Sectiones conicae: parabola (1), circulus et ellipsis (2) et hyperbola Imago graphi parabolae Parabola [1] planum et conum sive sectio conica .
Aequato canonica in systemate orthogonale est:
y
2
=
2
p
x
{\displaystyle ~\textstyle y^{2}=2px}
Aequatio quadrata
y
=
a
x
2
+
b
x
+
c
{\displaystyle ~y=ax^{2}+bx+c}
a
≠
0
{\displaystyle ~a\neq 0}
y
=
a
x
2
{\displaystyle ~y=ax^{2}}
principio coordinatarum , sed in puncto
A
{\displaystyle ~A}
x
A
=
−
b
2
a
,
y
A
=:
−
D
4
a
{\displaystyle ~x_{A}=-{\frac {b}{2a}},\;y_{A}=:-{\frac {D}{4a}}}
Calculatio coefficientorum aequationis quadrati [ recensere | fontem recensere ] Si ad aequationem
y
=
a
x
2
+
b
x
+
c
{\displaystyle ~y=ax^{2}+bx+c}
(
x
1
;
y
1
)
{\displaystyle ~(x_{1};y_{1})}
(
x
2
;
y
2
)
{\displaystyle ~(x_{2};y_{2})}
(
x
3
;
y
3
)
{\displaystyle ~(x_{3};y_{3})}
a
=
y
3
−
x
3
(
y
2
−
y
1
)
+
x
2
y
1
−
x
1
y
2
x
2
−
x
1
x
3
(
x
3
−
x
1
−
x
2
)
+
x
1
x
2
,
b
=
y
2
−
y
1
x
2
−
x
1
−
a
(
x
1
+
x
2
)
,
c
=
x
2
y
1
−
x
1
y
2
x
2
−
x
1
+
a
x
1
x
2
{\displaystyle ~a={\frac {y_{3}-{\frac {x_{3}(y_{2}-y_{1})+x_{2}y_{1}-x_{1}y_{2}}{x_{2}-x_{1}}}}{x_{3}(x_{3}-x_{1}-x_{2})+x_{1}x_{2}}},b={\frac {y_{2}-y_{1}}{x_{2}-x_{1}}}-a(x_{1}+x_{2}),c={\frac {x_{2}y_{1}-x_{1}y_{2}}{x_{2}-x_{1}}}+ax_{1}x_{2}}
↑ Archimedis Opera (1544), p. 142: "Archimedis quadratura parabolae, id est portionis contentae a linea recta et sectione rectanguli coni." Verba citata in Oxford English Dictionary
Nexus interni
