + a Gdx - 3aX pA  2aXydus
seu dog. tX
dy (12) 4 a X y - 6X - a y + 3aXY
3axy - 2a X3 y = ax - 24y
(13)
yya =X
= (per 8)
a3
Hui 4Xy -86aX ay43 aXy = 30x5- 2aX7- a Xy Day
seu ordinando, 3ax Y - a V
Etipsam 10. B. diuendo
-2a..
- 3aX y + raX y
X
245.
axy -axy - ax y
a
videndum an hae duae aequationes possint haber
tionem 25, quae est et sic enuntiari potest: Xdq = gy. jart 
varens modu
era
q
42
1t2
haXypraxy + aX  2a X y)
+ aX (14)
=6a X
+ x5
o
(15)
= 0
communem divisorem. Sed quia id prolixiu
adhibeamus brevigo exemplum xia + y.    dy. dx fit av. dque + dav: da z  = 42 ddv. 1z uy eto dt)
tit X: a +y: X = 1ya:, xay - x3
et
Ergo
do ddo
du da
aa