# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068212:0010
# Permalink to this reading: https://leibnizlegible.com/page/00068212:0010?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 7, 19
# Folio 5v, page id 00068212:0010
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 6r); this page is its left half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068212&page=10
# Source image: https://digitale-sammlungen.gwlb.de/content/00068212/jpgs/default/00000010.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 81 lines, status machine
# Lines: 81 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.

Met radum valere et pro differentiis gradus secundi
Pontemu iss ed K  puncto C1X, sumta quaecienqe eques
i differentiis differentiarum et Eum in finem assumatur
assumantur tria pun t curvae puncta  tres ordinatae
XIY 2X2Y 3X3Y, utcunque assumtae, et assumatur
recta atu  ecta. Ex quibus ipsa 1X. Y, permaneat eadem
Sed 2X2Y, et 3 2X 3Y continue ad eam accedant, donec ambae
simul in eam incidant, quod fiet si 2X accedat ad X, ea celenitate
celeritas qua 3X accedit ad 1X, sit 
ad cX
inratione IX3X ad 1X2X.  proAfsuneatur reca (d) X semper
eadem pro quocunque situ ipsius 2X, et 2(d) X semper eadem pro
quocunque situ ipsius 3X semperque F pro  2d) X fiat (d) 
ad (d) X ut DaY ad 1X2X, adeoque (d) y semper manente (d) X semper
=
su
mutabitur donc dum 2X aecedit ad 1X. et similiter fiat 3d) 7 2(d) y
ad 2 14) X ut 2D3Y ad 2X3X seu ut  y + dy (id est 2X2Y) ad
2X2T adeoque 2(d) y manente (d) X  semper mutabitur dum
V
3 accedit ad 1X. Sumatur autem  semper  ipsa recta +X
Variante, 2X 2Y variante, e ut et sit 2X_ aequalis ipsi (d) y, et
similiter sumatur 2ajy in ipsa recta variante 3X3Y, et sit
3X2Cd E aequalis ipsi (2Y 2(d) 1. Ita  dum 2X et 3X
su continue accedunt ad rectam xF 1XIY, etiam, 
2XIC0, et 3X2co continue ad eam accedent, et cum ipsis 2X, 3X
porro in quavis curva ordinata ut
1X. Y notatur punctum quo co incid continue accedens in ipsam
in eam incident.
incidit, quod sit  s2, et erit 1X 2 ipsa ultima  (d) y
quae est ad x (d) X permaneatem, ut ordinata Xis ad subtangea-
al tialem 1 X. Tprosito T.Y curvam YY tangere in 1. F idemque
Cumque id fieri possit, ubicunque in curva assumatur punctum
haberi
Y. patet. Prodituram hoc modo curvam s A quae est
rifferentiatrix curvae YY uti vicissim curva Y
summatrix curvae  S ut facile ostendi potest
si d X ponatur semper eadem seu a,
ext
erit
ex
Nam
(e
no cendIxtacisus sit p
utisdx
nova (dd)X manebet assignabiles M
a
e
ant pertio
et dxax: a odx = (Ad (d) X Ns recta novastass quae
prodibil aequatio ab iis  rationibus quae evanescere possunt
Et hactenus omnes rectae ad hibis (a ax
X(a)a + ~ 4 2 ( 2d0 + 2(a) dv dx. ddes
aut assiguo
eiunt do
fiet dudx: addx= nocta fo manebit assignabile
ini et aeuali siet ralis do(v: dasx ita tandem
Quantum licet purgata, cd) ay
a coincudentia
a 
01 +
files
Id)X, y e
quama
idv 20 pdeon
+ 2. e + e 
2X non coinci.
pudibit aequatu in
ax
abject
ois) actax
addx ad dxedx ut addx at
ux a a paderus enimitaque
ad) 
1
= sau ut y
(id est 1X. V
ad 1X 1
quia nempe
tune Y et 2Y
coincidunt