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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 120r, page id 00068198:0239
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XXtB, X dx A  (Siteau d vrraum = Sxe +sixtm sdo: semper
in idem revolormur videndum an pervenatur ad aequationem
(dn
 ubi n = t vel 3 vel 5 etc
quaeramis 2 + 2 +  + = eto = dun sud an = 2 v = pa
de = d = = - = + 1- = (= nn - 2M du - an Fam- n 4 - dn
-2. 2 = 4
Y, 1+2
nt an
Ergo sen - (du
un xntan
hoc habetur
n, n F dn
M. ntdn nn. ntdu
 jam sudn + sndo + du V = + - du v
(an
nintan
Ergo et hoc.
sed hoc
- vdn
aliunde
Ergo
Ergo hinc nil dis limus
dX ∞+ Xet sxd 1 3at d n-- n+ n 3rant sndnan + du
Ergo n3 = 3sn dn + 3d snan + du n Anv = _ nV L nt dn v + 2vdo tdo
sy  xga  AB et sit w = ntd
ino = 2nvdo + ndv + V ane
Et sit nn = 2 suvdo + snav + sean + am svao + in sav
sit _v =  fiet do- -du et fit L = 2v + dus an
un, htdu n. ntdn
nintan
n + dn = n
n,ntan n nodu n. ntdu
an ntann = a1
un, ntdu
n, ntdr
tan
un nntam
()t an
n nt du
un nntan n.ntdn n+ d = un
(s rntusu du (- 2nn 2nan (+ n
129 n= ntdn n. nedu
-= = 59 = 9h  ht
31 = -  = 93 34  oti 13
vona
= 6 - 3h9 + 3hg - G3-
generaliter se) i- = 
n. ntan
Horpotuisset praevideni
Gtih - 2tg. +99 -
ggtih
Gs3
+2 vandv + dno
+ sdu +2 dn sudo  ansad
e
e) t sou si g-n et h= ptan sit  i arau  n. nrcu
(9) 14X = 1+ Qx + e1 ∞ + C. 21. C, 2 ~3, P. B.1. P. 1. 82) X et
1. 2. 3.4
sit e =  fiet fi  ( CRe1 = -  2 2 = - 2 C- 3 = - 5 etc
x ae
e=  e. e. 1 = = 1.3. C. er1. e Y = + 13. 5 .3 2. 883e = 113. 57
() ix = 1 +  17 X + 13 5 X - 1. 3,. 3.7 X ete   circuli et abi pata sobe
16; 1.2. 3. 4 Cpndent a quadratura crrculi et abt quoium quogea
4; 12
8; 1.23
AEt e SX. X = e S-x1 + L X lx ex -  x. n. Aneno singula haec ued
Ex= Xx sit diru ter a d abscilla a vertice ex diancetio X. fet in circulo lax-xx
pro ordinata sit  ax - XX = Xx gy: aa fit a - xaa = xyy seu a aa +9
2- 2idque Eaarus   Ergo
et dx
et Sax -Xx - 47a. ya:, aa tyy = aay:, aatyy dX = do
Fax. Xx ex = -raa gydyB:  Blaaryus
yy:aa. Ergu adx = vydy: aa
F ax - ex = ax X- NX vy Ba axx = xgy a  - sdt - AC AT= L
m a  x = san - un ax + s a (X H. sax  =  Sax- Ax
X Vax-xX
a r- x, :y = Y: t XX = ry : t yy = 2rX - XX fi r-  = 1rX Axit seu t = 2YX - xX
Xa M: Pa -X = fax -Xx ce :, a - x
Sax - XX ex : xx = - 2yy dy:, aa tgu quae est A, medi proportionalis inter absusse
aa gy ab 200= a av  t, vecoco
et adinatam apudicula i t ad hy.
+aav  raaud + veoco fit v = 2aab: aa troco et do - aat cocoded d codio
seu dv = 2aa, aa = cocodeo, : aa +coco = 2aado - 2
a -aa VD = a v 3Z fit aa, a - v = a + v, 22 seu a -a = aar +73 at coco a. aa - 13
et do = a t + 77)  -a = a2dZ - aaa 2  seu -ce Z d - a7 - a uz  a  12 = 20 317
a+ v = a( 7() + aadi, cur = 2a aat hE  s  - 22 Z 7Z = a a vo du
aater
sed ita locum
an contra surdu
da +25
du voCdusr,)
quao
Son v0 + 2abav+ dudo
Ergo Qvdo= = Esao