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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 186r, page id 00068200:0373
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sive 16d
Expuncto dato minimam ducene ad sectionem
Conicam datam:
Punctum datum esto D, sectio conica dara AY cujus axis AX vert A
distantia puncti dati ab axe, DFd et distantia puncti f a vertie
erit AF. f. centro D radio DV describi debet circulus qui
curvam AY tangat in Z sive qui secet in duobus punctis Y et (Y
distantiae infinite parvae; ponamus punctum D. esse vertice A,
altius, et ipsa curva exterius, ut in figura vides; eut GL,  FA+ AX
ved G
D , DF= XY et ponendo AX X et XY
8, sive p 2aX + aX, fit et DZ, S fiet:
1 d - 2d Srax + a X + _ax + a X + f + 2fX + X
a
2
(dax e 2d Praxtax Bd + rax fa X + f  + 2fXx + X = s
de+s hatr
L 
et ponendo + 1 + a B , et 2aK + 2fX B bX. et d +f-5r, ta
a
et aequatio 2d Srax+ax et qudrundo ( +Y X +bX + ta
2
4
4daX + +d a X ( X tYbX, 2YtX, eb X r abtaK + tat
Ju v
a M
2
ur
+ 2VbX + 27 X + 2bta X + ta pjo
ta
+
1..
+ada.
-8a
estat una conditio ad determinandam hanc aequationem, quod scilicet
incognita X duas habet radices aequales, quam multiplicando per
u extde
a
Huddeniano invento; habebimus aequationem
Ergo te
qqo t
s
4V X 16)bX , 2b
a
Foa
n- 4 - 2b a
novam.
4γt X + 2bta X
2 b
i +∞ da
= 8d a
ed’a
possuntque diversi indagari
 valores ipsius + ut inde
eliciatur simpli cissimus
Sed satius est, opinor, in hoc quidem exemplo, Cartesii methodum sequi, is
umadices aequales habentem
nonotur
Xrex + epjo per aliam aeque arbitrariam multiplicare hubet, ut per  X +CX + 
qua ducta in X- 2ex te
ex Term. 2. C
ur
a
4
se
a
2Vb +2)C.
fiet aequatio factitia similis datae, nempe
2Ye x3
a
X
+C  =2C
peunt n eie
e
+ s
E lam. s. tra
+ et X + he
-2eh.
Quae si conferatur datae
superiori tunc habebimus
Aequationes collatitias sequentes
vel an 1e
per. 2d ax+ 2acp fX ju ex +a
X+ beaee
dvrax + ax
+(6X)
fiet ergo:
quadrando utrotique
ta ax+ea
So
pta
Hve, que X teg
raxere tre
Hia axAd2X et quadrando.
(
ad
abjectasque rursus
qqae
assugunt, ad et et ordinando.
edap
id
d
a+
X
bet rex 4d..)
a
vere
fat
764 dea eX + 16d
rbe +abex+aCX
1
2AX +2aC