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 mefhod 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 dvdXT)gfj.a besides that of 
Ptolemy; the author of it was Diodorus of Alexandria, a con 
temporary 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 
dvdXrgxga 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 trans 
lation 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 in 
cluded 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, ZQC 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 GOG' as diameter {GSM in 
1 Vitruvius, De architect, ix. 4. • 2 A nth. Palat. xiv. 139. 
3 Pappus, iv, p. 246. 1.