The text known as the *Canobic Inscription* is a transcription made in late antiquity of a lost
public inscription that Ptolemy erected in A.D. 149/150 at Canopus in Egypt.
The inscription records the numerical parameters of Ptolemy's models for the
motions of the sun, moon, and planets. Most of the data in the *Canobic
Inscription* agree with the *Almagest*, but there are a few significant differences which
are now recognized as proving that the *Almagest* was completed later than the inscription. (see also here)

Translation
of the *Canobic Inscription**.*

Edition of the text: *Claudii Ptolemaei opera
quae exstant omnia. II. Opera astronomica minora*, ed. J. L. Heiberg. Leipzig, 1907. [I know of no
modern translation of the inscription other than the draft linked above.]

N. T. Hamilton, N. M. Swerdlow, and G. J.
Toomer, "The Canobic Inscription: Ptolemy's Earliest Work." In *From
Ancient Omens to Statistical Mechanics: Essays on the Exact Sciences Presented
to Asger Aaboe*, ed. J. L. Berggren
and B. R. Goldstein. Copenhagen, 1987. 55-73.

N. M. Swerdlow, "Ptolemy's *Harmonics* and the 'Tones of the Universe' in the *Canobic
Inscription*." In *Studies in
the History of the Exact Sciences in Honour of David Pingree*, ed. C. Burnett, J. P. Hogendijk, K. Plofker, and M.
Yano (Islamic Philosophy Theology and Science 54) Leiden, 2004. 137-180.

The Byzantine encyclopedia known as the *Suda* reports that Ptolemy's works included "On phases
and weather-changes of fixed stars, two books." The work that has come
down to us under the title *Phaseis aplanon asteron kai synagoge episemasion* = "phases of fixed stars and collection of
weather-changes" is not divided into books, and it is generally presumed
that this was originally Book 2 of Ptolemy's work, Book 1 being lost. The
introductory section of our *Phaseis*
does indeed refer to a more mathematically technical work in which Ptolemy
discussed the calculation of visibility phenomena of fixed stars, but the way
in which Ptolemy speaks of it implies that this was a separate treatise rather
than an immediately preceding section of the *Phaseis*. A passage in a work of the ninth century scientist
Thabit ibn Qurra ascribes to "Ptolemy's book on the phenomena of the fixed
stars" an algorithm for calculating the conditions for stellar visibility
that is not found in our *Phaseis*,
so that this is presumably a reference to the lost technical treatise.

According to Ptolemy's summary at the
beginning of the *Phaseis*, the lost
treatise was a theoretical treatment of the conditions of visibility of the
fixed stars, providing the means for determining where the sun must be on the
ecliptic for a star to make its first annual appearance before sunrise, its
last appearance after sunset, its rising at sunset, or its setting at sunrise.
In *Almagest* 8.4-6 Ptolemy deals in
a comparatively cursory manner with the conditions of stellar visibility,
excusing the omission of a more detailed treatment of such phenomena and their
supposed connection with weather on the grounds that the *Almagest *was limited to what Ptolemy thought of as exact
science valid for all time whereas the dates of stellar phases shift over time
because of precession. He says nothing, however, about having written elsewhere
more fully on these topics. Presumably, then, both the technical treatise on
stellar phases and the *Phaseis*
were written later than the *Almagest*.
This is confirmed by the fact that Ptolemy had refined his theory of the
conditions of visibility of a heavenly body at the horizon close to sunset or
sunrise by the time he came to write the specialized treatise and its perergon,
the *Phaseis*.

The core of the *Phaseis* is a *parapegma* or weather-calendar. *Parapegmata* were a traditional part of Greek astronomy, going back in some form to
the fifth century B.C., although the oldest extant examples date from the third
century B.C. and after. A *parapegma*
was a list of dates of more or less regular weather changes, first appearances
and last appearances of stars or constellations, and solar events such as
solstices, organized according to the solar year.

Ptolemy's *parapegma* gives the dates of such events according to the
Alexandrian (or "reformed Egyptian") calendar, which, like the Julian
calendar, had a fixed cycle of three years of 365 days followed by a year of
366 days, so that at least in the short term a particular Alexandrian calendar
date would remain fixed relative to the natural seasons. The dates of the
astronomical phenomena in the *parapegma* are all computed, not directly observed, and Ptolemy provides the
dates for a range of different terrestrial latitudes. The weather phenomena, on
the other hand, are a digest of "observations" (presumably
generalizations based at some remove on local observation) made by various
authorities of the past, including Demokritos, Meton, Euktemon, Philippos,
Eudoxos, Callippos, Conon, Dositheos, Metrodoros, Hipparchos, (Julius?) Caesar,
and "the Egyptians."

Ptolemy believed that there was a causal
relationship between the astronomical phenomena and the changes in weather, but
that the correlation of these events was not perfectly regular or predictable
because other factors (especially the physical influences of other heavenly
bodies) come into play. Hence for him weather prediction was a special division
of astrology.

Edition of the text: *Claudii Ptolemaei
opera quae exstant omnia. II. Opera astronomica minora*, ed. J. L. Heiberg. Leipzig, 1907. [I know of no
modern translation of the complete *Phaseis* other than the draft version linked above.]

G. Grasshoff, "The Babylonian Tradition
of Celestial Phenomena and Ptolemy's Fixed Star Calendar." In *Die Rolle
der Astronomie in den Kulturen Mesopotamiens*, ed. H. D. Galter (Grazer morgenlaendische Studien 3) Graz, 1993.
95-134.

D. Lehoux, *Parapegmata*. (Ph.D. Thesis, University of Toronto, 2000).

D. Lehoux, *Astronomy, Weather, and
Calendars in the Ancient World*.
(forthcoming with Cambridge University Press)

R. Morelon, "Fragment arabe du premier
livre du Phaseis de Ptolemee." Journal for the History of Arabic Science
5, 1981. 3-22.

O. Neugebauer, *A History of Ancient
Mathematical Astronomy*. 3 vols. Berlin,
1975. [especially v. 2, 926-931]

Taub, L. *Ancient Meteorology*. London, 2003.

G. J. Toomer, trans., *Ptolemy's Almagest*. London, 1984. [especially 407-417]

G. J. Toomer, article "Ptolemy." *Dictionary
of Scientific Biography* 11, 186-206.

The *Handy Tables* (*Procheiroi Kanones*) are a revised and expanded version of the
astronomical tables in the *Almagest*.
Ptolemy designed this set of tables for practical use (especially among
astrologers); for this reason, although he wrote a short introduction giving
instructions for using the tables, he said nothing about the theory underlying
them, even though in a few instances he had modified the theory since writing
the *Almagest*. Most of Ptolemy's
revisions to the tables are designed to make them more convenient. Among the
additions to the tables are a chronological table (known as the *Kanon
Basileon* or "Ptolemy's regnal
canon") and a geographical table (the list of "noteworthy
cities", *poleis episemoi*)
extracted from his *Geography*.

The tables of the *Handy Tables* that reflect changes in Ptolemy's astronomical
theories are those pertaining to the latitudinal motion of the planets (i.e.
the tilt of their orbits relative to the plane of the ecliptic) and the
conditions of visibility of the planets.

The *Handy Tables* achieved a more widespread distribution in antiquity
than the *Almagest*. Fragmentary
copies of several papyrus copies of the *Handy Tables* have been found in Egypt. Interestingly, most of
these copies are codices (pages bound in quires) rather than continuous rolls,
the normal vehicle for texts in Ptolemy's time. Ptolemy himself may have
designed the tables with the codex format in mind, because of its greater
convenience for ready reference. In late antiquity many commentaries were
written on the *Handy Tables*. These
were mostly limited to explanations of how to use the tables, but an exception
is the so-called *Great Commentary*
by Theon of Alexandria (late fourth century A.D.), which attempts to explain
the relationship between the *Almagest*
and the *Handy Tables*.

Modern scholars have often supposed that the
version of the *Handy Tables*
surviving in medieval manuscripts was a revision by Theon of Alexandria (or
other writers after Ptolemy's time). This hypothesis is now discredited, and it
is now generally accepted that what we have is substantially Ptolemy's work,
although with certain tables added.

Edition of the tables: N. Halma, *Commentaire
de Th��on d���Alexandrie sur le livre III de l���Almageste de Ptolem��e; Tables
manuelles des mouvemens des astres*.
Paris, 1822. *Tables manuelles astronomiques de Ptolem��e et de Th��on*. II and III. Paris, 1823-1825. [This is still the
only printed edition of the *Handy Tables*, and not a very satisfactory one at that. Halma provides a French
translation.]

W. D. Stahlman, *The Astronomical Tables of
Codex Vaticanus graecus 1291.*
Doctoral dissertation, Brown University, 1960. [Reliable transcription and
commentary on most of the tables of one of the oldest medieval copies of the *Handy
Tables*]

Edition of the text of Ptolemy's
introduction: *Claudii Ptolemaei opera quae exstant omnia. II. Opera
astronomica minora*, ed. J. L.
Heiberg. Leipzig, 1907. [No modern translation exists]

B. L. van der Waerden, "Bemerkungen zu
den 'Handlichen Tafeln' des Ptolemaios." *Sitzungsber. Bayer. Akad.
Wiss., Math. Naturwiss. Kl*., 1953,
261-72.

O. Neugebauer, *A History of Ancient
Mathematical Astronomy*. 3 vols.
Berlin, 1975. [especially v. 2, 969-1028 and v. 1, 256-261]

A. Aaboe, "On the Tables of Planetary
Visibility in the *Almagest* and the
*Handy Tables*." *Danske
Vidensk. Selskab, Hist.-filos. Medd.*
37.8 (1960).

N. M. Swerdlow and O. Neugebauer, *Mathematical
Astronomy in Copernicus' *De
Revolutionibus. 2 vols. New York, 1984. [especially v. 1, 483-486, on the latitude
tables]

A. Tihon, "Les Tables Faciles de
Ptol��m��e dans les manuscrits en onciale (ixe���xe si��cles)." Revue
d'histoire des textes 22 (1992) 47���87.

A. Tihon, "Th��on d���Alexandrie et les
Tables Faciles de Ptol��m��e." *Archives Internationales d���Histoire des Sciences* 35 (1985) 106-123.

A. Tihon, *Le "Petit Commentaire"
de Th��on d���Alexandrie aux Tables Faciles de Ptol��m��e: Livre I.* (Studi e Testi 282) Vatican, 1978. [Theon's so-called
*Little Commentary* is a clearer set
of practical instructions for the tables than Ptolemy's own. Tihon provides an
edition and French translation.]

J. Mogenet and A. Tihon, *Le "Grand
Commentaire" de Th��on d���Alexandrie aux Tables Faciles de Ptol��m��e*. (Studi e Testi 315, 340, 390) Vatican, 1985���1999.
[Edition and French translation of the *Great Commentary*]

A. Jones, *Astronomical Papyri from
Oxyrhynchus*. (Memoirs of the American
Philosophical Society 233) Philadelphia, 1999. [Contains editions and
translations of several papyrus fragments of the tables and of early
commentaries]

The *Planetary Hypotheses* (*Hypotheseis ton planomenon*) represents, so far as we know, Ptolemy's last word
on the models for the motions of the heavenly bodies. The work comprised two
books, of which the first part of Book 1 survives in Greek, while a medieval
Arabic translation of the entire work also exists. The principal object of the *Planetary
Hypotheses* is to set out a physical
interpretation in three dimensions of the idealized circles that compose the
astronomical models of the *Almagest*.
Ptolemy seems to have in mind both a description of the real physical nature of
the mechanisms of planetary motion, and a prescription of how one might
construct an orrery-like tangible model of these mechanisms. Unfortunately, in
the large parts of the text for which we depend on the Arabic translation, it
is not always clear whether Ptolemy is speaking of the reality or the
imitation; but it is at least clear that he believed in the existence of
invisible aetherial spheres in the heavens.

One of the most interesting features of the *Planetary
Hypotheses*, which appears in a part
of the work that was only rediscovered recently, is that Ptolemy was the true
originator of the medieval cosmological system of tightly-packed nested spheres
traditionally called the "Ptolemaic System." When he wrote the *Almagest* Ptolemy could see no grounds on which even the
relative order, let alone the absolute distances, of the remaining planets
could be established with certainty, given that they exhibit no observable
parallax. Nevertheless he tentatively approves the opinion of "the more
ancient astronomers" that the sequence from the earth outwards is: moon,
Mercury, Venus, sun, Mars, Jupiter, Saturn, fixed stars. By the time that he
came to write the *Planetary Hypotheses*, however, Ptolemy had made a discovery, based on the models deduced in
the Almagest, that promised to settle the question even of the absolute
distances for good. Following a traditional physical interpretation of
kinematic models, each of Ptolemy's models could be described as a system of
nested spheres, in such a way that the whole model is bounded by two spheres
concentric with the earth. The ratio of radii of the inner and outer spheres is
determined for each model by Ptolemy���s parameters. Moreover, the actual
dimensions of the solar and lunar models are known. Ptolemy now discovered
that, with his parameters, the models for Mercury and Venus would fit almost
perfectly between the outermost sphere of the moon and the innermost sphere of
the sun. In the *Planetary Hypotheses*
he therefore assumes that the entire cosmos is so arranged that the planetary
models proceed outward from the moon's with no vacant space.

Translation
of Book 1 part 1 of the *Planetary Hypotheses** *[based on Heiberg's Greek text]

Edition of the Greek text (of the first part
of Book 1) and German translation by L. Nix of the Arabic version (of Book 1
part one and Book 2 only): *Claudii Ptolemaei opera quae exstant omnia. II. Opera
astronomica minora*, ed. J. L.
Heiberg. Leipzig, 1907.

B. R. Goldstein, *The Arabic Version of
Ptolemy���s* Planetary Hypotheses.
(Transactions of the American Philosophical Society 57.4) Philadelphia, 1967.
[Includes translation of the "missing" part of Book 1 and a
reproduction of one of the Arabic manuscripts of the entire work with
collations of a second manuscript and of the Hebrew translation of the Arabic
version.]

R. Morelon, *L**a version arabe du Livre des Hypoth��ses de Ptol��m��e*, ��dition et traduction de la premire partie, *M��langes
de l'Institut dominicain d'��tudes orientales* 21 (1993), pp. 7-85.

A. Murschel, "The Structure and Function
of Ptolemy���s Physical Hypotheses of Planetary Motion." *Journal for the
History of Astronomy* 26 (1995) 33���61.

The *Analemma* is a monograph on the mathematical and practical
determination of certain angles useful in the construction of sundials.
("Analemma" is the technical term for a method of converting problems
in spherical geometry into planar constructions by rotating components of the
three-dimensional "diagram" into a single plane of reference.) The
only substantially complete text that we have of this book is in a Latin
translation made in or soon after 1269 by William of Moerbeke from a Greek manuscript
that vanished soon afterwards. (This version is missing all but the first of
the numerical tables that, so far as we know, concluded the *Analemma*.) Parts of the original Greek text survive as the
older writing in a palimpsest manuscript now in the Biblioteca Ambrosiana,
Milan. It is possible that further fragments lie concealed on some of the
up-to-now unread pages of the palimpsest.

Edition of the Latin translation and Greek
fragments: *Claudii Ptolemaei opera quae exstant omnia. II. Opera astronomica
minora*, ed. J. L. Heiberg. Leipzig,
1907.

D. R. Edwards, *Ptolemy's *Peri Analemmatos* - An Annotated Transcription of
Moerbeke's Latin Translation and of the Surviving Greek Fragments with an
English Version and Commentary.*
Dissertation, Brown University, 1984.

O. Neugebauer, *A History of Ancient
Mathematical Astronomy*. 3 vols.
Berlin, 1975. [especially v. 2, 839-856]

The *Planisphaerium* is another mathematical monograph dealing with a specialized
astronomical problem, in this case how to construct a diagram in a plane
representing the celestial sphere, in such a way that circles on the sphere
(e.g. the equator and circles parallel to it) are represented by circles in the
plane. Ptolemy's construction amounts in fact to producing a stereographic
projection, that is, a projection through one of the sphere's poles upon a
plane parallel to the equator; it is, however, open to dispute whether Ptolemy
was aware of this fact. Ptolemy has in mind the construction of an instrument,
which has usually been understood to be a form of the plane astrolabe familar
from medieval astronomy, though his description more closely fits a star chart.

Edition of the Latin translation: *Claudii
Ptolemaei opera quae exstant omnia. II. Opera astronomica minora*, ed. J. L. Heiberg. Leipzig, 1907.

C. Anagnostakis, *The Arabic Version of
Ptolemy's Planisphaerium.*
Dissertation, Yale University, 1984.

O. Neugebauer, *A History of Ancient
Mathematical Astronomy*. 3 vols.
Berlin, 1975. [especially v. 2, 857-868]

J. L. Berggren, "Ptolemy's Maps of Earth
and the Heavens: A New Interpretation." *Archive for History of Exact
Sciences* 43, 1991, 133-144.