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# Title: Leibniz-Handschriften zur Mathematik LH 35, 9, 19
# Folio 5r, page id 00068144:0009
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ei
 sit aequatio differentialis, inter X, y, et dx, dius
AB, X, BC y.. 1CDax D2Cdy.
sit X+y = 7G. et 1CE sit co
L 2C2)
V
est erit ap  dy - dz = co
et XdX + ydy = Z dZ
sit jam aequatio differentialis quaecunque ex numero implicatarm
verbi gratia b XG rdus Xdx +  ydy = X du
id agtu id quaeritur, ut obtineatur aequatio diffferentialis pura
patet tolli posse duas X et y itemque alterntiam ex duabus
dus vel ax. Et prodibit aequatio in qua sole erit
evunt _y, du du, deo. Nam ex aequ
ex aequ. 3 fit Xdx
r
noch
L
2C
K
a+
-qudu dy + y ay
Nam
Ergo
 Nam ex aeg. 1 fit:
(6) l
seu
yy du. Unde ope aequationum 6 et 8
D ait
V
q2 ay = ZZ d72 seu y = Z 1 dy - dz
b
quan aequationem substitureado in aequ. b. sit
ima t +deZ d
bc
ed
ex rav. ex aeg. 3 fit =
3
cXd
= 277 Laty - dze dza + 77 dus (229
l
dy: du eo-dus +du 
id
L
sublatis jam irrationalibus
et mulliplicationib,s vel divisionibus facitis, ponamus aequitionem
Ci
nest
2. et horum
=cua. G.  B etit angulus cti.
2
s
a
potentias arteffcium Tantum opus est artificium tate desiderari
prot
vlile pri
prodires
ut nova assumatur litera unica
e
est
barn da
quae sola ipsis co, et dy
evanescant. verbi gratia sit aequatu
dicis
et
dus simul
dZ + dy a  = DQ a
2a
(2) a
sd a
et si ponamus du esse semper aequalem sibi seu costantem fiet,
Z.2
Q= dn a, seu S -sq = ma. seu SB- sz =
seu posibs y uniformiter crescentibus ausuler i arue circuli seu in constante ordinu
da
ductu, denta area ex Z ipsi basi seu au applicatis aequabitur quadrato psim
 dimidiato. quod si non sit qedus constans sed osunatur pore