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# Title: Leibniz-Handschriften zur Mathematik LH 35, 5, 25
# Folio 24r, page id 00068043:0047
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In parabola
AB aequ X+ a.
PC aequ V2ax + aa.
seu X aequ Zc
X + a vocetur Z
uxoqugus fatagosodu et PC vocetur pfet
p aequ 2a7- Daa (+ aa
C
C
AB  X.
In omni curva (nisi signis aliquando variltis) erit est
egoyin coa: dx: dy. y. D = X p0 B- yy aequ f∞ - 2D2 + XY
par signis tan
foce
fiet
ponamus autem nos ignorare quod curva haec sit
parabola quaerique a nobis quaenam ita sit:
B
1
a
in nostra curva pp aequ 2aZ- aa
et
C
per aequ 2 et 3 tollendo pp fit: ZZ = 27X + XX aequ 24Z- aa
en gy = 27 X + X
2- 29 a +2ar aequ 2ax -yy
+aa
+aa
cayy
6
9
seu y =x aequ Vrax - yy
a
seu Z aequ X + a + Vrax = gy et Z - x aequ a + 12aX - yy
Ergo per aequ 1. et 8 fit: dx: dy:: y: a + Frax -yy
(10)
seu dy y aequ. adx + dx rax-yy Quae quidem
aequatio divelli potest in duas inter se consentientes
(1
exceq. 10,
(2)
nam ponendo 2ax -yy aequ.0 fitc: dy y aequ adx seu
fit 2yy aequ ax, seu yy aequ2ax prorsus ut in aequ. 11.
sed plerumque non ita facile fravidetur e attalis solutio
Quaeramus curvam in qua sit q aa ppaeqo 2a7
fiet 24Z - yy aequ FZ - 2ZX + XY seu L
-2 ZX + XX aeqr Vaatrax-yy
27 a +a4
+2aX
 = x aequ a + daa +rax -yy. seu  per aeg. 6 et 1.
fiet
dx a + dx saa +rax yu aequ dy y. Quae rursus divelli potest in
duos hoc modo:
 a at 2a+ - yy09. 0. et dx a aquay y
Cm
et 9 fiet: b1ax quida Ba aqe dy b b + ax aequ e vy.
seu  2b 42aX aequ. yy. seu b equaa b manente
existente arbitraria, ergo conferendo aequationes 8 et 10. consentiunt ha
duae savationes, si modo facias 26 aequ aa seu b aequ aa
inter Centamina solitendi supposis line
d
es
diminis progressionis geomethicae est eti
hoc problema