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# Title: Leibniz-Handschriften zur Mathematik LH 35, 11, 18C
# Folio 100v, page id 00068193:0202
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Detelocitate n univerrum.
longitadines a mobilibus percursae sunt ut facta ex vesocitati
bus in tempus ordinatim ductis; epatia percursa seu tractus
e
in ratione compositu horum, factorum et voluminum.
Sit (Si
mobile A tempore BE percurrens lon
5
gitudinem A(A) in temporis BE instantibus B3, C, E, velveita
e
c
tes habens quaseunqe BF, CG, EH; et primum ponamus tempu
per plura instantia 16, 2C, 3C, etc. in partes dividi utrunq un
BiC, 1C2C, 2C3C, etc. per quarum unam quamque duret eadem
velocitas, ut velocitates 1CIG, 2C2G, 3C3G per tempora BiC,
IC2C, 2C3C, 3CE; si jam ponamus velocitates ordinatim m
tempora duci, ut fiant deinte rectangula FBIC, 1GrC2C, 2GEl
3G3CE, erunt haec rectangula in ratione compositâ elemento
rum temporus et velocitatum; itaque (per pruys. 6. hec) ut lon
l
-
gitudines elementares recpondentes a mobili At percursae Au
ut 2A, 2 A3A, 3A (A). Itaque sumae rectangulorum seu figura
scalares, erunt ut longitudines totae percursae, veluti BF, G
2G2C ad BFIG2G3GHE ut A2 A ad A(A), et spatia, qua
per def. 2. cap. de tractu) sunt in ratione composita longitudi
C
num et voluminum, erunt inratione compositâ horum ta
Aorum et voluminum; idemque’est si plures diverrorum mobi
lium velocitates in sua tempora orrinatim ducantur, modo
rectis proportionalibus tempora et velocitates repraesententur
Quod si elementa temporis, quibus eadem oyrat velocitas,
sint assignabilibus utcunque parvis minora, ita ut nulla pars
temporis assignari queat in qua eadem duret velocitas; figur
scalaris evaneseet m orthogonuum curvilineum, quod lon-
gitudini percursa erit proportionale.
Has
am
Mo
a