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# Title: Leibniz-Handschriften zur Mathematik LH 35, 5, 4
# Folio 28r, page id 00068022:0055
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pars AII. de serietque et summis
BDH X. 
az a 3
AB ,,Z. erit
J. Z H X. porendo AL p 2b latus transuersum
et AB, c et 2a latus rectum. pro pro Z substituendo
y  b - y frei X B b (ilys ∞y
Et 2 ab - 2dy = ab + 2 aby -ay
sive ab - a it pu X, sive resolvendo in amalogiam
 abr = a y p lX, sive
b H 102
b = y 1 B X sive b~ - b X
abscissam X esse CE, et applicatum
sed si relatio ficit non ad axem AL. sed ad axem MF
tunc sumendo FE appellando V. fier  et M F appollandote, fiet.
 et latus rectam ad cum pertinens appellando d, fier: 2d - = v  
et pro EF, V, ponendo c = X  CE, fiet: 2dc - 2 d X, - LC + 2d CX +X y
sive (DdC = adc∞ ( d ct 2dc B +X p) Cy, sive b C y  d42
X HEY
Jam ut curvam vypet Ellipseos investius emus:
qu ex aequatione 2aZ - a y2
et pro Z ponendo. Z+ β. fier: 2az = quaeramus BN. posito. ND esse tangentem
fet: nempe fr appellata BN. appellatu l, fiei: fal - fa Z1p Y X
sive lpi X. Et faciendo ND
2a) - a yv
eyx rvlorem, neupe a ad taege
et pro X, substituendo
bZ, fier.
ot B l Cujus quadratum est Aa Z - 4 a 73, a 74
a = 2 aZ + e2g 1 a7 + a. 3 7 e
a quo se auseratul BD, p,2aZ- 42, fat: a. + q. 3t n B  . 5. 12  a 7 B 
+Z aZ et liberando numeratorem a vinculis, BZ fiet:
44272- 4a 73+
 e 1aZ+ 4a7  - 24377 + ay2
fiat ut d  3aZ
cui addatur
cuju quad rato,
bo. b2)
 X fier: W β, a- a
 B a- 22, H
3Z, B + 2a Z - a92
2aZ - a qu
Gud a - a9
Y2aZ- 5Z2
aon addatur P, fiet:
(a - 192+ 4 Z0 + 202-
2a2 - a y
quae g. reraesentat momentum purvae Ellipseos.
a
Invente t ergo cu
dimensio  cujus Elementa sint: 9. et habebitur dimensio Ellipseos curvae
Ellipseos. sed quia h ea figura satis intractabilis videtur ultrqt
est. Nimirum quaeratur curvae momentum ex AC, axe; ducatur
V2aZ. 4y2 distantiam ab axe; fietit Elementa momenti curvae haec:
3a- 29Z + du22 quae est ad pertatum Ellipsiu, si Ellipsin si
b major quam a, at quia tunc etiam  major
est autem b ms aqua
52. sed ad Hyperbolam, si a major quam b.
bm quam a in nostro exemplo
cum oidinata ad axim minorem applicata est, et promde momentum curvae ex
Ape AL, minore est ad Hyperbolam
pro b substituas C, et
contra si pro a substituas, d
et proz. substituas v,
B Sam - 2 dV + a  quae est ad Ellipsui. quia C es mojor quam d.
+ 2d. - 3.
Momentum ergo curvae Elliplicae ADF
pendet ex axe majore minore AL dependef
ex quadratura Hyperbolae, ex axe rero majore dependet
ex quadratura Ellipseos vel a circuli
summa omnium NS. applicatarum in BG. ducta in CF aequatur rectangulo
sub curva ADF, et recta CF comprehenso. Nam g NS ISC
ergo Nspi
G relata ad
Nullus ergo novus tunc ducitur calculus
axem majorem
MeR, eundem habet valtrem, quem ad axem
mineam, nisi quod ut dixis pro a, bizue aliae quas digi lineae, d. c. D. substituendae