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# Title: Leibniz-Handschriften zur Mathematik LH 35, 9, 5
# Folio 20r, page id 00068129:0039
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sptta
Tempora t. Velocitates v,
spatia 
ds ut  v dt. E
But Ergo At ut ds: v et v ut ds: d+
etsut suat et + ut sds: v
Si gravi continue accelerato uniformiter socundum tempora
ubique resistatur  proportione velocitatum secundum spatia
videamus quomodo iniendus sit calculus. Siit tempora t.
a pravitate
vet   Ex natura accelerationis, accessiones veloci-
tatis a vitate, sunt ut adV1: 5 u ex natura
decessiones
diminutionis a spatio sunt ut ds v, ergo
dv = dsa: 5 = ds dv:a
si jam temporis  assumantur aequalia v 4: dt
meremunta
erunt vut dsL jam si ds constans piet: do =ds: at
et fiet - 1: at = Sa: 5 - v: a seu dt = l: d- ta : 5 + v: a
 si tempus sequamum posio quam spatium erunt accessiones
velocitatum at t. Sed suspectum videtur spatio alligare
accelerationes, periude ac si spatium a resistentia non
diminuerebur. Res ergo ad tempora revocanda est
quae sunt independentia. Itaque ex natura accelera,
tionis a gravitate, accessiones velocitatis sunt ut dt. F seu at. t: a
ex natura diminutionis a spatio decessiones velocitatum,
sunt ut ds V s seu  d5v: a, et feljam v = at t: a - ds v:a
per generalia ds = V dt: a ergo ds v: a = at Wv: aa
Lds
et fiet. dv = st F: a = dt vD: aa fer dv =  ds sas a v.   +
sit v - 1 t + 2t +3t + 4 f + 5f dc
+ VV = 1t4()t +(2) 1. 31 +() c. 4 t +(2) 15 f0
+
V= a+ ) ait La rtZC)a3t aSt + (3 a6Y
+ 1.1F+)12  1.3. 14  15
2.2 . 2.3
1.2.4
3.3
= dv -- 1 - (2) 2t - B) 3t = (2) at - (5) 5F (6)61 - (7) 3t
- + = - +
s
otandu hac etsi hic ca
s
non pertineat
5=(1. AA
sa av. laa vv dot vat Hoestoem proviali poterat, ea as -vat. Numeri quorum invicem ductu sips denominato ret sunt.
Sin pro tponas (a5 a: v, et pro Et Bd5 a: v
+ 22 l +(2)2. 3 l + ()2. 4 
V = a + 1t +2 t + 3++ 4 ++5 f t0
e
2
240+1 wel 5+8+1
4
t.
2R, + 1) 215+1
C
3
D:a
15 
interscribendum
erravi sunt potiu
et simplintem
ut patet
Ergo ad4 1 = a = (1)
2= (2) (1b: (2) = (1: 2)
3= 1F : 3 = : 3)
4=
2.2: 34 1,: 4 = (7: 4
2. 7:4+ 2. 2.3+1: 2. 2
= a2 +16 +37. 12
:12
si a= 0. fit etiam 1=0
et fiet 2 = 1  (15E
urie
et
1:
dd
et
2.5.
dicti
o
13
1=0
C