DOI Page / Citation link:
https://doi.org/10.11588/diglit.4423#0164
122
THE COLUMNS.
The ellipse is a curve not much employed in the forms of the Doric order, but it is
frequently met with in the Ionic order, and there are many examples of it in the Erechtheium.
Also the curved lines connecting the volutes of the Ionic capital in the Vestibule of the Propylaea
are elliptical, and the curved surface on the return side of the volute is generated by an ellipse
with a variable minor axis. Whenever this curve is employed, the axis major and the axis
minor are invariably the given quantities, and the arc is easily traced by points.
The Hyperbola.
trajusvcrse*
B
^LJ^IM:.
V "-■_/* a/xie
Definitions.
If two points, F and /, in a plane, and a point, D, be conceived to move in such a
manner that D/—DF, the difference of its distances from them, is always the same, the point
D will describe upon the plane a line DAD', called an hyperbola. The given points F and /
are called the foci of the hyperbola. The point C, which bisects the straight line between the
foci is called the centre. The distance of either focus from the centre is called the eccentricity.
A straight line passing through the centre and terminated by the opposite hyperbolas is called
a transverse diameter, and sometimes called simply a diameter. The extremities of a diameter
are called its vertices. The diameter which passes through the foci is called the transverse
axis. A straight line, ~Bb, passing through the centre perpendicular to the transverse axis,
and limited at B and b by a circle described on one extremity of that axis, with a radius equal
to the distance of either focus from the centre, is called the conjugate axis; also called the
second axis.
1st. The arc of an hyperbola being given, the centre, C, is determined by tracing and bisecting
the parallel chords.
THE COLUMNS.
The ellipse is a curve not much employed in the forms of the Doric order, but it is
frequently met with in the Ionic order, and there are many examples of it in the Erechtheium.
Also the curved lines connecting the volutes of the Ionic capital in the Vestibule of the Propylaea
are elliptical, and the curved surface on the return side of the volute is generated by an ellipse
with a variable minor axis. Whenever this curve is employed, the axis major and the axis
minor are invariably the given quantities, and the arc is easily traced by points.
The Hyperbola.
trajusvcrse*
B
^LJ^IM:.
V "-■_/* a/xie
Definitions.
If two points, F and /, in a plane, and a point, D, be conceived to move in such a
manner that D/—DF, the difference of its distances from them, is always the same, the point
D will describe upon the plane a line DAD', called an hyperbola. The given points F and /
are called the foci of the hyperbola. The point C, which bisects the straight line between the
foci is called the centre. The distance of either focus from the centre is called the eccentricity.
A straight line passing through the centre and terminated by the opposite hyperbolas is called
a transverse diameter, and sometimes called simply a diameter. The extremities of a diameter
are called its vertices. The diameter which passes through the foci is called the transverse
axis. A straight line, ~Bb, passing through the centre perpendicular to the transverse axis,
and limited at B and b by a circle described on one extremity of that axis, with a radius equal
to the distance of either focus from the centre, is called the conjugate axis; also called the
second axis.
1st. The arc of an hyperbola being given, the centre, C, is determined by tracing and bisecting
the parallel chords.