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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 2
# Folio 109r, page id 00068195:0217
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Ex puncto dato ad sectionem Conicam datam ducere
rectam minimam
Hoc problema du quaesitum est a Geometris, se et sed constructio commoda
non produt,  etsi prolixis calculis analyticis a vires doctis sit determinatum,
Nobis vero  commodior Analysis sic tentanda visa est
Curvo
sit sectio conica quaecunque cujus vertex A axis AB. P datum
jam sit punctum, unde ad punctam ducenda est minima DC, patet circulum
centro D radio DC descriptum tangere curvam Conicam in C.
sit conica
csel latus rectum Y, etransversum q. Abscissa ex axe AB, sit X
ordinata BC sit y. Constat generali aequatione curvae conicae Aequationem
ad curvam conicam fore yis = 2YX + (Y39)XX Ex puncto d agatur
ad axem recta normalis D, et compleatur rectangulum EBCF, data autem
sunt DE, et AE, quia datum est punctum D AE v DE vocitur , et
AE vore DE vocetur f, et AE vocetur g. jautg et fl DF siet f-y et
CF fiet X+g. Cum ergo sit DEqu + CF qu = Dc qu. fiet ff + gy - 2fy +gg tXx trge - 
sed cum in hac aequatione X et y habeant duos valores aequales, sed f, 9, h sin utrique
communes, ideo ex calculo differentiarum fiet 2ydus - 2fdy + 2Xdx + 29 dx =0, seu
fiet dy: Ex = Xtg, : f-y
Rursus Ex aequatione superiore ad Conicam
fit 2ydy = 2rdx + (r: 9) 2Xdx seu dy: dx = r + (Y: 9) X, : y quas duas
aequationes quos duos valores aequando inter se fit yx +gy = fre + ffrig r- ry-sr: qy∞
si esset - r: q = 1 foret haec aequatio ad rectam, sed nunc est ad Hyperbolam
Sid ut obtireatur tentetur aequalio ad Eiiculum mutetur conicae
diameter recta, et quaeratur an possit haberi recta Directrix ad quam
ducantur parallelae angulo quodam assumtitio, ita ut possit haberi aequao
ad crculum
ZE. B 12  + m X nB + 4  20 uideatur quod haec sit ad ticulum