Axes of the ellipse 141SEGMENTAL ARCHED SHAPE
Figure 8.4: Span AB is bisected to give C on the
springing line. The rise at D on the centre line can
be at any distance from C, but must be less than half
the span. Bisect the ‘imaginary’ line AD (not nor-
mally shown when you become geometry- literate)
to intersect with the centre line to establish E. With
E as centre, describe the segment from A, through
D to B.ACBDEFigure 8.4 Segmental arched shape.DEFINITION OF ELLIPTICAL
ARCHED SHAPES
Figures 8.5(a)(b): An ellipse is the geometrical name
given to the shape produced when a cone or cylin-
der is cut (theoretically or in reality) by a geometric
plane (or an actual saw), making a smaller angle with
the base than the side angle of the cone or cylin-
der. The exception is that when the cutting plane
(or saw) is parallel to the base, true circles will be
produced.AXES OF THE ELLIPSE
Figure 8.5(c): An imaginary line (like a laser- beam
or axle of a wheel) that passes through the exact
cylindrical centre of a cone, cylinder or sphere, is
known as an axis and the shape or space around (at
right- angles to) the axis is equal in all directions. But
when cones or cylinders are cut by an angled plane,
as illustrated below in Figure 8.5(a) and (b), the
shape or space on each side of the axis enlarges – butBisecting an angle
Figure 8.2(b): This means cutting or dividing the angle
equally into two angles. Figure 8.2(b) shows CAB as
the angle to be bisected. With A as centre and any
radius less than AC or AB, strike arc DE. With D and
E as centres and a radius greater than half DE, strike
intersecting arcs at F. Join AF to divide the angle
CAB into equal parts CAF and FAB.
SEMICIRCULAR ARCHED SHAPE
Figure 8.3: Span AB is bisected to give C on the
springing line. With C as centre, the semicircle is
described from A to B.
ACBFigure 8.3 Semicircular arched shape.
AEBD^1 D^2C^1 C^2Figure 8.2 (a) Bisecting a line.
AEBDCFFigure 8.2 (b) Bisecting an angle.