A Dictionary of Greek and Roman biography and mythology. By various writers. Ed. by William Smith. Illustrated by numerous engravings on wood.

PTOLEMAEUS. PTOLEMAEUS. 573
mentioned the versions of the genuine work which works of Ptolemy is as follows:-From Simplicius,
are found with those of the Almagest. niepl epe7ofl-'wCs,tovdiAos-, to prove that there
5, 6. De.lnalemmnate and Planisphaerium. can be only three dimensions of space; IepAl peo7r
These works are obtained from the Arabic. Fa- BCGAiov, mentioned also by Eutocius;'roLXEra,
bricius, who had not seen them, conjectures that two books of hypotheses. From Suidas, three books
they are the same, which is not correct. The Ma1Xavucclv. From Heliodorus and Simplicius,
Analemnma is a collection of graphical processes'Or1rTl'K) rpayasreLFa. From Tzetzes, Ifep7Tys77s;
for facilitating the construction of sun-dials, and from Stephen of Byzantium, nIeparAous. There
grounded on what we now call the orthographic have been many modern forgeries in Ptolemy's
projection of the sphere, a perspective in which, name, mostly astrological.
mathematically speaking, the eye is at an infinite It must rest an unsettled question whether the
distance. The Planisphere is a description of the work written by Ptolemy on optics be lost or not.
stereographic projection, in which the eye is at The matter now stands thus: Alhazen, the principal
the pole of the circle on which the sphere is pro- Arab writer on optics, does not mention Ptolemy,
jected. Delambre seems to think, from the former nor indeed, any one else. Some passagesfrom Roger
work, that Ptolemy knew the gnomosic projection, Bacon, taken to be opinions passed on a mannin which the eye is at the centre of the sphere: script purporting to be that of Ptolemy, led Monbut, though he uses some propositions which are tucla to speak highly of Ptolemy as an optical
closely connected with the theory of that projec- writer. This mention probably led Laplace to extion, we cannot find any thing which indicates dis- amine a Latin version from the Arabic, existing in
tinct knowledge of it. There is but one edition of the Royal Library at Paris, and purporting to be
the work De Analemmate, edited by Commandine, Ptolemy's treatise. The consequence was Laplace's
Rome, 1562, 4to. (Lalande says there is a Vene- assertion that Ptolemy had given a detailed account
tian title of the same date. He also mentions of the phenomenon of astronomical refraction. This
another edition, Rome, 1572, 4to., perhaps an error remark of Laplace led Humboldt to examine the
of copying). Nothing is told about the Arabic manuscript, and to call the attention of Delambre
original, or the translator. The Plavisplhaeriutn to it. Delambre accordingly gave a full account of
first appeared in print in the edition of the Geo- the work in his Histoire de l'Astsonomie Ancienne,
graphy, Rome (?), 1507, fol. (Hoffmann); next vol. ii. pp. 411-431. The manuscript is headed
in Valder's collection, entitled " Sphaerae atque As- Incipit Liber Ptholemaei de Opticis sive Aspectibus
trorum Coelestium Ratio....," Basle (? no place is translatus ab Ammuiraco [or Ammirato] ]Eugenio
named), 1536, 4to. With this is joined the Pla- Siculo. It consists of five books, of which the first
nisphaerium of Jordanus. There is also an edition is lost and the others somewhat defaced. It is said
of Toulouse, 1544, fol. (Hoffmann). But the best there is in the Bodleian a manuscript with the
edition is that of Commandine, Venice, 1558, 4to. whole of five books of a similar title. The first
Lalande says it was reprinted in 1588. Suidas three books left give such a theory of vision as
records that Ptolemy wrote r2wastoLs trppaeifae might be expected from a writer who had the work
aicpzpas, which is commonly taken to be the work attributed to Euclid in his mind. But the fifth book
on the planisphere. Both the works are addressed does actually give an account of refraction, with exto Syrus. perimental tables upon glass, water, and air, and an
7. e0pl d7ro0oewov'rcv 7rAhavce'pEvw, De Planeta- account of the reason and quantity of astronomical
rum Hypothesibus. This is a brief statement of the refraction, in all respects better than those of Alprincipal hypotheses employed in the Almagest hazen and Tycho Brahd, or of any one before Cas(to which it refers in a preliminary address to sini. With regard to the genuineness of the book,
Syrus) for the explanation of the heavenly motions. on the one hand there is its worthiness of Ptolemy
Simplicius refers to two books of hypotheses, of on the point of refraction, and the attribution of it
which we may suppose this is one. It was first to him. On the other hand, there is the absence of
printed (Gr. Lat.) by Bainbridge, with the Sphere allusion, either to the Almagest in the book on
of Proclus and the canon above noted, London, optics, or to the subject of refraction in the Alma1620, 4to., with a page of Bainbridge's corrections gest. Delambre, who appears convinced of the geat the end; afterwards by Halma, as already de- nuineness, supposes that it was written after the AIscribed. magest. But oil this supposition,it must be supposed
8.'ApomUIKV ZY ]sL ya'y. This treatise on the that Ptolemy, who does not unfrequently refer to
theory of the musical scale was first published the Almagest in his other writings, has omitted to
(Gr. Lat.) in the collection of Greek musicians, by do so in this one, and that upon points which are
Gogavinus. Venice, 1.562, 4to. (Fabricius). Next taken from the Almagest, as the assertion that the
by Wallis (Gr. Lat.), Oxford, 1682, 4to., with moon has a colour of its own, seen in eclipses. But
various readings and copious notes. This last what weighs most with us is the account which
edition was reprinted (with Porphyry's com- Delambre gives of the geometry of the author.
mentary, then first published) in the third volume Ptolemy was in geometry, perspicuous, elegant,
of Wallis's works, Oxford, 1699, folio. profound, and powerful; the author of the optics
9. le Cpl p1vp'oU Kcal 71jyeitovco6, De Judicandi could not even succeed in being clear on the very
Facultate et Auzimi Priucipatl, a metaphysical points in which Euclid (or another, if it be not
work, attributed to Ptolemy. It was edited by Euclid) had been clear before him. Delambre obBouillaud (Gr. Lat.), Paris, 1663, 4to., and the serves, in two passages, " La ddmnonstration de
edition had a new title page (and nothing more) in Ptolemee est fort embrouillde; celle d'Euclide est
1681. et plus courte et plus claire,".... "Euclide avait
In Lalande we fin4 attributed to Ptolemy, "Re- prouvd proposition 21 et 22, que les objets pagulae ArtisMathelnaticae" (Gr. Lat.),-1569, 8vo., raissent diminuts dans les miroirs convexes. On
with explanations by Erasmus Reinhold. entrevoit que Ptoldmie a voulu aussi ddmontrer les
The collection made by Fabricius of the lost m6mes propositions." Agasin, tile refraction apart,