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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 120v, page id 00068198:0240
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Xydx + Xx hy = dexty Xyydx + Xx ybu = dxxyy
Sae xdx ANa = L nx rar
AK, Y ABZ BC, y.
5= Sex  Pellereree sxyax + sun y  Xy
(xxdus  asse dus -sygay  er saay- :  sedus xy- sydx. Ergo
Ergo  ex 7 per A, 5 fii sxgax = xg nky + 2r Syax + : yd
seu (xyta = 2Y syda -2= (x Sipe. Xu
quaenitur sipinter XX Sirx Xxd = g xxyAx  (xxyax + sxdus = xy. jam
Xdy = (er IrXX du = Xyyduys 2YXdy = (per 1 arrX dys - gryydy
yy r ly =.
du  fr- fx, ex, : YY. Ergo Xyyes? x ,)  rxy Xxgdx a X. r. X. yax = rXyaE - XXydx
Ergo per 1o et reliqua fit (Exxude = Xy - 4 rrsedu + Erydy Arspydx  (axydx. Ergo nihil hinc
a  sit a arco, t tangens sa = RY rad fit a = (a: rrtH  sinu verts X, rectus y fit
Aliter Xdy y ahat:
sector =  ra Syax = ira -    cy r g: F : c: 4Y Ergo gy: ec = H: YY
yy = 2rX -XX CC = H -2rX +XX
AT, B 2Y = X, : y: r: B seu 2Y-X : EY- XX Xrr: BB fit 2Y -X,: X:: rr: DB seu Zx: X = rr+ BB: BB seu X - 2rbB: m a
3dx = ; vati rr+ H = LC dy _(-  ydc:) ydx
Xdb = 2ydu SBaq = 2sy dx - xy SBa = sxa +B - sxdB. Ergo 2 sydx -xy = xB - sx dE. seu Sydx = x yB - ( aB
Lvidet ad hoc praestari aliquid posse diffrentiando, verb. gr D multi per X. fit DX = X  sb et differem
tiaudo d DX, fit Pr. X + X. AX. s+bX. =,  ubi quilibet ipsus ) trminus diviitur per x, et per nto
vel per entr omisso. et ita B. +X
123.+ 5b  er sit VIbX X haoc spries maltiplicabitur per X se 
Alius usus serici infiatae pro provehendis quadraturis:
dath +
it IX+ b. Xut - + 8
Sx+b. X de = 1. ot2
(X SixbX ad
+ en + Co FY T poterunt addi, sed video jam
enrco, sed 1par o prelcudi pt im A, et rin β. Ergo nil nobi hire
nec haec juvare quin en +0r7 = 1= ent
TItbX = L +
5.2
s
1. 2 b. X.
2n 1. 3. 5
nth 1.3
b. 222F2 13.
intcoC
.Xa
(4 n +5
1  etc = es
1.23. 4. 16; 4u +3
Bentto 135 b.  ed erc = D (4
= 12 3, 8. 3n+ C
1. 2. 34, 16; 4n +Cd
.2it red
b
ris p2j4; An +to
quivis terminus ectum, quorum seres infinita facit O, vocetur W, et quivis terminus quectum
quorum series infinita facit D vocetur H 
fit O = su et D = si  pt - W
ergo similiter se si  X ejusdem est gtadus cum 1d 1 - 1. 3.5 etc se enti et eodem
.. Ergo 1p x et 1 sunt ejisdem gradus quoad X, scribamus
1.2. 3 et, 2. en+ W
Ix = 8 fiet Yb = 9. videamus an hec duo possimus ita multplicare per constantes in
g entcd
tota ferie, ut  ex ipsis conjunctis vriab
sed e est valiabilis; sed tamen ipsius us
dus co
Et primum majoris simplicitatis lausa sit Cd = D ubi x= (it  quod places g)
quia alioqui si melhodus universaliter succedeet haberetur setragonismi sircularis reductio d quadratur
absolutam, qualis plarabolae, quod absurdum.
1d per On + A. et addamus poducta sit pnas
Ergo si Y o sucedit depressio
ergo V+X s seu L mult. per β3n. +), et
entt quod - eenn + ejn + Z), :, ea, en +
eDnn + C
idditorim fuisset nihil
slsans
facitrims V = = βn, procedet duplex depressio, sed hoc non licet
si faciamus ) = 0. d pressio quidem fit, sed secundum n, se non secundu
uni ex prioubus it jam inde id agi, ut secundum e potius de primamus
ildeamus an
en + 3 cividere possit nominattore, inultiplicando per _n, fit
e Mn +3 ( = e pun+ dunt rn tAn + 3 en + 2Y fit m = Bn + Y
effici possit, ut
e + s
entco Cn+
et addamque in unu
et videamus an numerator divisibilis e
Ergo recurramus ad
Cen + 3 + e Aen + 1C
entco, ent3
fine e ent In + 3+ 1C = pn C +  C
fiet en t an = pun seu β+ A = en
sed ita raisus nic lacramur
3C + 2c = Zβ + ZA. Ergo c0 = 3
frit een +Nen prsr en neenn + n eM + 3B; entco, ent2
eenntvey +2a
quia ed desomisset asse integer
HCo + (2 H) = (2 + B + A. seu β3 = nCo - LA- a
ergo (Z, HC0) - 2  = E. A +. cos + Nco + ZH = (2 NC0) sed mdm audeon hiberefidem
ferro + L + H. (- Cen + ZB+
A=- B, et co = 3 quo facto nit latramur. sed quod si ceapco + d + H = e M sed e hoc
+= 0 sit B ee qu + Crn C 1X + A Zu e + Z en A  = -+ 19. n B rn 2 69. : , 2n + con
nihil quiae B simmul sumi possunt
H. in e2)e Xeo  qu. Co enH
Nam Qpotet esse certa telcuminata, quae vubbit si QCon  + Brd. 1 +co 43 C. ACo Z,  = 2E+ Nco Z: -2Cd
proquodrandis multis n
= = 3+X qcoZ9: 3 + Co3
(3 C ZA +c. β + (Z ( 110) 3+1
+ qeomasit sid eu eet integuis.
tX 2 40 quod videtur procedere
jevansi