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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 200r, page id 00068200:0401
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les ententi
1090
solutiones quarundam problematu quibus quountur
linea ex data proprietate velocitatum descriptoriarum
seo differentiali aequatione supponendo Zdp = dy. Et quaerendo ez
s
sit Generaliter q= dy: dx. jam sumavius ZX = y. seu N = y: Z fixy. E
= fit _  dx = dy. Z - dque y177 et tollendo x pr fit Zdx + Xdy = dy. et
Lo
 tollendo dy per aeg. 1, ob restet solum Z. dZ. X. dx. fint (2d∞) + x dZ = (Zdx) id est 47 =0
cque estendit l cuncessa ad Ergo Z est constans. Quod ostendit locum esse ad
e+lineam rectam. ubi sane dy: dx = y: X e = a: b
(4)
p sit 7X = - y fit Z de + X dZ = - dy = ZdX (per ag. 1.). Ergo fit dx: X = - dz. 
C2)
 seu 2sAx: X + a5 dz. X = a seu log XN 1 A log Y = x a V. posito b esse
 numerum cujus lag 1 est log ipsius 1. esse ,
+seu bis l0g. X + log. 7 = a. sed log. Z = log _ - logu + log -1)
Ce
+
a
6)
a
o Ergo fit log y + X = a seu log. yx = a seu yx - b
2
d
in
posito b esse numerum cujus log. est c. et log 1 esse 20
staergo aequatio ad Hyper bolam quod et verum est
e
at
y
4
fit
S
Z. X Ergo , dy  X dZ dx.
16
jam per 1 est du =Zdx Ergo sit XX Z ex = XdZe - dx
ZXX = sdy: Y +a
(1
fit 1Z: 7 et = XXdx + dx seu log. _ Z = Lx + x + a
log. Z = log X + sog. y fit erqu log. 9,  3 x + X + a = log. X
sn ex dx:y = x dx + dx = dx:  X. Ergo dy: dx = _ x X 1, :X :: yX
et foret 5 = X +x+C,: XX dy  9X ly +29x dX = 3X dx + AX
Ergo ay: dx = 3X F1 - 2XY, . Xx = pexarenus yx foret
3X +1 = 2∞y = X3y. (eu y = 3X+ + X+ 2X quae non consentiunt
C
Z = yX y E Z: X X dy = dZ X - Z dx XZ ax = d ZX - Z dv
Mur quae Causa latentis erioris
2 (
Zax = dy.
seu X Z dx + Zdx = dZ X seu X X dx + dx: X = dZ: L
Zdx = dy
seu
 ZXX = log. Z - log X + a seu jam log Z - loy X = log. y
Ergo fit EXX = log. y +a, ut constat ut constat aliunde
(+Z+XC du et ax + By = bq dy = d dZ = a dx = Z dX
(2
fiet ea X + C  b( dZ: a +3
A a X + by = CXZ + CyZ. fiat cZ- a = m et eZ - b = n.
fiet _ mx + ny = 0 ( Est autem din = dz = dn es
Asique ccz vel s differentialis 1y = = mx: n cujus differentialis est nn dy= Bxd   ax t mxaz
sed Lvictoria
seu per 1 et g. nnZa =. nn Zd∞ + m aX = MX dZ = X dy
graitam aesit et in derimum destigia rettatit annum
cu dxl: X = dque m-n : nn Z + mn dantur autem in et n per Z. Res ergo reducta
est ad quadraburas, sed
lale per se sola
poteramus aliunde quia x ety servant homogenei
Xax = ag. y
yX = Z
 =xy
Z: X = dy
=Xd
s
XXdY =X
q = Xaytyax
= Xxdys +ZH, p
JXX
E
seu