The Syntaxis early became the subject of commentaries. For Book vi. and part of Book v. the commentary of Pappius
i extant in Greek. Theon of Alexandria's commentary in II books was first published by Joachim Camerarius of Basle in 1538; the first two books were appended by Halma to his edition of Ptolemy. The Syntaxis was translated into Arabic for the Caliph al-Ma`mun, himself an astronomer, by a translator unnamed, in 827; later it was translated by al-Hajjaj, the translator of Euclid, and again by 'shag b. Hunain (or perhaps his father I:Iunain b. 'shag), whose translation was revised by Thabit b. Qurra (d. 9o1). The first Latin translation was made from the Arabic by Gherard of Cremona; this translation, finished in 1175, was first published by P. Liechtenstein at Venice in 1515, but without the author's name. George of Trebizond made the first Latin translation from the Greek in 1451; this was revised and published by Lucas Gauricus at Venice in 1528. The editio princeps of the Greek text was brought out by Simon Grynaeus at Basle in 1538. The next com plete edition was Halma's (1813-16). All former Greek texts are now superseded by Heiberg's edition of the astronomical works of Ptolemy (1899-1907) to which, so far as the Syntaxis is concerned, a German translation by Manitius has been added (1912-13).
Of the other works of Ptolemy the following should be mentioned: (I) the Analemma, the object of which is to explain a method of representing on one plane the different points and arcs of the heavenly sphere by orthogonal projection on three planes mutually, at right angles, the meridian, the horizon and the "prime vertical." The problem is to find the position of the sun at a given hour of the day. Only a few frag ments remain of the Greek text, but we have a Latin translation by William of Moerbeke from an Arabic version. This trans lation was edited with a valuable commentary by Commandinus (1562) ; and Heiberg has included it, with the Greek fragments alongside (where extant), in vol. ii. of his edition of the astro nomical works. (2) The Planisphaerium survives in a Latin trans lation from the Arabic, which was edited by Commandinus in 1558 and is likewise included in Heiberg's vol. ii. The book is an explanation of a system of projection known as "stereographic," by which points on the heavenly sphere are represented in the plane of the equator by projection from one point, a pole. The pole taken by Ptolemy is the south pole. (3) 431to-Ets arXavrio ao-74pcov. This is a calendar of the sort which the Greeks called parapegma, or a table of the risings and settings of stars in morn ing and evening twilight, with weather-indications
(4)
rc7n, rXavcogivcov, Planetary Hypotheses, in two books, the first of which is extant in Greek, the second in Arabic only. These works are also included in Heiberg's vol. ii.
Two separate geometrical works are mentioned by ancient com mentators, (I) a single book HE/31
On Dimension, in which Ptolemy apparently tried to prove that there are only three dimensions in space; (2) a tract containing an attempt to prove Euclid's Parallel Postulate. The gist of the latter tract is given by Proclus in his Commentary on Euclid, Book i. (ed. Friedlein, 1873). Simplicius mentions a mechanical work IIE/31 borc7w, On Balancings, while Suidas credits Ptolemy with three books on Mechanics.
The Optics of Ptolemy exists (save for Book i. and the end of Book v. which are lost) in a Latin translation made by a cer tain Admiral Eugenius Siculus from the Arabic in the 12th cen tury. It was in five books, the last of which is interesting be
cause it contains what is apparently the first recorded attempt at a theory of refraction of luminous rays through media of differ ent densities; it deals also with astronomical refraction, of which it gives a better account than that of any astronomer before Cassini.
Lastly, Ptolemy wrote Harmonica in three books, a treatise on music. This was edited in Greek and Latin by John Wallis (1682) ; it appeared also with Porphyry's commentary, in Johan nis Wallis Opera Mathematica (1699), vol. iii.
For further particulars the reader may refer to the article on Ptolemy in Smith's Dictionary of Greek and Roman Biography, vol. iii. (by De Morgan) ; Delambre's Histoire de l'astronomie ancienne (1817-21) vol. ii.; Rud-Wolf, Geschichte der Astronomie (1877) ; A. Berry, A Short History of Astronomy (1898) ; and for the mathematics to A. von Braunmiihl, Geschichte der Trigonometric (igoo) ; Gino Loria, Le scienze esatte nell' antica Grecia (1914); and Sir T. L. Heath, History of Greek Mathematics (1921) vol. ii.
Ptolemy is hardly less cele brated as a geographer than as an astronomer, and his r airy packudi WI-rims (or Guide to Geography) exercised as great an in fluence on geographical progress (especially during the period of the Classical Renaissance), as did his Almagest on astronomi cal. Its exceptional position was largely due to its scientific form, which rendered it convenient and easy of reference; but, apart from this, it was really the most considerable attempt of the ancient world to place the study of geography on a scientific basis. The astronomer Hipparchus had indeed pointed out, three centuries before Ptolemy, that the only way to construct a trust worthy map of the inhabited world would be by observations of the latitude and longitude of all the principal points on its sur face. But the materials for such a map were almost wholly want ing, and, though Hipparchus made some approach to a correct division of the known world into zones of latitude, "climates" or klimata, as he termed them, trustworthy observations of lati tude were then very few, while the means of determining longi tudes hardly existed. Hence probably it arose that no attempt was made to follow up the suggestion of Hipparchus until Marinus of Tyre, who lived shortly before Ptolemy, and whose work is known to us only through the latter. Marinus' scientific materials being inadequate, he contented himself mostly with determinations derived from itineraries and other rough methods, such as are still employed where more accurate means of deter mination are not available. The greater part of Marinus' treatise was occupied with the discussion of his authorities, and it is im possible, in the absence of the original work, to decide how far his results attained a scientific form. But Ptolemy himself con sidered them, on the whole, so satisfactory that he made his predecessor's work the basis of his own in regard to all the Medi terranean countries, that is, in regard to almost all those regions of which he had definite knowledge. In the more remote regions of the world, Ptolemy availed himself of Marinus' information, but with reserve, and he explains the reasons that induced him sometimes to depart from his predecessor's conclusions. Among other things Ptolemy's work shows the increased knowl edge of Asia and Africa acquired since Strabo and Pliny.