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# Title: Leibniz-Handschriften zur Mathematik LH 35, 6, 16
# Folio 1r, page id 00068061:0001
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Esto
djicitumus aliud exemplum, in quo ex data Tangentium proprietate
Niminum
quaeritur curva. sit ordinata Z abscissa y, tabyentialis (seue prte axis
sub tangentialis ut Hugeniono verbo utar seu ine intercepta
inter portio axis  intercepta inter tangentem et ordinatam) sit 
quaritur curva, in qua  sit t = gy-2y, :a. Est autem ex
legibus calculi differentialis t: g = dx: dys. Ergo dx: dus = y. 8,: a seu
adx= odg Xdy adx + Pdys = ydy. seu ddz: dy +Z- y = 0
Z= by +cy + ey+ fyt eteliet dZ: dy = b + 2cy + 3ey + 4 fy ete
itaque +adze dy = ab + 2ac y + 3aey + + afy ete
4
1
by + cy + e y3 et
d
Ergo ut omnes termini destruantur fit ab =0 adeoque b =0 et rac + b - 1 =0
seu e = 1: 2a et e = - 1: 2.3a et f= 1: 2. 3.4a ete. et proinde
fit Z = V -3
+d
 12a 1.234 1. 2344
_1
et
s
1. 2. 3,4. 5 4+
Ex hoc exemplo patet etiam saepe interventu
posse inveniri valorem finitum Nam si a-x sit numerus, et
et y logarithmus  erit per dicta paulo ante, Xe = y - Z. itaque
seu Z+a = ytave es quo e y+a x. Hoc e et,
sit aequatio differentialis Si quaeratur curva cujus subtan-
gentialis sit yu 277: a poterit sasatis fier, A si y sit
logariemus et 2+ a summa ex  numero et Logaritamo,
Si
Caeteram et variari series possunt, quia
revera in hujasmodi problematibus plures, licet cognatae lineae satis faceri
modo dicto sumtis
solent, ut si fecissemus z ah + by + cy + e yt, alia series aliaque linea
 Utas saepe etiam series ostendit modum
inveniendi Gneam geomelriae ordinarise quaesito salisfacientem. Sed
provenisset.
se qua aliti)
habet eascres suam propriam Methodum generalem, quam ubi
otamenea
elaboraver quam et indicare paucis memini, sid quae praeparationi
adiget, qpas ubi et sed ut prolixitas vitetur praeparationibus indi–
verum
aliquis intelligens susceperit
gentem quam ubi elaborare vacaverit, vel vel amicis intelligentitur
quas
veliti vel
tame plucuerit poterit ieometriae aliquando zeometria abho ex hoc loco
a difficultate tam late susa tama perplexa liberari
tug