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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 61r, page id 00068196:0121
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tor certa
e
seplembr 1690 sit
Si . aequatio incrementalis du: dx = X, Y
seusi valor ipsius rationis relocitatum generatricium, expri
matur per Xnetus sice entervent. Colarum homogenea
x et es interventionem u sine aliqua
sum
parametro seu recta constante assumla invervi
Judum problema posse reduci ad quadraturas.
C
uod si interveni ant rectae constante, ut
a, b, C, etc. reducantur omnes ad unam recami
a, ad quam ratio caeterarum exprimatur in numeris
ta ut sit. b = βa, et c= Xa et Ita porrothis
positis sit aequatio  dg incrementalisu
de dy: dx = X, y, a hoc est vator ipsinc rationes velo-
Citalum generatricium exhibeatur per rectam relationes
renter solas rectas homogeneas (X, y, a, vel faciendo
faciamus  sit AB X; BC y AH, a
es
et sit L tangens, vocmus ipsam BTvocems
ut Et sit p: y
duide ax: du.
itaque ex aeg. 1 et 2 habebimus relationem
inte
l
C
2o
_, a. Quae si
talis est ut X et a interse servent leges hosmous erectum
pet se Alae, atque adeo fet retiam per se
ol
labebi
poterit inveniri D: y seu ratio D ad y se ratu dx ad hy
per e et a. Ergo habebitur dy-
a
Ax X,a siu
e
dx xa id est res reducta est ad quadabnias
taque eata aequatione e inciengutali videndum est
si fatdet ay: dx  v:  vel X:Z utrum in aequatione inte
 X, a, V, 8, vel in aequatione inter V, a, H, . et rect