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# Title: Leibniz-Handschriften zur Mathematik LH 35, 2, 1
# Folio 233v, page id 00067993:0468
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uli
Inquiramus nunc in Curvas figuris cognitis, ut Triangulo,
Parabolae, homologa si
Trianguli aequatio est. X = y.
X = fied. YX = a = y et posito pro X posito a + X,
fiet a + X + 2aX - _ = y, = 2ax + X. Ergo
Figura Quadrahix Hyperbolae curvam habet Triangulo homo-
logam.
Intimei Jarabolici aquatio est. X  ax. X - y _ X = y.
fiet regula nostra: X = x - a = ay. sive
Xa = ay, et pro X posito a +X, fiet 2ax + +
a + 2ax + X, D = a + 4aX + 9aX + 4a X + JaX +X
sive a + 4ax + 6aX + 4 aX + X g = ay.
et hujs figurae quadratrix curvam habet Trilineo
differentia
mege mologam. Ipsa figura autem videtur esse ex
necculu
Hyperboloerdum genere Unde  ficret a + x = B ay + a
sive pro a =+ X posito X fiere:   = X = ay + a
vel X = Y + a = y + a, a-7
n naz n. 2y
vel SX = a = ay ut aute.
aetema eodem modo omnes quoque reliquae paraboloeides
tractari, possunt, sumenda tamen in exemplum compr
sita X=ya+X y haec tractatur non ut Trilineum
sed ut Hyper parabola ipsa, fit enim sax y.
atque adeo a fit enim tatus curvae homogeneae:
t
a
a3=  Et quadratum ejus
A = Z,  detrahatur 1. fiet 
a
a
6-a - 3
vel - X unde figurae X- a - y habe uadialri
demva huic paraboloedi homosoga. Figura autem
ista dabit X- a - ya
paesitum. Io in
cujus quadratura dabit
In simplic. parabola aX y = aY. unde
y= ax  seu 3 = X, hujus quad. a = 0
a vg
cudi addatur
Vax - a vel sax = y. Et huju nimirum ipsius
nambola quadratix figua tunum habetio parabolae
si a +Y = n
ergo a- yF 13)
( a
20
Ergo nitia huc dimi pt
quare Geomenrice
describi potest