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# Title: Leibniz-Handschriften zur Mathematik LH 35, 5, 4
# Folio 9v, page id 00068022:0018
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Eltipsin vel Hyperbolam
Tentandum an aequatio ad circulum 242477+y, 0. per aliam quandam
multiplicata qualis est Py + 4y + xZ +s, reddi possit similis propositae
formula generali., fier enim + p. X + payiqe v a - 2 ap ZY + qV 4 44 17 = rags
+
v- 2a2)
S3 + 3sL
 ceo
sed videm addendam esse  + y. et aequationem ad Hyperbota, vel
S1
Ellipsui ponenta, esse completam:  y +bZ + CZ + dy + e. p0.
dicendam in Fy3, + P Y + 9y + YZ + 5+Csed quia ita inevitabiliter
prodit +y5, quae in  formula generali non reperitur, ideo
necesse est formutam generalem multiplicari per  Ly + nz +n
quo tacto sed cum semper quaedam defficultates sint obstiturae, ideo
multiplicata formula generali per ly + nZ + n. ut loca ejus
Quantum licet repleantur; particularis ad conicam datam, multiplicanda
erit per formulam completam unde sub exitum calculi 
apparebit, quae elidi possint aut conferri. Esto X
sive 2g Xy - b2
at
Taer
ax +DX  bBV, explicatis
L
Ho
X et V, per Z+ ductisque omnibus in ductaque et aequatione
provemente) multiplreata per ly + mZ + g + c yX
puor auter explicata pabit: a X + NysqZ + byZ + EY + dy + e. p0
quae ductu in ly + iZ + 9 + p YZ, da
dabit teriminos:  omnes praeter X)
Generaliter omnes frgurae quarum aequationes aut earum
multipli, formulae  huic aut ejus multiplo aequari
possunt sunt quadrabiles
E
figuris
Exemplaqu etiar opus est s formulae pro aequalionta
affectiarum quadrandis.
Ope secicis
lae
3 et.
D. habentur sed ipsis β non dum expunctis, haberi
potest o modus quo summae haberi possunt numerorum
irrationalium finitorum pariter atque infinitorum, quod hactenus potuit
inquorendum est in Methodum similem a pricti, cujus ope sive per senthesui
nemo
cujus ope appareat quaenam serie habeant differentias in fine
exhaustas, differentias inquam vel differentias differentiarum cujuscunque grdus.
sane munifestum est ultimam differentiam esse rectangulo homo geneam.
Ergo praeodens eit penultima, erit Friangulo, antepenultima, parabolae, et caelgo
parabolocidibus, patet ergo hoc fieri non posse nisi in iis quae procedunt per potestates
 Alimra jam sumamus si ponamus ipsam seriem primarum differentiaru E. FG. H2
CX
ea
ab, a au 2bdC a hb. adca d a- 2b +bcu ad re
b -2C + v - 3E+3d -e
C c-2d+C
procedeve per potestates videndum quales
inde oriantur serces ut si series.
a a- b a - b+C, a - 3b + 3C d a. Abybc. d 
ponatur esse progressionis arithmeticae, ut
sit (a, - a- b, b a - b - a+ 2b - C, sine C fiet c 0. et
ac proinde ista non procedunt in progessionibus deraescentitos
puto tamen in ascendentibus a adenta ab a + b, relinquit b. a+b ademta ab
a + 2b +C, relinquit b+ C. at qui non potest esse b,, b+c. fiet enim misus
C 1 0. Deoque ista non procedunt. a - arbes b b. (a - b, C a+ 2b - c, b - c.
aF2G49) (- a 3b =3 + digu b+ du c b - 2c +d.. Unde patet differentias
senei E. F. G. H. L. esse seriem M. N. P. Z
b-c
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