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# Piece: https://leibnizlegible.com/api/records/29364/text
# Catalogue record: 29364 — [Fragment einer polit. Schrift]
# Incipit: 14) Ainsi puisqu'on commence à changer
# Date: 1686-03
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=29364&katnr=42052
# Work: https://leibnizlegible.com/work/00068196
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folios: Bl. 174 (from the shelfmark LH 35, 13, 1 Bl. 174): 2 pages, canvases 345–346, page ids 00068196:0345 to 00068196:0346
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068196&page=345
# Lines: 209 recognised on 2 of 2 pages, mean confidence 0.76
# Catalogue: Leibniz-Katalog / Arbeitskatalog der Leibniz-Edition (https://leibniz-katalog.bbaw.de/), ed. Arbeitsstelle Potsdam I der Berlin-Brandenburgischen Akademie der Wissenschaften, CC BY 4.0.
# 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.
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# After the first blank line, page by page: a "## Folio <label> — <page id>" line ("## Canvas <n>" where no folio label is recorded), "# " lines naming its source image and model, then its recognised lines in reading order, one per line.

## Folio 174r — 00068196:0345
# 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
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

## Folio 174v — 00068196:0346
# Source image: https://digitale-sammlungen.gwlb.de/content/00068196/jpgs/default/00000346.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 66 lines, status machine
sit cuma 5G ciusque quadratiotC sic ut differentiae ipsarume
GG s sint proportinates ipsis BG, 
it alia curra HH cujus adinatae BHI sint prop
se
sint curvae GG, A, DD, HH, sitque ordinata BH proportionalis rectanguli
Assumatur alia curva CC, summntria mvae quadratux ipsius GG sic ut diffeentiae ordinataum BC
ex ordinata Bd in ordinatam B. Ga
sint proportionales adi ordinatis BG, et sumto ungulo recto. A BAE, sit AB sit abscissa commanis
jam
EF = Bd, et fiet semper AEF A _ ABHA quia ipsae EF seu DB ductae sunt in differeneris ipsam
C2
+
E seu BC proportionales ipsis BG, etBH sunt etiam propentionales ipsis DB ductis in B G
In calculo sit BG = X et BD = Z
(posito Z = l + m∞) et BH = X. Z. eL
0
 BC = _ L. XeF = v et BD = EF- Z = G l+ mX = y.  ergo ut tottatur  reperiatur
illatio inter X, V et y sine X, sint
u co
Ergo X. (+mX
co
1)
et
et
1: er = X = in
e v
1c
1:c0
=l.m. seu v = , (eril.
l: 2x se invicem pendent
d
i -
Unde habetur et Nethodus praeclara omnes
1
+ l d
alios valores binomios reducendi  ad polestates simplicium binomiorum
seu
H ti h
X limX dx = m er
dinidatur et pultiplicet. per Y siet. X. limx dx = C  D. M. C
to:
nonsmus
ponamus esse
sed hoc non licei:
ne
ha h: C+1 h. et1
Tor
+ l. V du
es
=h = 1 et
co
evanesceret enim v, videndum quid oostent, nempe non pte fieri
D
ponamus het et C+1 - hCCF
 et h= e+ 1. fiet erit (X limx reducta ad
e
me Fl.
Mart
 Et puisqu’on commence à changer les anciennes coustumes à l’egard des
Ainsi
uns, la raison veut qu’on en fasse autant à l’egard des autres, qui leur sont
egaux, et qui ont eu un traitement égal auparavant. Autrement c’est
temoigner du mepris pour ceuxcy. Et cela est d’autant plus juste
que les princes de Brousuic ont bien voulu changer l’ancien ceremonial
ou style à l’égard des Rors, dont ils doivent par consequent attendre
favorable que l celuy qu’on fait à leur egaux