Academic journal article Transactions of the American Philosophical Society

The Teaching of the Almagest in Late Antiquity

Academic journal article Transactions of the American Philosophical Society

The Teaching of the Almagest in Late Antiquity

Article excerpt

(ProQuest: ... denotes non-USASCII text omitted.)

My objectives in this paper are two: to reveal the richness of the tradition of the study of the Almagest1 between the date of its composition in the middle of the second century AD2 and its appearance simultaneously in Byzantium3 and Baghdad4 in the late eighth century, and to hypothesise about the origins of one of several commentaries on the Almagest that were composed during this period.

The earliest documented attempt to discuss critically any portion of the Almagest was written by an otherwise totally obscure Artemidorus in the latter half of the second century or at the beginning of the third. A passage regarding the lunar theory of Books IV and V of the Almagest is quoted from this Artemidorus in the anonymous commentary on the Handy Tables edited by Jones and shown by him to contain an example that can be dated 24 April 213.5 Artemidorus established a tradition - fortunately not followed universally - of failing to understand or of misrepresenting Ptolemy's statements in the Almagest.6

It is clear that Artemidorus, however deficient his understanding, approached the Almagest as an astronomer interested in the way in which Ptolemy's solutions to problems work mathematically. The same can be said of the two Alexandrian scholars who commented on the Almagest during the course of the fourth century. Pappus composed his ...7 after 18 October 320, the date for which, in his commentary on Almagest VI4, he computed the time of a mean conjunction of the sun and the moon.8 Of Pappus's Scholion there survive in their entirety only Books V and VI; as we shall see, some fragments of other books - it is not yet clear how many - can be recovered from other sources. Rome conjectured that Pappus followed a tradition established by some earlier commentator of dividing each of the thirteen books of the Almagest (excluding, presumably, the Star Catalogue in VII and VIII) into sections called ... echoes of this practice survive in the commentary of Theon9 and in the later scholia.10 These divisions may have been more useful in the teaching of the Almagest, which was strongly directed toward the students' acquiring computational skills, than were Ptolemy's chapter divisions, which reflect his concern with the logical development of astronomical theory. Despite his emphasis on computations, Pappus makes in Books V and VI about a dozen errors in calculation, and in eight cases seems to have deliberately falsified his results in order to make them agree with the Almagest.11 His students could not have been very alert since they seem to have let him get away with his slipshod habits.

Theon composed his ...12 on the Almagest most probably in the 360s and 370s. Now that Professor Tihon has discovered most of Theon's commentary on Book V in the margins of Vaticanus Graecus 198,13 we have all of the ... except for Book XI. Of the eighteen manuscripts of the commentary known to Rome the oldest is Laurentianus 28.18, copied in the ninth century and at present preserving only Books I to IV and VI. In fact, ten of the manuscripts contain nothing beyond Book VI, and they, without the Laurentianus, form Rome's Class II. So there existed an edition of Theon that broke the text at the end of Ptolemy's discussion of spherical trigonometry, and the theories of the sun, the moon, and eclipses. This is also the dividing point between the two volumes of Heiberg's critical edition. One wonders if the survival of Books V and VI of Pappus's ... may not be due to their being the end of a first volume of an edition of which the second volume in its entirety, the first in its beginning have been lost.

Theon assumes a fairly low level of mathematical ability and accomplishment in his students. They need, for instance, to be instructed at great length on the multiplication and division of sexagesimal fractions and on a variety of geometrical theories, while in general Theon teaches them nothing beyond the replication of Ptolemy's calculations. …

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