# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/DE-611-HS-973581:0017
# Permalink to this reading: https://leibnizlegible.com/page/DE-611-HS-973581:0017?run=307
# Title: LBr. 396 · Hermann
# Folio 9r, page id DE-611-HS-973581:0017
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 10v); this page is its right half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=DE-611-HS-973581&page=17
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-973581/jpgs/default/00000017.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 307, 2026-09-10T21:35:29Z — 33 lines, status machine
# Lines: 33 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.

Clmo Hermanno Mathematico egregro
Basileam
sir clarissime, Tautor honoratissime,
Spero redditum iri nuperas meas, nec minus quas
nunc soribo. Adjeceram illis demonstrationem
profuturam ad intelligendam periodorum in seriebus
Numerorum Arithmelicae progressionis ut cunque
replicatae necessitatem rationemque. Voco autem
progressionem Arithmeticam replicatam, omnes
si
summas aut summarum summas utcunque re
plicatas Arithmetica progressionis, atque adeo omnes
Arithmeticorum potentiae ejuodem gradus, aut
ex sis conflatae formula
sunt Termini progressi
onis Arithmelicae replicatae. De Geometrica trans-
Scribo, quae amicus ingeniosus ad me scripsit, cui
volupe fuit nonnihilin hac inspicere, me invi-
tante: In progressionibue, inquil, Geometuscis du
Seu Decadicae
expressis notae primae columnae redeunt eadem
omere i secunda postvigesimam quanque
post quartam quamque, in serlia, post centesimam
quamque, in quarla post quingentesimam quamue
L
Oi
Numeris ordinalibus semper in quintupta pro-
gressione crescentibus. In progressionibus Geo-
c
metricis tripla, octupla, et alis quibusdam
ut credi par est, eadem lex observatur. No-
tantum tamen, se octuplam a numero 
incipias, Nullas meras prodire pro prima