A history of Greek mathematics - Wilbourhall.org

288 TRIGONOMETRY
the diagram is one position of it,
coinciding with the equator),
and it was called eKrrjfjiopos kvkXo? (' the circle in six parts ')
because the highest point of it above the horizon corresponds
to the lapse of six hours ;
the circle
the second, called the hour-circle, is
represented by any position, as BSQA, of the circle
of the horizon as it revolves round BA as axis.
The problem is, as above stated, to find the position of the
sun at a given hour of the day. In order to illustrate
the method, it is sufficient, with A. v. Braunmuhl, 1
to take the
simplest case where the sun is on the equator, i.e. at one of
the equinoctial points, so that the hectemoron circle coincides
with the equator.
Let S be the position of the sun, lying on the equator MSC,
P the pole, MZA the meridian, BOA the horizon, BSQA the
hour-circle, and let the vertical great circle ZSV be drawn
through S, and the vertical great circle ZQC through Z the
zenith and G the east-point.
We are given the arc SO = 90° — t, where t is the hourangle,
and the arc MB = 90° — (p, where f
vVH
G
/V: \