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# Title: Leibniz-Handschriften zur Mathematik LH 35, 9, 1
# Folio 38v, page id 00068125:0076
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Dudum accepere, e fortasse jam edidere ideo propo-
sitiones tantum aliquas subjicium, quae adinst.
ar praecedentium demonstruri possunt. Ba suspri
pr
cum motus per se uniformis amobisi ubique simisi
retardetur proportione velocitatum tuncprimoe
Locitatibus residuis existentibus ut numeris, spa-
tia percursa sunt ut Logarithmi, secundo si tempora
in sumta certa quantitate constanti aucta sint; ut
numeri, spatia percursa sunt ut Logarithmi tertio
tempora constanti quantitare aucta sunt reciproce
ut vesocitates residuae. Casus posterior cum motusâ
grauitate (hoc est aequabiliter secundum tempora) acce
Leratus a medio ubique simisi retardatur proporrio
ne velocitatis. tunc primo. si rationes interse summam
e differentiam velocitatis maxima, eminoris assumta
sint ut numeri, tempora quibus assumptae velocita
tes sunt acquisitae erunt ut Logarithmi. secundi
nelocitas maxima est lalis exclusive, seunun
quam atbingi potest undesequitur non quidemgra
uia accelerari desinere, sed tamen Limitem cele
ritatis nunquam assequi, etsi in infinitum ac
cedant, i ementistandem prorsus insensibilibus.
cercio si velocitates acquisitae sint ub sinus, er-
unt spatia percursa ut Logaribhmi sinuum comp
Lementi, posito radium seu sinum tobum esse ut
velocitatem maveimum. quario si spatia percun
sa sint ab Logarithmi sinuum, tempora in sum
ta sunt ut Legarithmi rationum quae sunt intersi
num complementie differentiam ejus adupso
sinus totius
LBA) uideris haec tam mira theoremara
es fine.