# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068196:0345
# Permalink to this reading: https://leibnizlegible.com/page/00068196:0345?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 174r, page id 00068196:0345
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068196&page=345
# Source image: https://digitale-sammlungen.gwlb.de/content/00068196/jpgs/default/00000345.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 143 lines, status machine
# Lines: 143 recognised, mean confidence 0.73
# 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.

pro Wvanisians quadracuris demonstrandis et Amperfucandis Mart. 1686 schedai
Et
sit C= a-y. Quaerita
sit Z = a + X. et quaeritur d xC so. fiet:
C- 1 Cd
X
Hinc posito co = 1. fiet X. a +X
vel post f fill
ex
co
Z
L et
a
2
a+
Z-
o
e l
t
e
et X
B L L.)
.dx
t
co+1
cox
a
e
C
A
Hinc dato YX - XX datur  siu X
102
d
3:2 -1: 2
co-
dx
seu si detur factum ex potentia X, et potentia Z dabitur eju
summa si detur summa facti ex una potentia ex unitas ex
a+x. dx seu 72+a. Z4c
X a+ Ax
t0
a
et f glo- f
et
70. 
3 0-1
3
0
r+1
ta.
. 7 = Rx 7. Nihit dat quia ob
l,dC.
modo intermedium inter +C et + e+f
∞e
non sit O. 5:
=
+C) C12+ a. Z. aZ
intervenientum c. enanescit
et 4 co-2
X
 L
ve
finc dato circulo seu YX - XX seu X.. Z, datur X. L seu BCYX. et X.
 et eF
73.2
25X
seu
Video tamen hoc ipsum jam ex methodo mea pristina quodammodo pendere, et eode
ac si multiclices tam per x quam per 1-X
C.
Z a. Z. dque qualis proinde pigura semper quadragi ut
et 3 con 3
et X
dari
12
t aentis aucta altera dininnta
pieut
a
Dantur ex se invicem:
eti co-1 et 2 co-2
X..
Unde sequitur dato (X
f
B  C.)
omisso dx = de Fax itaque c harum duarum summarum co
una ex alia data, datur. Hinc posito cd1 fiet
Hinc posito C0= 1. fret e
posito 
seu
a
C
a
BI
ec
relire
a
Eadem et alia dat sit V1- X quae datur Quae si multiplicetur per X et per 1+ X fiet x XX, et L1 - X
quae ex se invicem dantur item si multiplicetur per X et 1- X fient YX = X et 1 - X Si-X
ea dantur ex se inrirem sed hoc per se patet. Itaque tantum in intfractis intercurrentibus prodest
Valo V1 -X datur n LX
X: 11 -X. et X: Y(I1 X et X: Y()1 -X etc
Haec omnia videntur demonitrationem progressionis vallis canae reddere faciliorem
Aliud in eam rem ut e
es
s
n
el
C  let se
Aeiud. sit L= a =x. fiet d pego=
et generali si sit Z = a + X fiet
e
c0
seu d X. a +X = C
ad huc generalious s
a
d. Xe  = C
e-
X
a +bx. lamX
co
1o f
C. XC- C
-1 
=. a +b. X
e
 VI-X
ettri
26-
+ Hco. X. L
X
et 1. co-1
+2C. A
eth.
2
c0-1
2
1- X
XXIX XSx Yix
0-1
b1
h-1 s co
hb. X. LtmX + C0. l+ mX B. M. X. a +b. X
e