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# Title: Leibniz-Handschriften zur Mathematik LH 35, 11, 18C
# Folio 98r, page id 00068193:0197
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De Velocitate in universum.
ad ett definitionum diserimen.
Prop. 3.
Velocitas quaecunqe aequalis est velocitati motus aequidi
stributi mobilis aequalis, eandem continuata per aequale
tempus constanti velocitate aliquo sud puncto percursuri
u
lonjitudinem, quam propositum continuata sua; adeoque eti
am aequale percursuri spatium.
Sit (fig. 154.) mobile AB motum etiam motu non aequi
s sx
dutributo, et ponatur ejus velocitas talis m 1AIB, ut seadem
velocitate manente) per tempus J sit motus 1A2B longitudo
antem motus hiujus, seu longitudo percursa (seu longitudo tra-
etris explicata def. 2. cap. de tractu) sit linea IlZC; sit jam
L
aliud aequale mobile vel idem 2 A2B motum motu aequiditer-
buto uniformi 2A3B, a cujus puncto 2C longitudo percura
la
per tempus aequale ipsi T, sit 2C3C: Ago velocitatem motus
2A3B etse velocitati mobilis As in 1A, B eaistentis aequa
uum. Nam velocitas iprius ArB per 1A2B, ett ad velveitatem
ipsius 2 A2B per 2 A3B, ut longitudines aequalibus temporibus
percurrendae velocitatibus aequalibus continuatis (per defin praeced–
velocitatis) Sed longitudo ab 1A1B percurrenda eadem veloci
tate intra tempus P ert 1C2C (ex hyp.) et 2C3C est longitudo
S
percursa a puncto 2C mobilis 2 Ae B aequivelociter et aequidi-
stribute moti setiam ex hypotheti) et longitudo lincae a pun-
cto aequidistribute moti descriptae est ipta longitudo mobilis
percursa (per prop. 11. eap. de tractu); erit ergo velocitas 1AIS
ad velocitatem 2A2B, ut 1C2C ad 2C3C, qua cum sint aqua
les (ex hyp.) erunt etiam aequales velocitates. Ddem ett de spa
ys quod de longitudinibus, quia voluminibus aequalibus spa
tra