Hypatia's work on Ptolemy's Almagest

Hypatia's work on Ptolemy's Almagest


  • Theon of Alexandria's commentary on the third (book) of the Mathematical syntaxis of Ptolemy, "the edition having been prepared [paranagnostheisa] by the philosopher, my daughter Hypatia."

    From The Primary Souces for the Life and Work of Hypatia of Alexandria, by Michael A.B. Deakin

    Theon was Hypatia's father and he devoted much of his professional life to the production of student editions or "commentaries" on earlier mathematical classics, notably the works of Euclid and Ptolemy. The translation of the brief sentence at the start of Book III of his Commentary on Ptolemy's major work is the subject of much debate. It is seen by some (Rome, Heath, Knorr) as attributing authorship of the material to Hypatia and most likely indicating that a computational advance (an improved technique for long division) was devised by Hypatia. For details, see W. R. Knorr's Textual Studies in Ancient and Medieval Geometry (Boston: Birkhä user, 1989). Others (Cameron, Jones, Dzielska) interpret the sentence otherwise, and see Hypatia merely assisting Theon in some way in the preparation of his Commentary. For this side of the debate, see A. Cameron, "Isisdore of Miletus and Hypatia: On the editing of mathematical texts", Greek, Roman and Byzantine Studies 31 (1990), 103-127.

    From Hypatia's Mathematics: A Review of Recent Studies, by Edith Prentice Mendez

    From Rome, who edited a modern critical edition of Theon's commentaries on the Almagest, stated that it was difficult to determine the level of Hypatia's intervention [40, cxvi]. He attempted a statistical survey of three stylistic terms to see if the book attributed to Hypatia was different from the others, but found no evidence for this. He concluded that, as her father's daughter and student, Hypatia was likely to follow his model in speech as well as in teaching [40, cxvi-cxxi]. Hypatia was known as a stylist; Synesius, describing himself as a writer with "grace and harmony of style," sent Hypatia two of his books, and said he would let her decide if they were "worthy of Greek ears" or to be forgotten [44, 250-254]. Knorr feels that Hypatia's sensitivity to style warrants looking into stylistic changes within Book III since the word paranagnM-tstheisa in Theon's heading "literally indicates some process of 'reading along'" [24, 757]. He further hypothesizes a higher level of intervention by Hypatia which shows up in several passages, in particular in the markedly different style of presenting sexagesimal division, a precise and deliberate style which also appears in Book IV. Knorr also suggests that Hypatia could have co-taught Theon's lectures and that the books of their commentary, which were notes of their lectures, might have been continually modified [24, 757-763]. Cameron takes exception to Knorr's hypothesis, claiming that Hypatia only revised Theon's commentary [5, 108], but goes on to speculate without documentation that interpolations "detected in the Almagest by G.J. Toomer may in the main be Hypatia's work" [4, 48].

    Classroom Discussion (based on Knorr's Textual Studies...)

    Discussed Rome's attempt at finding stylistic variations between Books I thru IV. (results were not conclusive).

    Discussed Knorr's theory that Rome did not find conclusive stylistic variations because the literal translation of [paranagnostheisa] is "reading along" instead of "prepared". He found the same term used for Eutocius' commentary on Archimedes, and compared this to a second Archimedes version. Eutocius had aded new paragraphs, and modified others, but the text was mostly unaltered. So, Knorr looked for sections of Book III distinct from the rest of the commentary and from the other Books.

    We examined p. 802-804, parts of Books I and III (in Greek) and p. 780-786 (English translation).

    Specifically, we analyzed the mathematics in the bottom of p. 780 and some of p. 781.

  • sexigesimals (base 60)
  • Division showing that 365 14 48 is 6 5 14 48 base 60.
  • Computation for row 2 of the table (multiply from right to left, as usual) to show that 2* (6 5 14 48) = 12 10 29 36:
    48*2=96 which is 36 base 60 with 1 carried over to the next column.
    14*2=28 +1=29
  • Computation for row corresponding to 50 in the tableto show that 50*(6 5 14 48) = 304 22 20 0:
    50*48=2400=0 base 60 with 40 carried over to the next column.
    50*14=700 +40=740 = 20 base 60 with 12 carried over to the next column.
    50*5=250+12=262=22 base 60 with 4 carried over to the last column
  • Use of table to figure out any digit of sexigesimal division of 360 by 365 14 48, which yields the daily motion of the sun in degrees along the ecliptic.
    Write down the number nearest but less than 360 from the chart -
    360 00 00 00
    304 22 20 00
    divisor is 50
    Subtract 304 22 20 00 from 360 00 00 00
    Answer 54 47 13 12
    Repeat the process.
  • Discussed the fact that in Book I, a similar computation was done very differently - instead of using the chart, a method of long division for sexagesimals was used to find successive quotients by trial one digit at a time. The answer found is an approximation, as opposed to the precise answer found in Book III by the table method.
  • Discussed that stylized differences in the writing were also found.
  • Discussed that Hypatia might have worked on this section, but that it might have been Theon or someone else, and that we will never know for certain.