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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 288r, page id 00068194:0575
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Ex puncto dato minimam ducere adsectionem sonicam datam
Esto punctum datum D minuua quaesita DY ducenda ad
sectionem conicam cuius vertex A. ordiata ex verte puncto
Y quaesito in axem demissa XY  y. et quam illa
exaxe inde a vertice A abscindit, nempe AX, esto X.
DX. producta si opus est, occurrat axi in B sitque X P, P
Datur porro DF diystantia puncti D ab verrice, d.
Datur e AF, f. distantia puncti F, a vertice A.
GD1 d - y, vel ~d + y. vel +d + y. sive Xd +d - y
8 L
sive  4 F d  F et 
y
2
3
et GY ∞ FX e  f + X. vel () X - f() f. X (3 f. x + d + y
Quare satius narum umbignitatum evilandarum causa
non G3 vel GD, sed potius PY quaerere Nam erit FP it
eutue FP e (+ +) f (+ + )s + f) p. e dP, et
+p
. +.
.+
7. L.-.
explicando ZX Est autem V e S_ 2ax + X, ergo quadrando
fier:  +f - 2fX - 2fp + X + 2p X + pE
mulliplicand. + X +15 X +25 X 12a5 X. d
se
4fa
+ qua
-2a fp
+rapr
du
cax +X
et
Tentandum est auhaec aequatio ad cubicam reduci queat arte quam dicam:
sumatur alia aequatio, duas cujus incognita X, duas habet radices aequales
nempe X - 2 ex + e, multiplicetur per aliam + X +CX + ha e, o
biet + XY + ZCX q e X + eC X + e ta + 0. habemus duas aequationes
+ C.. -2ec .. - 2eha
+ ha
conferendas unde 4 collatitia
nam, et 4’indeterminatae,
e. c. h. p
Rectius, ut aequatio data quam quaerimus duas habeat radices aquales
centro D, radio DZ describatur circulus, qui curvam conicam secabit in duobus
punctis Y et (Y) quaere ut curva DY minima sit, necesse est distantiam
duorum punctorum Y et (Y) esse infinite parvam. Patur jam recta DF d)
datur recta AF et f datur recta X Y B Y 1 d2aXF X, datur
recta GD, d - sxax F x datur GX seu _F _  f+X. Erit DY S _
Ergos  d + 2aX +x = 2d 2ax fx + s + 2)X + X. Hic duas habemus vias altera
4 -2dy +3
alteram communem eliminandi V, alteram
et tunc quidem communi opus est methodo tangentium, alteram
retmendi, et tunc mea opus est tangentium methodo, ubi conferenia aequatio data cum alia factitia
duarum incogularum, quarum quaelibet duas habeat radices aequales; a qua methodo etsi
novitas me nonnihil obsterreat video tamen ita statim obtentum iri,  in fallor, ad aequationus
locysit ad circulum, cujus intersectionecum sectione conicadata solutum esset problema, modos
sublata esset, X, et y non mutatis. Videamus an alio modo s tolli possit
e 5