# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068200:0042
# Permalink to this reading: https://leibnizlegible.com/page/00068200:0042?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 21v, page id 00068200:0042
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 22r); this page is its left half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068200&page=42
# Source image: https://digitale-sammlungen.gwlb.de/content/00068200/jpgs/default/00000042.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 57 lines, status machine
# Lines: 57 recognised, mean confidence 0.91
# 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.

His positis problema
Ut autem calculus in calculo facilius appareat progressio
ad hibebimus pro literis characteres numerorum vulgares
ne et sunt exempli causa literae tres  propositae
b. c. d. faliamus bp 1142O, 138, 14 15, P1GF 17+ 18L19+ 110 + 111 8
X
et c1 21 + 22 +23 +24 + 25 + 26 + 27 +28+ 29 + 210+2118 164
ex praefixa  dux Dujus
et ita porro, ut ita statim in progressu calculi agnoscemus tum
ex qua li quantitate sumtus sit character, tum ex reliquo
vero agnoscemus quotus sit character in sua quantitate
ita facile pervenicinus ad progressiones. in eo enim  (V E14 16
consisdit arcauum inveniendi progressiones ut charactere 417 (Ci,5
ipsi initio assumti quandam relationem servent
Illud tamen notandum quoties  numeri fno neno
integri rationales quaeruntur, tunc invertendum satius
inverti valorem hoc modo
S 111 + 110 + 15+ 1B + 17 + 16+ 15 +14 + 13 + 12 + 11
quanquam sub generali illo in infinitum rendente
et quantitates rationales, in tegrae contineantur
ponendo sequentes in infinitum (post aliquol praece–
es
haract
dentes
valerenegu
calculemus quasi b esset  11 postea quasi esset bfur2
sed pro infinitis et
deinde quasi esset bp 11+ 12 + 13, et ita porro donec
appareat progressio
Deinde quia in calculo hoc perpetuae sunt propositiones
disjunctivae prout scilicet sequens praecedens s dextrorsum
summa confecit excessit unitatem hinc artificio illo
ad utemur transformandi aequationem dispinctivam
 ut duas aequationes dispunctivas
in se invicem ducendo, quod hor loco nullum incommodum
in simplicem
facere potest, quia, nullae inde oriuntur. potentiae
quaeritur ene generalis methodus
expri quaedam relatu algorithmica inter
si
Exemplo utar.
numerum et suum quadratum.
veros numeres
+16+15+ 4= 13+ 12 + 11 17 b
+ 16 +(5 + 14 + 3 + 12+ 11  b
B te5 X, p (, 3 ∞) t 2 + 11 JB
fune quadratum facile scribemus ope Deorematis
siferatis aliunde noti, ex calculo literali commu
est enim  b, sit enim b ap b+c + d +C etc erit
b H .b2 + 2bc sed charactitestice omnia distinore
scribi debent eo ordine quo  caracteres in progressione
assurgunt,
nmmrum
10, 6 D16, 2
1319 13  13, 17
1918
il 21