# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068049:0002
# Permalink to this reading: https://leibnizlegible.com/page/00068049:0002?run=73
# Title: Leibniz-Handschriften zur Mathematik LH 35, 6, 4
# Folio 1v, page id 00068049:0002
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 2r); this page is its left half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068049&page=2
# Source image: https://digitale-sammlungen.gwlb.de/content/00068049/jpgs/default/00000002.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 87 lines, status machine
# Lines: 87 recognised, mean confidence 0.81
# 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.

parna proredente, secunda aeque olatione6
sed reu actu ipso tentemus pro invenienda dimen
∞(1,
fiet aa dio= 2rX x + at dx et ex aq. . fiet qa ta s. rx tatax surax tantx + a aaep
orxxtagex + aass
j ra Quaeritur  saus, Pyy -cc esit y = aX + h. fiet esqu.
oori
r= gg: 2a h= at - bg, : 9
(10)
bg X+hX t aete
  r = 1099. seu nog: 2a = 1299 seu n= 2a. 10
 a el
et ant = 2 10 agh seu f. a. 1t = f. sB. 9h ergo per 9 fit at = at - b, g. et fit 60
pp = 10 t et h= at: g jam pp = 10tih - 10. cc fit pp = 10a a tt  = 10 cC995dd
Similiter qu = gg seu 999: 2a =99 seu 9= 2a. et aqt ragh seu arat = 2agat: 9
pro nominatore,
quae est aequatioe
identica seu per se succedens ex positis per 19 et 14 denique restat
55= (hh - ee = aatt - ggee, : 90 Ergo fit  fy b
(23t (5x + at, ex, 1099XX + 2. 10 ate 1  aa tl - c199
Ergo fit  ex 7 fit Z: aa si a
e9xx + 2a + X + L aatt - ee0d
posito esse co = 8 agr yy 2agpty + arC
+et y - 49t
: 9
Eb q. e 21 si pro x ponatur - X, (aderq pu dx - dx) et pro + ponatur - t,
sed ex his b patet ipsam  non esse arbitrariam,
 sed determinari. Nec quicquam aliud hinc discimas
yu Lcc
yy- ee
says.
quam posse quadrari
in penultinis 1, 2, 3  paginae pracedentis, habemus. Ibi ponumus
2. 30y+ 31 duct. in 70y+ 71 seu 230. 70yy + 31. 70y + 31. 71
+ 2.30.71 y
aeuari coincidere cum 20. 307y+ 20. 31. y +20. 32 et fiet
+ a. 31
70 = 230. et 71 = 20. 32 + a. 31,. 31 ergo fit 31. 2. 30 + 2. 30. 20. 32 + a. 31 = 2031
seu 21. 2. 30 + 2. 30. 20. 32 + 2. 30. a. 31 = 20, 31. 31 et fi 7 23 -20- 23031 - 243031
arxy + +20. 3- 303 = a. 30 + a. 3, 1p0. 30 Y, 21030 31 y + 2 1. 20.  1y , 2 20. 30
703 l.31 yy +210.31.32y410.3232
Fu∞30 yy + 1131 y + 132
unde faciendo 31 = 9 fit (9 - (dy
nde palto  posse nheeus a 10. 30y +210. 36 3L yy + 10. 32. 52
11432
+ 110
tia12
nde parto eliam posse oni 32 =0. Uuo video posito 3 = 0. fieri
2aa
Ergo sic res procedet trevissime.
aliquam ex his 32 vel 30, vel 20 =0
Sodx Siax LuXE, ) O e sit x ytax eydy
sit ergo:
( - 23 fydg sitar 2130yy +32 et adx = 2 30ydy et fiet
20 X +2
O =  (2. 30y dy (10. 30y , 2. 10. 30. 329y + 1032. 32
20. 30yy + 2130
+ 11. 30 79 + II. a. 32
+ 12. aa
iffertur jam multiplicetur summandum per unum factorem alterutium divisoris
Summae ex quadraturis productorum sponunt C, itaque dantur
sit (C) sux 1XM Sio XX + UX +I2 sit  ax= 30yy + 32 et adx 2 2. 30yty
fit (= 2. 30, 30. 40yy + 3240A + a. 41 (10. 30 y + 1. 10. 30. 32yy + 10. 32. 31
20X+
 11. 30479 + I1. 32a
+ 12. a4
20.30y9. + 20. 32 + a. 21
Habemus. Ayy s, y + ju + y _ et sdu sy . gy + y. prius ex aeq. 4
vel faciendo num. et xomaiquates
ponendo 3240 + a. 41 = 0 = 20. 32+ a. 2). P posterius ex 4q. exdem, ponento 40 =0 = 20. 32+ 44
habem, et 57dy 15a.. yyt.i, ponendo 40 =0. et fygay+.fy. y. y
gyt.  fauendo in in uta nempe faciendo ut inag. 4 numd e hom habertit diisorcauem
(e seu sartere csre
2aco+. at 0
posito esse c0 = rXX +atX: a per 2. set qquia X = ay - a t; g9 per 67)
fiet
d
et fii 
du
ex L= i S83sux Sodntriaom iteh
y- ee
 ia fB ix Aexxaphan patit
(11.
Sione curvae Conice sit   = S, deo Snct.  sit aco L r I afit C =   2. 72 50
900+55
(26)
8d