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# Title: Leibniz-Handschriften zur Mathematik LH 35, 9, 5
# Folio 18r, page id 00068129:0035
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De Resistentia Medii et inde nascente
Linea Gravium Projectorum
directio et
 mobilis corporis velocitas AC composita intelli,
satur ex velocitatio AB, et BC, et ob resistentiam medii
quibusdam irectionibus et. daabus
composita
inde fiat A(C) eadem proportione minuentur velocitates
velocitas nemo
alia mine
conpos componentes. Nanes si ex AB fiat A(B) et
ex BC fiat (B) (C) manifestum est O triangula similia
et proinde latera
triangula ABC et A(B) (C) esse similia
Manifestum autem est
 maeiMfess locum habere propositionem
homologa esse proportionalia. Sc
etsi glures quam duae sint velocitates componentes,
nam reduci possunt ad duas quae propirtione minuentur et harum componentes duae
rursus eadem proportione,  donac redatur ad plures componentes propositas
a resistenti medii proportione
percurdie
for
alibu
n
sunt enim decrementa quantitatibus decrescentibus proportionalia,
quod solius progressionis Geometricae proprium est. Itaque si velo,
citates MV nfigura 2) sint ut numeri, spatia percursa
iisdem positis etia temporum en progressionis Are
AM sunt ut Logarithmi (incrementa erunt
Geometricae Nam spatitis  uni spatiic incrementis positis
aequalibus reim Nam incrementa spatii
sunt in composita ratione incrementorum temporis, et velocitatum,
aErgo si incrementa spatii sint equalia incrementa
temporis erunt reciproce proportionalia inerem velocitatibus
ergo temporis sunt progressionis Geometricae vescentis
velocitates aucrmut
si nt erha hil quotenaque eprogressioenis
BV infinite appropinquans
asumplotae AM, spatium ordinata AB esgr infinitum ordinata AB
si sit linea eomLogarithinica
asgmpto AMMea et curva ABVVXC comprehensum, aequatur
ctangulo  BAO comprehenso sut ordinata AB, et intervallo
su contosa
tangentis DB BD et ordinatae AB in axe sumto, AB
Hinc gona logarithmicae numeris ut A3V ordinatis duabus
3M3V comprehensa
equatur rectangulo sub earum differentia  constante intervallo
eer ad asuemptotam seu numeris AB et
D est intervalludia ordinatae
intentis et ord, et recta constante C, quae  aequalis ipsi AB
summaniernorum progressionis Geometricae inter
suae tannentis in asymptors
protermini
serie
ncra est differentia duorum
erminorum progressionis Geometricae sit sint duo termini progressionis
certos liurtes comprehensirum.
erit summa terminorum infinitorum
em  comprerenspum es
s
itaque
posito b esse
rasoem progersudifferentia inter, bs et b.a
intervallum langentis ostans