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# Title: Leibniz-Handschriften zur Mathematik LH 35, 11, 18C
# Folio 76v, page id 00068193:0154
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2.
formali
Seit. III. Cap. 1. Do Actiono motus et Effectu
sione Geometrica crescente, erunt et actiones formales mo-
tuum in progrettione Geomitrica crescente.
Srit velocitates A, B, C, pragrestionis Geomitrice seu A
e C
ad B ut B ad C, et sint actioned L, M; X; ajo etiam etse L
c
ad M, ut M ad N.
s
Nam arsumatur alia velocitas Ha-
qualis ipsi B, qua fiat alia actio actio Z aequalis, ipri M;
t
i 1
5
Qvia A ad B ut B ad C (ea hyp.) Ergo A ad S ut H ad C,
M  e
eae conttructione). Ergo et L ad M ut L ad N, (per prop. praeced.
8 sI
Ne
id est (por construet.) L ad M ut M ad N: Idemque’est si pragres
sio Geometrica continuetur utcunque. Crescentibus autem ve
d
locitatibus erescunt actiones, quia erescentibus velocitatibus
et manente longitudine, tempora decrescunt
(per prop. 8. Cap.
de veloc. in motu aequidistr. et unif.) et decresuntibus temporibus
manente longitudino cui impenduntur erescunt actiones (per
sa
axioma huc)
Prop. 6. Lemmas
Si duae sint, progrestiones Geometricae simul erescon-
eorem al
s
tes; termini unis erunt m multiplicata aut submultiplicata
ratione terminorum respor 
t
Geometriae progresoiones ve om
Smt seruo A, B
C
cadimore D, E, fi. et L, M, N, P, Q. Ajo etto
O
A ad B in ratione multiplicata L ad M, vel contra L ad M
t
eadem aui
m multiplicata ratione A ad B. Nam interpolando conti-
nuo seriem priorem, omnes aliae quantitates homogenea vl
ab illis indefinité parvo errore differentes m eam eadent;
itaque et m seriem priorem ABC cadet series porterior LMH
et quidem intervallis seu logarithmorum differentys aequa
libus, quia ipsa quoque LMN progretsionis Geometricae est.
 quo calu erit A: B in Submultiplicata L. M.
Jam.
A
M
at
e