A history of Greek mathematics - Wilbourhall.org

THE ANALEMMA OF PTOLEMY 287
and arcs of the heavenly sphere by means of orthogonal
projection upon three planes mutually at right angles, the
meridian, the horizon, and the ' prime vertical '. The definite
problem attacked is that of showing the position of the sun at
any given time of the day, and the use of the method and
of the instruments described in the book by Ptolemy was
connected with the construction of sundials, as we learn from
Vitruvius. 1 There was 'another dvdXrj/i/ia besides that of
Ptolemy ; the author of it was Diodorus of Alexandria, a contemporary
of Caesar and Cicero (' Diodorus, famed among the
makers of gnomons, tell me the time ! ' says the Anthology 2 ),
and Pappus wrote a commentary upon it in which, as he tells
us, 3 he used the conchoid in order to trisect an angle, a problem
evidently required in the Analemma in order to divide any
arc of a circle into six equal parts (hours). The word
'
dpdXrjizfxa evidently means taking up ' (* Aufnahme ') in the
sense of making a graphic representation ' ' of something, in
this case the representation on a plane of parts of the heavenly
sphere. Only a few fragments remain of the Greek text of
the Analemma of Ptolemy; these are contained in a palimpsest
(Ambros. Gr. L. 99 sup., now 491) attributed to the seventh
century but probably earlier.
Besides this, we have a translation
by William of Moerbeke from an Arabic version.
This Latin translation was edited with a valuable commentary
by the indefatigable Commandinus (Rome, 1562); but it is
now available in William of Moerbeke's own words, Heiberg
having edited it from Cod. Vaticanus Ottobon. lat. 1850 of the
thirteenth century (written in William's own hand), and included
it with the Greek fragments (so far as they exist) in
parallel columns in vol. ii of Ptolemy's works (Teubner, 1907).
The figure is referred to three fixed planes (1) the meridian,
(2) the horizon, (3) the prime vertical; these planes are the
planes of the three circles APZB, ACB, ZQG respectively
shown in the diagram below. Three other great circles are
used, one of which, the equator with pole P, is fixed ; the
other two are movable and were called by special names;
the first is
the circle represented by any position of the circle
of the horizon as it revolves round G0G r as diameter (GSM in
1
Vitruvius, De architect, ix. 4.
8
Pappus, iv, p. 246, 1.
2 Anth. Palat, xiv. 139.