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# Title: Leibniz-Handschriften zur Mathematik LH 35, 6, 19
# Folio 5v, page id 00068064:0010
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res reducta et ad G de =  aa dst :, sae d - a 
Aed - a d = ad ad aed -5a b L 3, : 26 a d - a d = C d2: Sa d - a d da - 3 a NA dd: a d - a p
seu d sae d- a + = a dd + gatis aa -A2. Ermo lantum opus summari det . MN
Jaa- 2A =  sit a = ANaa = aA V  - ZA a2 aa = 2a A y d ep. + a 2p p 2) (quia ex est -, cum dd st L
aa- aN 2
ota
44 24 d d ip = - 2A dd - V dA. datur autem se d+ ex A . Ergo sa d datur ex S4 d
2a
Sady ex sipda,
Addi Y-  Aa  SAdA Va datur ex _  (a2 s aa 
di 1. Vdi = Et -(2A A d A +a  A EA N∞dD,:, A 2 a  = - dA + a dd: 1A
Erpo dip = dst = aa dA: AN, D a Fda: aa - NA. Ergo supcosset ut inrenantus (aa d A sda (a dst 
ob aeg. a - 1N a 4 = A ib Y fiet ast A d ip = d a d ip - d qp d ip
Ad2,: faa AA
Tsta: Faau Ad = Z a A 2 1 d ip = A d A a Yaq. M - 1
d san- AX
AA Saa-AA A Na faa -X
jam esd = d
saaud = +d a Y ac - 423 - dst saa - 1
ra
Na
 l
ex his pendet AA de
sed 3 Adip reducitur aliunde ad d ipdX. seu ad Sa- Na hinc ex se imice dantur scd- at et dd saci
+eY
= e sit X HN 4
Na
d 3s da
is
draad dea - a X = 3AA dst: sae - p
+ aa  4 2K ∞ - 92
ne
pa
l, SaN - 2 = 2aa d d1 = 4 a X 1d :  fat 1 d raa = 2
aadd
dsa X - a X
aaA Cer = 3a Ad d
sa _- a 3
pa
Nat ca veaaM + est tidet redea
add sit nn = ad fietq et. cst = 22 d e
et d Et 2ndn.  pa oa
a ude a- nd et hinc ergo pende
e
unenap
a a 
ds saa- ad-    C ta. set v-
+a - ad
fac quaeritur sumuu de
ans dx fa
Nat -a N
3(1a Sat. 0t - letiade
Aex Bcy xy - bb g = bb. x dy = LL- - 1b dx : XX Idy + dx -  Y 1x 1b+ + ~: Xx
indu sa-
 sa) = n(n fine dd = Epatrva t a d A: (adt - a N = 2 p dp: Ya n - (n6 = 2a d p: sa - p +
neraa
a
aa
a h sa te + K R: Taa m _ =  fiet Eh aa + Ier + KK + 2LK = BB
aam et
= BB
+sip dA =
= tih M M +hhaa
that hh  + KK  + 2hkaa - 2 hK MC,: aa - 
ubi si facius hha +K X + 2hk aa = e sir t B = ( Y - hh ma - tk -   ia- ua
seu
prc seu haa +K = o
a - e n
a  enta = 2 a dp = 5 dem
Na a = e t a = 2n an: a fit dd l aa. M =
a
raC 
- nt - 4N der:,  a et Cunde si pro inden ponas d ada, et pro mer ponut ad sii = a d1. fa
coedatur
sissit n sen3 dea hot datur fi ergodatur et ( dx aVd = a    quod Ergo
um
sit _ nn = aE: 44 +5 hoc vero summabile eo jor patet
lA aa - 
at aa = DA = a aa N - 3 = a a - X pp seu A = aa = A a pp Eg. A: aa - = 1to
at et
na = A A = a + X 99 a - x = a + X 49. seu a - a44,:, 1 +49 = a. quod aequamum qto
a x Saa - XX dx = LaaX - L X, sa aa- xX H = s. a - 2au XX + p, dx - + 2X - 2a aX + L. X
_5∞ -3aX 13aX - X, dx = = a - 3 a X + 3 a X - L X
sueculiter (1e1 - XX dx = i X - ex + C. C.t X - C. 21. et X etc
6;1. 2
751.2.3
(1et 1- XX dx =  + X = C X + C. C. 1 ∞D = e, ent, C. 2 X 13 ete.
13;112.3
9; 1i2
Vs, aa -XX = G + X =  X K. X = : x - =x etq ad habeatur interpolatio similis Wdallisum
3
DV1 - X4 = 1 + = X + 1. 3 ∞8 + 1. 3. 5 X ete.
251
8; 1. 23
4i12
+ + L X + 1.3 X 13
de la  per rectificationem curvae sic efficiemus dc dda ddia dividatur, in duas
S. - X
G. I. 2
partes  quarum latera summabitia per ordinariam geometriam seu in dBdB et dvav sic
253
unt possint invemri (h et, habelitt quae emal coordueatae ad curvam, cuj(+ aBdB+dV
(dn sae.  fial a deam -e dussu = a + 2) atB LCXX + f_ m 1n X+ p H
(Ha _V pro v spa - vo fuct v = M + 4 fiet 2 + q sip a -29n -  n.
a
49
si etddantur inum (.Pbre  A =B
aabb + 2beM + 2ab5 pp. + 2cf N = ff (n + ggrrap- qu -qurrme
tirpa = irqu-nM
rrgque
+ cC 
= qqure
et
possumus ponere f  et ra s tet sialie  14
seu p = 24Gur - qur - gqr3 + 9qY,: rra
Si rm2 fin p. 144 P = 447  44, 1412,: a s2
b-2qur- rrpa - 4q: rr.
q+ quf rarrq
et p = 29grr- 49r 4- 4quf,: rra
Ergo sH  - 1
q
2af
que. 20