_______
/ \
/ \
| |
|___________|
Q| E C A |P
| |
\ /
\_______/

[Illustration: FIG. 2.]

___M___
/___|\__\
// N|\\ \\
|/ | \\ \|
|_____|__\\_|
Q| E C A |P
|\ | /|
\\___|___//
\___|___/

[Transcriber's Note: Approximate renditions of these figures are
provided. Fig. 1 is a circle. Fig. 2 is a circle which contains an
ellipse, tangent to the circle at Q and P. Line segments from M (on the
circle) and N (on the ellipse) meet at point A.]

FIG. 1.--In Ptolemy's excentric theory, A may be taken to represent the
earth, C the centre of a planet's orbit, and E the equant, P (perigee)
and Q (apogee) being the apses of the orbit. Ptolemy's idea was that