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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 83r, page id 00068196:0163
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dy: Ax = xr + gG_,: aa
Ax Cg. log 12 exca clara 
aitqu = du sax 3a) b2. d
sit X: a = 5 ddz: dZ et y: a = sddz. dv,
et fiet dy.: dx = (Z. d): (ddZ: d7) = dZ: dn = qu Sdd Z. eZ + qu sdar dv, sit jam
de constans, fiat daz: dv -7ddz. 21 5lZZ + 2 (dtZ: dv) fdaz. du. Et fiet sadzu. do =
ddq: dv = 2 (daz. X) sddiA : 2(da. av) = L (az: dv - qsatz. 1) ubi sublata
irrationalitate potent haberi de. Porro tollantur deinde Be utur tante
 (XId
restr est autem dz = do br a et dez = dodx b: aia videtur tandem
de haberi per _ X, a, et dx. seu per quadraturas quod si succederet mirarer,
fiet L. - a (aa2. d2) satr a2 = l (. . - . ) et 4 - ddz. 17 saaear P (daz. lu) 5 aaz. d2 = dZ - q ser
2,
daz: a
seu 4
(ax : X
ddz: du
XX. BIN.a = (X a X
+ a a
(x. a). pF. a
ax pria
do
dzdaz. dodo
pia = b. a = ex: aa quod est absurdum, nam nimis res determim
seu + - E  de X: aa L XX _
natur ipsa nempequantitas X a
a dZ: d =  _  qu sadz: dz + qu Saiz. dv, potest et sic exhiberi.
A: B0Ao  et dzidv- 2xex aa F s0
: v. Nam si v constans fiet y. a = (daz. d0 = 42. do
sed ita differe habebitur relatio inter bria seu dZ. dv,  et inter X: a quod non licet
dy: dx = xK +gy, ica et X: a = sddz Z et y: a = s (dZ:, dz + dv)
praestat ergo sic
et fiet dy: dx = dZ:, dz+ do = XX: aa F qus daz:, d2+ du
Et fier (dZ ddz t dv daqu (( AA Z)- Adzllio, equi de v) = 2x x + dique (dazue
seu
qu. Z rav)
dulaq ee  = 2xdx (dz tdvi) =
daq (d2 + du)
aa
aa ddz
(ddz
dytar
Thrdn azdo
et dva 2 XXdx 4 xdvdx (= qu fadri) dZ
Sazidn
= XY
dztav
aa
et pro dque ponendo du bXsra) et pro daque ponendo avax a. a et evanescet iterum dv
qu (dzodu  add zuldz
aa ddZ
si a x: a = SdaZ dq et g: a = 4Z. dv, et du constanstiet dy: dx = dz: dv
unde Av L = qu 5AZ + d2d2 et 2 Sdd2 de = dv dd 2 - 24 adz
et
E. _ dodu
 et Sat =
du
242
47d d2
a dZ+Z
dvdv
ded2 dodo
dody + d5t -. d+ = dv - dear
et qu dar = 4 d)d3
43
de
P
dz dodn
 sdd2 = log dz, freret  et y: a est 17. d p,
quia sopta de constantet
ds fieret tali Hypothesi X:a = loque ( y: a) quod non licet
Eedem  fere ratiocinatio locum habet, etsi facias X:a = sitaz:tZ et
y: a = (ddZ: d2+d0, posita d constante  nam fit xia = log (dZ: dv)
et et et et d ddz  = xaz. a. Ergo g: a habetur  PX d Z : dZ+ dv
sed dex = dC log lz. du) Ego habetur hy: a ex dz: do, ergo exX: a
X: a = fodz. dvtZe) et y. a =p dv. dZ dz. dv, sit duodque, fiet
1i
fiet  dxetu = ddz: daz = do sed etiam sic datiur X: a ex gia,
dutdz
doidz dua
y: a = ((d z : d v - dZ)
quid si x. a =  dZ F: a = s ddz:, dvt dZ
dy: dx = dv+ d2.:,  dv -dZue, sed ita nerumque differentrando de venietur ad d