Greeks,Practical andTheoretical 75AGBN
TPQKXO LEM DFZRHSY θFig. 10Picture for Appendix B. Earth at E, sun on circle centre Z.Appendix B. From Ptolemy’sAlmagest
(Ptolemy 1984, pp. 153–4)
Note.As already stated, lengths are in sexagesimals with the radius of the circle set equal to 60.
The sixtieths are denoted by a small letter ‘p’, corresponding to the degrees sign for angles.
In order not to neglect this topic, but rather to display the theorem worked out according to our
own numerical solution,we too shall solve the problem, for the eccentre, using the same observed
data, namely, as already stated, that the interval from spring equinox to summer solstice comprises
9412 days, and that from summer solstice to autumn equinox 92^12 days. [Ptolemy then details his
own ‘very precise’ observations in 139–140ce, which confirm these figures, due to Hipparchus.
These figures are all we need.]
Let the ecliptic be ABGD on centre E. In it draw two diameters, AG and BD, at right angles to each
other, through the soltitial and equinoctial points (Fig. 10). Let A represent the spring [equinox], B
the summer [solstice], and so on in order. [E is the Earth; the spring equinox occurs when the sun
is in the direction of A (in Aries), and so on. The circle just drawn is the ecliptic as we see it in the
heavens, and determines what we see.]
Now it is clear that the centre of the eccentre [i.e. of the eccentric circle] will be located between
lines EA and EB. For semi-circle ABG comprises more than half the length of the year [187 days,
as we have seen] and hence cuts off more than a semi-circle of the eccentre; and quadrant AB
comprises a longer time and cuts off a greater arc of the eccentre than quadrant BG. This being so,
let point Z represent the centre of the eccentre, and draw the diameter through both centres and
the apogee, EZH.^11 With centre Z and arbitrary radius draw the sun’s eccentreKLM, and draw
- The apogee is the point at which the sun is furthest from the Earth; from the picture, this is where the eccentre cuts the
radius EH.