# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068202:0135
# Permalink to this reading: https://leibnizlegible.com/page/00068202:0135?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 2
# Folio 68r, page id 00068202:0135
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 69v); this page is its right half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068202&page=135
# Source image: https://digitale-sammlungen.gwlb.de/content/00068202/jpgs/default/00000135.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 109 lines, status machine
# Lines: 109 recognised, mean confidence 0.78
# 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.

fradices negativae quantitases pymficant quansum punctum
non esse antrorsum, ubi quaerebatur sed recorsum; sed negativae radices
ex negativis pinificant, punctur quaesitum non e intainga rectta ubi, quaerebal
ed extra vil. quallis. Algal. c67
stenditur scit non pnutum
eas in esse impissibaem, sed, quid faciendum, ut frat possibilis seu quomodo
mutandae hy pottrestis ulfipttabis
H
1.2 1.2. 3 1. 2.3.4, 12345 eu
6
24 120 et
 b. debet esse media inter 
dasis. poe Alu
erit arcus quad autalis
1 + L + L + 
b15, +
P
quaeritur interpolatio. Non videtur dari
id
-1 - 1 + L + 1 - 
+
7
7 9
- 1 + 1
et.. - = +  + L eti
23
16
1- XE
in Aiithmelica infrnilorum Wallisii Hic pro
0+1 + 2 3 = Z
25. +2 6
0+ 1+ 2 +3- 65
3 +3+3 +3 12
o+1- = 2 = = + = 0+ 1+4 = 5 = = +-
1+1
71
4 et =
Eteq X + X + X er cujus dif X + X + X22 + ∞3 et C. =
ambo simul dant: L= X
2
et
3 6 4 + 4 +4 12
2
27 e+ e1 1  8  oore
2+ L = L = 2 - - 4
1+1
+1
1+1
+1
C adjuagamus nea
eoner bee) b15
=
3 2 6mnroeu
2
E
(Generaliter u ,X.l
O+ 144 + 9 = 14 -  + 2 = 3+ 18 vbuonspotas 8 b
9+9+9+ 9
36
36
o+ 1+8+ 27164 100
B Hactenus rem prosequitur se sed in biquadralis difficitiores repent
1 = = 4 7
2
3
erc. Generalier in
etc
1Juer et 2Ht 69 2s 2
Generaliter 4 4. X.
et 1416 -3 =  + 
e Regulam tamen dat ese ibi e modum inveniendi pro conlinuaione etsi perplexa
16416+16 48
Nos aliunde hic universatia haberuus, interim ha exerptum
progressionis in successu non bene respondentis suis initus
d.x = e. X dx
aVx in = G X  = _ X = 2 _ VX = 3 
dallisius dat tantum summationes in toto, non in partibus quibus vis
(it s s ejus diff. est e. X tt sit da tB  fiet dy = e. x de. Ergo s jum si. y ( r es p so 
J. X goe Ga = s X IX = e  xetI Syax: yx = C 1:, e+1 posito y - X
_ N y = + +X (yde = ~: eri + X . ned
seu Sydx: yx =
ydx: yx = _ AF, X + eri 
eri, neI Xt 
nFI XC + F X itaque hic non est eadem ratio inscripli ad circumscriptum
et1, ntI, X +X
8t, XZ = ntu + ZbX Ergo (atE qda = xZ it _ X  et Z - fit v et fiet dx = e. v: et d.  l0
ergo XdZ + ZH _  et du = (M  p  _ n. v dv Ergo datur
Zel f+ V = hn   F.I F. m.  + pleten do
sit h. hy-hec
sit n-
sit hn - h +n = 0 fiet n = h8: , 1eh adeoque f+ pr  = th ((.) 1 + 5. x  a0
i hn - h+ n  non sit 0. sed h sit fractus, = , quaerendo ita ut X sit integer, quaeritur
an hn A -h et hin - h +n possisit esse integri s fit nat.k inlerer et . = hnah- i intergo
sed posius sit h- 1 = l: co fiet
ergo n = ki + 81, et hu-h, = i+ ki + 1
h = = co+ 1 : cd et h8 En-h : - c + 1, n - 1, :co =  4. cn+ n - cd - 1 :cd
= i integr fit n = c 1 + 1 + cd: cd+ 1
13
1
21 2
= 1+ 1 -
a2
- 1
ho-h - (hbu Hf. 1h
5 - 1 - 18. 17 31
54 54
Ergo
et 144+9410- 319
3