# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/826603459:0348
# Permalink to this reading: https://leibnizlegible.com/page/826603459:0348?run=74
# Title: Qua Continentur, Oratio Inauguralis. Mathesis Universalis; sive, Arithmeticum opus Integrum, tum Numerosam Arithmeticam tum Speciosam complectens. Adversus Meibomii, de Proportionibus Dialogum, Tractatus Elencticus (shelfmarks Leibn. Marg. 84:1, Stück 1; Leibn. Marg. 84:1)
# Folio 302, page id 826603459:0348
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=826603459&page=348
# Source image: https://digitale-sammlungen.gwlb.de/content/826603459/jpgs/default/00000348.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 46 lines, status machine
# Lines: 46 recognised, mean confidence 0.90
# 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.

302
RC) VI
D. Progressione Geometricas
CAP.
RV)L. LCRC)T in AV =) Z. Ouxcendum igicun
quota pocestas dacae rationis communis R. Cuam denominacio-
nem dividens, exhibebie quancitacem datani RV 2) Z. quippe
Porestatis iltius exponens live index es T, numerus cerminorum
quaesicus. Vel etiam (nam eodem recidic) mutacis Cedibus,
C) RE = Z) R
Uc quaerendum GC, quoca porestas daca
rationis communis, per suum indicem sive exponencem divila,
exhibebit quancitarem cognitam Z) RV 2. quippe potestaris
ictius exponens eAt P, quaesicus numerus terminorum.
67 Dacis iildem, reperitur cerminus minimus, a. nam per
Praeced. haDetur T. adco9; A, PEF PF. 20.
ACquehae quidem propoliciones omnes hactenus cradice, re-
spondene coridem propolicionibus C ap. ZXVII. de Progressio
ne drichmeica; singuli Cingulis eodem ordine.
Scgnitur Theorema, quo, in Creometricae progrectionis sum-
ma inrestisanda, ucuntur tere omnes arichmetici. Nempe
68 Si cerminus maximus in communem rationem ducatur.
e ex producto auteratur terminus minimus, rehduumque pex
racionem communem unieare minutam diridatur; quociens
R
exhibee proerestionis torius Tumma. Hoc eAt, R = F L S.
Duis hanc primus inveneric resulam, aue quibus mediis, c50
plane ienoro; e quidem, ucur ex pleriqs ucantur, non memini
eamen me illam ulpiam demonstracam vidisse; cum camen vel
maxime demonstracione indigeat. Probis itaque hane libuit
demonstraci comminilci.
CUm HIC, DeF PP. 19. V = ARd, adeoque (PrOPEer T = DF 1)
VE = ARE, e ProPterea
VR A ARE  A
I1  1
R = E Facta di-
visiOne quanLitaLS ARC L A, per quancicatem R = r, (c0
modo quo supea ostendimus dum diritionem Symbolicam do-
cuimus,) quorientis loco prodibit series exposica A L AR L. AR
_c. hoc cA, quancitas S, sine terminorum omnium Cumma.
Exlempli gracia. Ponamus numerum terminorum Y = 4.
adeOqHE ARE = AR + EC dividenAA PROBONACIE AR ~ = A.
DEC R = 1. CUMI ISITUE SIE R) AR = (AR 3; Prit quocIenCIS
membrum primum AR 2, quod in dirilorem ductum dac AR. 2
un kLL.. hoc ex dirideno subduerum relinquie AR  A.
Deinde