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# Title: Leibniz-Handschriften zur Mathematik LH 35, 10, 7
# Folio 19v, page id 00068160:0038
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Investiganda est ellipsi descersus mobilis in Ellipfica
e- B
obitu lati circa ambilicum Ellipseos p, descensus
sit
1cD. ex datoradio PC, et circulatione D2C.
in moli
quae temporibus existentibus aequalibus est radio
reciproce proportionatis.
i
sit AD axis parabolae
cujus verlex A, umbilicus p. suma atur in axe puncta B
et Q. sic ut BC BC perpendiculanis ad axer, et QC adcurma
AB = X
BC = y
pa Ellipseos 2aX-
a
 PC = V cons ex natura
GXX = yy. ubi a latu rectum q transversa
seu seini axis rajor. Ergo er differentialem ipsius
aeg. 1. fit a dx - a x dx ydy. jam seu ax du erit
et
8: a - a x:: ap: dy: BC  seu y: 8g. Ergo BQ = a -  X
A entque jam CD. DZ( 1CD. DrC t B. C: BQ. Ergo
pet jam pB = PA - AB, sit PA = h. fint P B = h - X et PCF
e
et PCseu 0 = h - 2hX + X + 2 aX - a xx. sit a-hs
et 1- = n. fet v h + mx + nxX Et sie vdv max tnxdx
et V:n=h. n + m: n C, = X+
i
Ergo fiet d vdr: dx =(n _- nm) + Gu v. n - ht m. 
2
X
no ntets. m-hu = ete. fiet vdv: dx= Vvn + et
seu ax
vav: vnter
Est autem. DC = dv. C, Et quia
dus dx a ax:g ba et dy + dx
siet dt. a 2a
ap
u Ergo
X +4 X. 2ax -ax. porro dite. porio
2
C2C = CZ 1x: y Ergo 3C2C = CZ dx :gy jam yy = v - h. X.
seu s jam h - x = h + m: 1 = v: n +et jum m a h et m: 2
= ab   XC a-A: 1  sit h + m:n = r, fiet Y 2Y (V. nt C vnte
fiet y = v2 - Y + 2Y v: n + Cr +v: n + 37
X
fot y = a v + 2r Nvon +er + O2 et CQ = y + BE..
cg.-
y= VaX = a xx
denique dx + dusr
aequationum tolli debent
ope tolli debent
per 6 et 4. fit
X
.
ax. a - = x - 7 dy
av + 12
ex vav. sente
 et 1-n = a
ergo fiet
on +e +B + a- 22X + a. et Bq
vdv = m dx C nX dx. v2 C
4
e
ope raum
+ eiquatione
rarum
Y, dx, dy. ex in 3 ex 3 tollendo ax et
vdv: Lente