# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068124:0042
# Permalink to this reading: https://leibnizlegible.com/page/00068124:0042?run=73
# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 30
# Folio 21v, page id 00068124:0042
# 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=00068124&page=42
# Source image: https://digitale-sammlungen.gwlb.de/content/00068124/jpgs/default/00000042.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 75 lines, status machine
# Lines: 75 recognised, mean confidence 0.89
# 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.

quotiens iterum dividatur per h, et notetur residuus secundus; atque
ita continuetur, donec amplius dividi per h quotiens non possit. Ita cuilibet
divisori ascribantur sui residui. Sed ex his divisoribus statim illi rejici
possunt, quorum primus residuus nullus est ex divisoribus ipsius p, et
ultimus nullus est ex divisoribus coefficientis summi termini veluti w.
Hoc peracto sumatur alius numerus (h) vel ()) loco prioris h, et eo
dem modo procedatur, rejectis tamen statim divisoribus, qui residuos
nullos exhibent ordine coincidentes cum residuis alicujus divisoris
hypotheseos prioris. Quod si conferendo divisores ipsius n, orti ex priori
hypothesi t, cum divisoribus ipsius sins orti ex secunda hypothesi
 aliquis d
(h) non reperitur divisor posterioris hypothesis, eudem habens ordine
cum
eandem habens seriem residuorum
residum um aliquo divisore prioris hypothesis: formula proposita C
A+
dividi rationaliter nequit. Sin reperiantur duo divisores diversarum
hypothesium consentientes; progrediendum erit ad tertiam hypothesin
assumendo (h) et inde ducendo (in), ejusque diitsores tractando eode
trodo, rejectis, qui non exhibent residuos consentientes is, quos prio–
+ in quacunque nova Hypothesi
ne
ed
potheses collatae jam dedere. Etaque vel nullus reperitur perte.
quodi erso quamctus residuorum consensus; et divisio non procedit; vel reperitior
consensus; et tunc pergendum est ad novam hypothesin.) uods
int ergo semper habetur consensus, succedit divisio quaesita.
Nempes si assumto quocunque h, semper habetur respondens m, qui
peris ita consentire
coefficientem,
c
termintnt infimum formule datae
binae autem series aliquae Necesse est etiam binas residuorum. ut primus in primum ductus facta picultinm e et intimus in ustimum fariat
ries ita sibi respondere ut appavat has est pose residuo, illos posse ete attimum faciat id (posit hunc esse ou summuum coessicientem
unimi termeni formulae data
semper,
=siu vero consensuis,
hypetheseest habeatur
succedet
omulae
via ino
ddiaiium tamen
quia
Formulum datai
abia imo dutsiquia
femu la ditenda
siqu quia sempe
uo
nimu
ivisibile
re
oportet phinc
excepto casu quo
vadratica est, ubi
duae dividentes formali
aequantur
6
a bis conti
le residuorum
conferisus. q
assum
trypothesi
o pa
non
est
qui prius ordne
ine
eries residuorum
totidem seriebus
resideorum cujustivet
alterius hypothesee
consentientes. Et devel
Numeru residuorum unius seriet
est dud rinimum formulas uidentes
ea