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# Title: Leibniz-Handschriften zur Mathematik LH 35, 11, 18B
# Folio 70, page id 00068192:0070
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relocitates sunt, at Linca eadem manente
esocitate descriptae (per defin. 2. capoprae
cedentis) ergo relocitas in iA est ad velocita
tem in 2A, ut IA CIA) ad 2AC2A) Sed inter
velocitates ratio est aequalitatis; ergo d Linee
sunt aequales. Utaque punctum aqualibus tem
poribus deseribit aequales Lineas quod (per-
defin. mocus uniformis) est motum puncti
esse uniformem
Ineo quod motu aequariter distributo
movetur coincidunt hacduo: Motum mo-
bitis esse uniformem, et ae quivelocem.
Nam si mobile movetur motu uni
formis quodsibet ejus punctum moreturmo
cu uniformi (per prop. 2 Mot. Unis.) ergo
quodlibet ejus punctum eandem retinet
velocitatem (per prop. 1. dic). Ded in motu
aequaliter distributo eadem est relocitas
puncti e mobitis (per prop. 3. Cap. praeced)
Ergo  mobile eandem retinet reloci
tatem. Vicissim si mobile cujus mo-
tus est cequaliter distributus eandem
retinet velocitatem, etiam quodlib et
ejus punctum eandem retinet relocita
tem (per dictprop. 3. Cap. praeced.) Sed
punctum eandem retinens vedocitatem mo
rebur motu uniformi, Cperprop. 2. hic) et cuju
quodLibet punctum moretur motu uniformi.
id ipsum moreturmotu uniformi (perprop.
de motuuniformi) Ergo mobile morcturuni.
formi. Iaque in motu aequaliter distri:
tam
Suto, et ex motu uniformi sequitur eadem
quam
relocitas,  ricissim ex eadem reLocitate
mocus uniformis; quod est motum unifor=
mem et aequire locem in mobitr ae quidistri
bute moto coincidere.
Sed in eocujus motus non et aequidistri
butus non semper coincidunt motusae quive
Lox e motus unisormis, quanquam id para
Doxum videri possit. Nam quoties mobi-
Lis puncta diversas habent velocitates, lune
Si mobisi ipsi roLumus tribuere certam
relocitatem mediam inter duersorum pun
ctorum relocitates, fieri poterit ut mobilé
quidem in summa eandem relocitatem re-
tineat dum quod uni puncto detrahitur, at-
teri additur, ipsa veropuneta singula
non retine aut sua s; quod tamen requiritur,
ut mobilis motus sit uniformis
Prop. 4.
In motibus uniformibus punctorum