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# Title: Leibniz-Handschriften zur Mathematik LH 35, 2, 1
# Folio 266r, page id 00067993:0533
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sedalium
Videmus an revertiliceat ad methodum Hudeniananoe Aequatio ista: S= v. y Y2vy -X = 0
duas habet radices aequales, multiplicetur per progressionem arithmeticam, ubi prius recte fuent ordinata. Sed nc
aurtu subesse. ed malum in eo est, quod recte ordinari non potest, cum exponens verus ipsius ipsius y. in
termino Z y, non sit notus quia y. ipsi e implicatum est,
Differentia inter applicatum lirculi e Hypertole. 2aX +X = EaK - X p 2
fiet. (2a X) +X 1 Z + 2Z trax X ( 2aX ( X)
Ergo  Z e 4Z vC 2ax. X p 4X (= aZ X) + Zt, 9Z aX (= 4Z X
Aliter a +X a 15 - ae -y e V, unic aty 1B + a - yd sive (a    V + 2VS.. ( a) - 
sive _i 27    1vs. et quadiando 4y (4yYt vt  4v a = 4V y)
qu  4a - v, 2 2a - v rato
Ergo +y B  -
patet aute omnia fogurae differentiarum vari momt quadratorum summarir; pendere a
v - +v a + a  a- 4y
monculo segnerhexcentid. V  SV Sa  jum V, ita investi gabimus
Unde   a - v, 2 a - v , a - 2 a + 2, sive
a + v, D, a - viI ( a + yS2  a - V12, a +ry;
+v 1 a p, Sa =- 4 , et vr + sat qui. + a
8ra= s.
4y H40 a - v+, inde 16yd (p BY a. V, eyo ls) 16y
x 1+ 9p L. Erro Z p lv + 30
Ope differentiarum inteo duas figuras commensurmbiles novae habentur quadraturae
v9. a X - a 2 ay, H X. Ergo XX + a X H 2ay2
Y7 a
p C X - 2a, + a X p7 0, pore _X - 2a p Z fier yZ + a Z + 240
gu parabola: yVZ - aZ + 2a 70
differentia inter Y et y F; Y a X et inter Trax.
a - X
pax -X  2a = SaX + 7. Unde 2aX - X p, aX , 1Z Sin 4 2
2a-
ea -x
sive hax = X = aux - q p 22F.. sed nihil inde
X
Saa +gy = Saa-yy aequ 7. Ergo 2aa + Saa a- B y aequ. 2Z.
seu Sa=- y aequ. Z2- aa. seu saatgyu. Saty. Sa-y aequ. 7+a. Z- a
alscissae
7+a aequ Sa  Ergo momentum ipsius Z4a. ex y. a,
 afigurae ex axe conjugati datur ex data Satitaus
 27Zaa aequ 2+ y
promentu in X
sin (a -y aequ Z E + a) = 2ZZaa et fit:
seu yy aequ. Z f2aa -ZZ. Et y aego Z 220a- 77
Vbb + cyy + dd + e yy _. aqu. Z. fiet:
bb + cygego ZZ + dd + eyy = EZ dd + egy
b +2bbcy +Ccg  + Z + 277dd + 2ZZCt  d + 2dd eyyt ee d  a
4
qu
= 2bbZ- 2bb dd - 2bb Cy  - 2 cy2Z - 2 cydd - 2 ce y
Tollamus ZZeyy faciendo +2e- 2t 40
aequ. - 423 dd 4 2zeyy aequ. 0.
seu eaequ-e 
ita tollamus alia qnvolumus
Ergo