# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068160:0013
# Permalink to this reading: https://leibnizlegible.com/page/00068160:0013?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 10, 7
# Folio 7r, page id 00068160:0013
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 6v); this page is its right half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068160&page=13
# Source image: https://digitale-sammlungen.gwlb.de/content/00068160/jpgs/default/00000013.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 116 lines, status machine
# Lines: 116 recognised, mean confidence 0.75
# 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.

lX = 2X
Ex aequatione differentiali patet fore
y = a sdx:  sax = b sydx: aa
y asderao la
2
jam dx: sax habe sy
22
potest. Est enim = ax. X :n X: 1: 2a = 2  X: a
Ergo y = 2sax = b sy dx: aa. Unde pore fit
Y uade porro y = 2 fax. b (2rax dx: aa + b
in posteriore y ponatur ejus valor fiet . y = 2 ax - b (2V aX - b sy ax: ad 
seu yC   y=2
1.2
12q
132
d
Ha
312
Unde ransus substi mendo, fit: y = sa X -b a. Y
P.2,3.2, 40
a = 1. A et Xb =h
1. 2  x3.2
y = BNa X - bsa L + bb) sydx. aa 
4
pl. 2
1.2.
bb sa 3
5.2
l. 2, 3: 2A
f. 1. 2, 3. 2, 5.2, 47
b seu si ponamus ace fiet et _ X ZCo= IX, f et
li
o
c
E
C -h6 se
seus= si- scosi AD scoscosi -ho sd sco et. i l. 3.G
1.3,5.7
y =
ubi
ie
ubic eritatibus positis ut Z, tempira sunt ut co. Nempe si co = Ix fit ao- X. ex
Nempeu
a
ta
9se
 ed
a
rrctione ni
m x rcodio. sed s
et Ly seu Z =
l
corico
et deo 2 X. X et dx = sddeo
i sed hoc veagur non devestus ineeumser
et y rculib sycono
nco- b(coydco sub
periuo
eahe
7.
s
e com
a
e
Ergo y = 2cd 2b sy cocleo
co - b (2Z co deo : seu Z= co - 2b(7 cocteo. et si h= 2b.
fiet denique: 9. co = h (y eo deq. unde denique fisz.
es
2
cohco +h c dc
3
1.3.
ut ante. Notanda hic et diigenter consideranda sgnorum ratio, et quod
neglimi desuit mutatio ipsius in alioqui calculus prest, quo
e
pocilo uneandem aeqi tonem nivinamnvnerainque nonted
Venio jam ad alteram viam, qua seriei nfinitae ad fimitam
tentator es
a
reductio. Nempe et y xseu summa omnium velocilas  a
relicta
considerand scilicet potest at quomodo
a medio ademlarum aliter computari potest perse medio sit imminuta
cllibet gradui impressae a gravitate velocitatis mediam
residuorum
 et summae adeitionum
uae sunt
dabunt quaesitum. sint spatia AB, velocitates impressae BE in ratione subduplicata reciproca spatiom AB
sius
vel AR vocemus X
velocitas BE diminuitur toto spatio B b Bi durante, continue in eadem
sem per ratione seu in progressione Geometrica et resultaas post diminutionem
sit BF. similiter velocitas B2E diminuitur coto spatio 2BH in eadem progressione
Geometrica, et pelocitas inde resultans sit 2B2F et ita porto usque ad ultimam
invelocitatem HK, quae manebit quanta antea erat, nempe HL (= HK) et area
totus figurae LABFL, repraesentabit residuum velocitatum: Investigabimus primum muturam
lineaed FF deinde modum summandi ejus aream, BE sit v, diminuenda i ratione e, cujus potentiam
exprimit linea B =. H sit BF =  v. Ca quod si a summo, A, incipiamus et AB
itant BE  B sit =  a: saX, sitt BF a et AH vocemus h, ut  sit = h- X,
fiet. BF si D= a: Tat
fe
h.a. Et summq omnium BF inde ab A,  (faciendo a = 1.) erifi
hox ∞ol2  dait qergo sit 
C
eu
per dx, fit: X =V. E in, 1 = C
eva
dx) = V. et o2Xtit  = dy = dx: sx = bydu. Ergo divitisbibus
supr
 = b . Qvod est etemplum ad mirabile sotatae aegutionis diserentalis per exponentales
D
2
6
213
a
2