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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2c
# Folio 80v, page id 00068199:0160
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sit
a = C
sue
Hic multa bona et vix pro differentialibus per exponentiales
Ergo Xla = y Ib.
eromi porra
Y et qomitti possunt si intervallatam
sentium in axe aequantur unilate
9.(do.y
itaque si an et bus sunt constali test irunt ictae aequationes ad rectam
X
Sit X  a Ergo
Seu
XS dx 2X = y
a la
dX : X = γ dX = X dy: XX: a
dx X: to = ydX = X dy.
Hinc Si Ponamus crescentibus X decrescerere is
erit fydx =xdy = Xy. set fiet
 aequatione differentiali dx X = ydx- xdy satisfiet
per absolutam XX = XY, id est x = y quo
etiam est ad rectam; syp
e
sed secq est si crescente x crescat etiam y, tunc enim
aequatio e explicanda est per v = a
a
ixge R.
Generalius
un
fiet
t
X.y X. y =  a pX. V)
dabit.
e
L
va
Ry log. X. Y = X7. loga.
a
 hoc est logo x. s =, X. y. log. a:  Xy
ca
cgtn Xeta
W
ax
 tog. a d. eXy: X. y
similiter si sit
a
N. y (X. y) = a) h. 7
in b
an
s
_ 5 d. 5.y: X. G = loqu a X. Y + logb Xy, : X. y, sed
u
unt
logarithmice
taur
adeoqu
d. Xy: X. y = X y log.a: Xy. seu _ d. X. y : X. y =
r
IX
e
fiet
quonum raro ad hanc formam reduci possunt aequationes differen
Possunt aeq rationes esse huienadicclaresie
kales.
compositae ex pluribus logarithmicis, r quantitatibus vert
a
a
gratia ponamus scribi _(d Xig: X. Y + X. y  d. X. y : X. Y
X. V
sed hunc ne sempee ees rdu differentialis  primi graedus ordinarie nec
non habetur potest reduci ad tatem aequationem
a n
a
exponentiales
na
X. y in X. y (X. y) = a num. a (X. y: a
imo hinc patet omnem aequationem etiam communem reduci posse ad expo
antiatem, sit enim XX + ry =aa. fiet Rumb (xribanum b
num ((xx: b) in num. 6 (y3: C) = num. aa, et ita ora semper ad duos
terminos reduci possunt