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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 2
# Folio 71r, page id 00068195:0141
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ver. tim . A DE. a DE esse ut CD ad SD, ubicunque in figura ossumantur, faltim ess;
nec implet conditionem. Curvas ergo similiter positas esse, est omnes earum tan
gentes esse parallelas quod non fit nisi earum perpendiculares coincidant
Eligenda est jam recta in figura, quae sit constans, si qua haberi potest. Ea
dimidis
autem est in Parabola ipsa GZ, latus rectum datum ea ergo data est simpliciter.
 cumque sit a ad b t , ut G8 ad AZ ut GH ad AB.
ad
fiet: ab = sa x + 2 a Z sxa, sive
a+2x+c
airic
a
s
ab
exa
a +4ax+ 2ac + 4X + 4Xc + C
sive a b  ax + 4aX + 2aC X + 4X a + +X Ca + CaX.
ab.=
X 4X4 + 4XC4 + 4X  + Ra + 2X aC + XAC et posita a +c-g
X’+ aXg + Xg
Similibus
Nota in Puraboles absciste sunt ut appli ordinatae sive abscissae sunt lateribus rectis propor
 eut X- sic X- C vel i 
b
lionales. Esto enim faX X=
 mas
saxs st Cx bq
, ita b ad y, sive b ad exa.
1 = e 2- 4  Ergo be sea
1Xa a sive na a
XH
bi X2
sive X ab x = aeb. Ergo X = spb. (quod si ducatur in ab, fit
vel 10 ab  tiet 19a b  = X, vel 10 a b = =
Ergo ex Sive ex ab exhatenda est radie cubica, quod ex suj ex se suposita paratota
gai data vota regula ac circino praestari pote
In Hyperbola, posita asymptoton assumi pro axe, aequatio erit a= Xy = 0. vel
= yb = 0. Ergo E =   et y - a
VX+ OL   b.
= 2
Sositis jam duabus istis hyperbolis similibus
rectansulo
Ergo si hyperbolae sunt similes, idem est utrobique 
ai latus secundum quod possunt drdinntae ad aspagtotor
Ergo
a 8b -
 in va y Y 1d est si Hyperboloe sunt similes quadrata
laterum rectorum simt proportionalia d lateribus homulii sive rectis respondentibus
se eodem argumenta debam. Ergo =Eo
horpola
Y 4 inm X ad 8 (a2) est ut a (1 y) ad b. Ergo Xb - E , hir XbG a
Ergo GJum ob raturum dyperbolae, b est media proporto-
nalis inter AT- 2As = 27. = 28 et AZ - AC + CG X + G2. quae GQ setiam
talis L7.  media proportionalis inter 2X ipsam GZ. et 2C9- 2x, ideo GZ = Y a 2a
a
a et C+ 21 2a.
ide. b, media proportionalis venter Z a - 22,=2 aeb
sive b= Exc + 2x + 4X. si ba = 2X + 2XC + 4xa, vel
ba = X  + XC + 2Xa
Aa soloi potest, problema in Ayprtota si ex curva non in ordinatam, fidusingtotem
sed in diumltum cadant ordinate,
b
sin a
ut 11it