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# Title: Leibniz-Handschriften zur Mathematik LH 35, 11, 18A
# Folio 219, page id 00068191:0219
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prop. 5
lbatata
In seric plurium velocitatum
linearum
et respondentium rectarum
velocitates
ipsis proportionalium; quae aequali
bus lineis proportionales sunt, eae
sunt aequales
sit velva sint cec lineae utcunque
magnitudine variantes AB, AC, Ad, et.
et his respondentes velocitates utcunque
gradu variantes BL, CM, DN. sit velocitas V
proportionalis rectae AC, erit
aequalis ipsi CM. nace aequalie q
nam si insqualis est ipsi CM, ergo
cad et v aequalis ipsi cadet vel supra C ut in B
vel infra ut in D, contra Hypothesin.
prop. 6.
Eadem est velocitas mobilis
motu uniformi moti motu aequaliter
distributo moti, et ejus puncti.
rAB
Nam velocitas no est proportionalis lineae ob aliquo
no cuo puncto des crittae (per def. G hic)
1AEA
Senda AB
id est lineaea puncto mobilis quocunque t A,
descriperdae quia in motu uniformiter
aequaliter distributo (per def 2. de Fract)
omnes omnium puncto rum lines esc viae
sunt aequales. Sed punctum cum etiam
sit mobile, velocitas ejus proportionalis erit
lineae ab ejus puncto, id est ab ipso descript describendae
id est lineae 1A2A. Ergo (per praecedentem)
velocitates mobili ipsius AB, et puncti A
sunt aequales.
iisdem taonoribus
si ejusdem mobilis tractus sunt aequalibus temporibus absoluta sunt
spatia
aequalea etiam velocitates sunt
aequales; et vicissim
bsoluta
cuma enim tractus sint ince ratione
composita mobilium et velocitatum,
(per prop. 3) id est cum mobilia aequalia
sunt in hoc loco (cum idem sit mobile)
in ratione velocitatum, ergo
tordinatim applicatae
tam
lnam velocitas mobilis AB
uem punca est proportionalis lineae, quae
motu unisnit ducta in mo-
bile, et aequat tractum molus
uniformiter continuati:
jam si motus aequaliter dictri
batus uniformiter continuer
tui, manit aequaliter
distributus; tunc ergo
r
ALB,A.B2 A2B
et velocitas puncti A est propor.
tionalis rectae viae, A2 A
n e propri haec enim
ducta in punctum dat ejus
tractum per Cper prop.
hic) eadem ducta
v
 Mobile
AB dat tractum
er prop. 8 a
dat tract
Ergo vilocilas
ipsius AB est propor
tionalis eidem
lineae 1A. A
ergo (pet praece
Dentem) velocitates
ipsius A, et ipsis
AB sunt aequales