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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 104r, page id 00068200:0209
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V jam ope aequationis primae inveniamus valorem ipsius y sim
plicem, e cumque ubique substituamus in alia quacunque differentiale
utique siblato y restabit tantum dus ddus
Verum quia si
ponamus aequationem primam non haberi sed quaeri, datamque esse intr
aequationem differentialem tantum quaerendum quomodo et quatione
inveniamus in qua sint solum dy. duus. dddus daddus et ita nom
et ut aequatio illa sit rationatis, seu ut in terminis rationalibus
roqu faciendum sive habeamus primam aequationem vel non
sit differeatialis: Saae ry erit dus 1 = 2pX  Ergo dus y X dx
rusus s
do
eB X By
du y + Xax p
ddy y + ddx X po Ergo ddus p jl  xf - y de 
dys
dixx
d’
dy ddx + dxadus (+ du () Ida
dx
X
. Eyp allus u (+) na, ar prar h, t
+ Bx ex
aquando duos valores ipsius adus. et produs poneada
ctietur aequatio, in qua pro dus, ponendo valorem ejus- = dx
habebitur aequatio in qua sublatis differentialibus ab
ejusque potenti
ipsa y. restat sola y  per x et ejus diferentiales
expressa. Haec aequatio erit:
Fxy ddx f y X deX  ~ d X (+) yX d X (f) y dx +  a sdx
ubi faciendo ex constantem, evanescet ddx cuit 0.  et fier
termini
divisis evanesces qua per ipsum multiplicantur; sed quia
et residuis divisis per d dx evanescet d’X, et
fiet: + 3X  = X B (+) y Xx (Y) yt
sidinando X AB  F X L Xy (4) y L, V X 0
seu   X - y + X 4) y 10
sive
et fiet vel. X -y p0: vel X +y 70  sio
tres
Unde sequitur duas esse lineas curvas quaestioni satisfacientes
unam rectam cum fit X-yp0. seu cum sit XHy. alteram
X  a Hyperbolam cum facimus X-y 1i+a vel X + y  + a
tertiam circulum cum facimus: X +y a. semper enim idem
prodit calculus differentialis, quia in eo a evane scit.
Quae soluto plane minabilis est: et ideo nondum
ausim ei fidere, quia nimium efficere videtur: neque enim
video quid successum in aliis impediat, cum tamen res semper
succedere non possit
Et sane deprehensum in sequenti
pugina errorem fuisse non in calculo sed et in ratiocmatione
+imo male etsu
enium sit p0
non ideo tamen
omnia evanescum
ducitur enim
in abiam ordinaria,
ergo productum
aequatai facto
ex duobus infinte
parois