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# Title: Leibniz-Handschriften zur Mathematik LH 35, 9, 5
# Folio 20v, page id 00068129:0040
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AB spatium percursum.
motus accelerat
pavitate relarduto aresstentia
medis; AE spatum percusm
unctu mobilis perse aequabili
a resiptentia medis retaiduto
V d5 = vdt. Ergo
1B2B = val
et 1E2E = ()
dx: du :: v: (V). jam
 ∞) a= n
 v: iaa- p: a
Ergo haec est aequatio curva.
Car
Voa-P: alsie
dus
n:a
Aliter brevius:
X = Javdo: ad- vv
St) sauso=
2.5. 8. 11.14
positis  temnonibus e Y viuritatibus.
Numeri autem 2, E e I 14 Nc. sunt seriee
cytermin  progressionis Arithmeticae incipientis a binario
et ternario crescentis.
Numeratores autem colliguntur considerando quod
modis numeri sequentes, progressionis huius arithmetice
ex praecedentibus combinentur, combinatis formari possi
∞) it  log.
av a et A)-y  (V
: Vilognabum
 Atsa. n ergodatum relalie inter tet v e
. (dv: - vn = 25 av: i+ v + = (dv: 1nv
enet et R
st
2.5. 811
se V. (VI. aauv Ee a vo: aa
tB: (): p. R aV. aa vB
iatulus
respecto (0) quod iodur notum, sed reria ne nunc differe
ogn l
Erxsit: dx: dy::  aavdv: aa vn:
a aa
2.5. 8
Ergadoa- vn= vyn iibe
et dx = avdx: aa vv = vdt
et _BSav: () = Y log. 1. seu a
ise
lunatu
de = Ct Y= d
 =  t = _ s. v = Z F-s Z t+ S t s5 = sdg. si
itaque
++
ha
non Ldv: 1+V + L dv: c- D = = dv+ 2 dv( : vdv - L var: 1. vr
Erg sed i Fa: tB est log sio, et similiter
ni fAx: D est log. Si-
Ergo 5dv: 1 - vn est log. 1+ V - logu Si -V
seu est coye cre seu est dimidius log. et v: 1- v
1+Voi-D est num. de: +. et 1+v0c- v est num de L
rata
mo et du. y. aa v
deiq dx: dy:
aprvinde y=
+ 5:2
+:2 5:2
Cax.
facient
et D1D =  N t- vNL t et v = N : f - 1: 1+ N= L
rursus 1- vV = N +5. et vV = i - N = S et V = Y- N = 5
h9 = qP +29 p +
si p= 9 fiet liceret sumere feret
49t2 = q++ 5.2 + 29+15. 2+ p22
namx+ N+, seu A g = N5+t
=492:  + 2g.2+
65: 4 = 24.
qu. N = f - +
ot.2 +1. quae sanc
et fit N = F = 13: 1+ NL F = Si = N =5 et (Qu. NL + seu) NF - 2N + F+1 = Nt + 2N + F+ 1. 1 - NL 5
l aa-un-
et El aa-vo
bavv
aa - vv
seu N-2NLt+ = xF F2NL t + Y O- Nt. NE5 = 2NL L NL5 - NL5 
seu 4N2
deu l Saa -vr = vB: aa- vV,
et l1: Saa-vv =
N ++L5 +2 N Z+ + LS + N 25. Sed suppositur, aliquod spatum
et corrrsponden e tmptas endem
a XIx = dx iddx
ds: vat.  v = ds: dt.
et A∞ = dasAt -iZ d5: ai
substitus in . at = dB + ∞ d5. fic. 
t~AIc. dt- aet
ser et
velopiessit
L. t: dt
erit 5, spatium log. secantis (d= lvdv: a vv = l1: saauon
= dvaa: au- v
si a radius  sinus
u aa: taa-on est secans
posito a v simus a raduo
aac ten  5
et v = Praa - P. A
ai
xvaliaa
 initius rest
seu r. a
especta at
log ratmns 1, a + v. D a. V
log- logD = logd:D est spatum
Tilogue _D + log. B: D = flog. 
log (9 - log. (DZ2log. 7
E 4 5 at  at 1
1os as
vgarithmiao
1at = sdt = e (av + )ds = log. v +s
Aas
infinili
cog. ds
ds = v at d+ = de + Y
r= v d5. Ergo dt = dv + vd5
Ergo d5 = vde+vas ods
et ds = vdv: ( i- bF
et s= (Vdva: - vr.
log C + log. D = log3 B est temsus 45: dF, seu s est log. Si -vi  
15. et
ddF = ddv +. dr i B
dr = vdds + a5 du
fit ddt ddv + vdastdsar
das = V ddt +dt dv Sck
V a5: dF = lt - Av = d+ das
eficas = st= at das
a: aa
s.2 mirum