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# Title: Leibniz-Handschriften zur Mathematik LH 35, 11, 18B
# Folio 105, page id 00068192:0105
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c
cum disferentia Logaribhmorum
Seriei ABCD sint ad differentias
Logaribhmorum seriei L. MN P,
ut 2 ad3 Erunt termini seriei
posteriores in ratione mustipse
cata terminorum prioris secun-
dum rationem 3 ad 2 Seu ratio
L. ad M (2 ad 16) est rationis A
ad B(Seu 2 ad 4.) orip Licata sub-
dup Licata, cum enim ratio L adM
sit ut cuboram ratio A ad B est at
quadrabor um (Nam 2, 1b, 128, S Cat.
est ab L, 8, 64. X Caet. ratio A ad B est
ut quadratorum (nempe 2,4, 16, ebc.) Eademque
Locum habent in aliis omnibus,
etiamsi indefinite sit progredien-
Dum in interpoLanda serie priore
ut in eam incidat posterior, quem
ad modum factum est in calculan-
dis Logaribhmis.
Ldres
Si eadem materiae quantitas
moveatur
or per Longitudines
aequales; rel ocitates 
m erunt actionibus propor-
dionates.
ram
sive numerum indicem vel
exponentem 3
vel ratio Aad B est rationis
Lad M duplicata subtri-
plicata;
differunt; Itaque per viam
Simisitudinis comparatio dis.
ferentium velocirate actionum
obtinenda est.
drop.
Si velocitates in eadem ma
n
Feriae quantibate per Longibud
enda
nem eandem inferenda exer
citae assumantur in propres.
sione Geomebrica crescente erunt
vactiones formases moruum in
progressione Geometrica crescen
Be.
sint vesocitates AD, C, progrus
sionis Geometricae seu A ad ButF
ad C es sint actiones L. M, N, ajo-
etiam esse L. ad M, ut M ad N.-
Nam ascumatur aLia
velocitas +.  aequasis ipsi B. qua fiat alia actio
Laequalis ipsi M. quia A ad But BadC
(ex hyp) ergo A ad B ut H ad C (ex
constructione) ergo SL. ad M,
ub. Z. ad N (per prop. praeced.) id est
(Per construct.) L. ad M ut M ad N.
idemque est e progressio Geometri
ca continuetur ubcung. Crescentibus