Abstract
Among mathematical texts from Antiquity, Theon’s commentary on Ptolemy’s Almagest, together with his two commentaries on the Handy Tables, are rare examples of works that can be credited as having an explicitly ‘pedagogical purpose’, for the simple reason that the prefaces to these three commentaries explicitly say so. This simple fact raises some simple questions, such as: is it really a good teaching program on the Almagest? Does it make it clearer? Is it an efficient pedagogical artifact? What does it reveal about the way in which the Almagest was explained and taught in Theon’s period? After having briefly recapitulated the reasons that have led historians to adopt a prudent approach to these questions, I will offer some remarks on the preface of Theon’s commentary to the Almagest. On this basis, I will show Theon’s dependency on the broader culture of commentary and then analyze, as a consequence, his position vis-à-vis Ptolemy’s treatise as a model for astronomical studies.
I thank Bernard Vitrac, Matthieu Husson and Ioanna Skoura for their helpful suggestions and corrections on the last-but-one version of this text.
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Notes
- 1.
The Almagest is the modern name, transliterated from Arabic, for one of the works of the second century AD Alexandrian astronomer Claudius Ptolemy (Feke and Jones 2010). This treatise is one of the major works in ancient Greek theoretical astronomy. His historical importance is partly due to the fact that it has served as the basis for astronomical commentaries, criticism and corrections from Antiquity to the early modern period at least. The first known complete commentaries on the text are due to Pappus of Alexandria (beginning of the fourth century AD) and, later on, to Theon of Alexandria (end of fourth century AD). The latter commentary originally had thirteen books, book XI is lacking and book V was retrieved in the scholia to the Almagest, (Tihon 1987, 1992, 120–1). Books I-IV have been edited by Adolphe Rome (1936, 1943). For the other books the only edition is Camerarius’s (Cam. 1538). The reference to the Greek text (in Alm) is to Rome’s edition. In general, these editions rely on manuscripts that are not autographs, which are probably lost forever: this means that the copies, on which the editions in question are based, are much later than the original writings. See, on this point, the general remarks of Ritter and Vitrac (1998, 1233–4).
- 2.
These are the so-called ‘little’ and ‘great’ commentaries on the Handy Tables. Both have been edited and translated in French by Anne Tihon (1978, 1991, 1999) and the reference here is to these editions (LC and GC). For a convenient summary of the content of these two commentaries see (Jones 1999b, 162–167).
- 3.
Part II contains a translation of the preface to Theon’s commentary on the Almagest. The prefaces to the two other commentaries are translated in an appendix (a French translation is also available in Tihon’s editions). The fact that prefaces would explicitly address learners is not uniform among the prefaces to mathematical treatises written in Greek. On this matter, see the general overview in Vitrac (2008).
- 4.
Rome has general remarks on the pedagogical characteristics and shortcomings of both Pappus’s and Theon’s commentaries in his preface to the first volume of his edition (Rome 1936, LXXXV note 2). In addition, many of his footnotes contain remarks on the allegedly didactic dimension of the two commentaries.
- 5.
See, for example, Rome’s notes on the end of Theon’s commentary on chapter I.4 of the Almagest: in Alm. 398.6–400.15, especially (Rome 1936, n. 2 p. 398; n. 1 p. 400).
- 6.
The perception of ‘difficulty’ is of course highly dependent on the time and social context; but in the present case, there is little doubt that Theon’s contemporaries considered the Almagest as a difficult text; see (Jones 1999b, 147).
- 7.
Anne Siety, in her suggestive essay (Siety 2001), develops the argument that teachers are –nowadays– very much the subject of fantasies that she describes as being specific to mathematics teaching. Interestingly, she describes these fantasies as essential ‘mythical’ in nature, therefore calling to a long history. See part I.3 ‘le prof de maths, cet inconnu’.
- 8.
This possible confusion lies behind the historiographical issues raised in the first pages of Anne-Marie Chartier’s contribution, concerning the interpretation of former aids to reading such as ‘psalters’.
- 9.
Other questions in which he was a recognized pioneer are the careful study and edition of geometrical figures and the special interest he paid to the design and building of astronomical instruments. Moreover, Rome never saw his notes as anything other than preliminary remarks (‘un premier débroussaillage’, Rome 1936, LXXXV).
- 10.
- 11.
The two books were the first edited by Rome (1931). The dependence of Theon’s commentary on the sixth book to Pappus’s one is without question, but it does not amount to mere plagiarism. On this question see (Rome 1936, LXXXIII–IV); I also refer the reader to Ioanna Skoura’s forthcoming PhD thesis (Univ. of Athens) on the question.
- 12.
This point is made in (Jones 1999b, 167).
- 13.
Borrowing the terms proposed by Anne-Marie Chartier in her own contribution (cf. §3.1 ‘the different levels of contextualization’), the fact that we only have access to the cultural environment does not imply that the didactic context and learning situation are inexistent.
- 14.
Sluiter (1999, 176–9).
- 15.
- 16.
Although I would question the use of the essentially modern notion of ‘model’ to describe Ptolemy’s enterprise. This is probably a better approximation to what the ancients had in mind when dealing theoretically with the movements of the planets (see Rochberg 2004, 283–286), but it tends to apply an idea of complexity and fundamental discrepancy (between reality and its models) that seems to me to be alien to ancient thought. On this point see (Bernard 2010c).
- 17.
For the essentially practical side of ancient philosophy, see the classic work (Hadot 2006) and, as far as Ptolemy is concerned, see the references given in note 15 above.
- 18.
Alm. I 8.1–16.
- 19.
- 20.
See Proust’s and Clancier’s contributions in particular. Much similar material can be found for the study of astronomy in Arabic Middle Ages, as F. Charette’s contributions to our workshops have amply shown.
- 21.
- 22.
- 23.
- 24.
A useful review of the available material and its significance is found in Tihon (1992), which deals with the specific problems raised by the edition and/or study of such documents. Some of these testimonies are still under scrutiny and in the course of being edited, like the so-called Prolegomena to the Almagest now being studied by Acerbi et~al. (2010).
- 25.
Thus, the manuscripts Vat gr 1594 or Par. Gr. 2389, which are among the oldest used for Heiberg’s edition of the Almagest, dates back to the ninth century and eleventh century AD respectively– at least seven centuries away from Ptolemy’s own period! The Laur. Pl. 22.18n, the main basis for Rome’s edition of Theon’s commentary on the Almagest, is dated from the ninth century, some five centuries away from Theon himself.
- 26.
See the useful synthesis of (Pingree 1994) for an overview. See also the final remarks to A. Tihon’s edition and translation of scholia to the Handy Tables, (Tihon 1973, 105–8) and the recent remarks of F. Acerbi et~al. on the milieu in which the so-called ‘Prolegomena to the Almagest’ were compiled (Acerbi et~al. 2010, 64–66 and 68).
- 27.
Tihon (1976, 1992, 118–120). Note, however, that the notion of ‘scholastic manual’ should probably be used with some care, since it is essentially a modern notion and even for the contemporary period it appears to be problematic (Choppin 2008). That edited texts would be essentially meant for teaching is therefore a doubtful equivalence.
- 28.
Such is the case of the so-called prolegomena, cf. on this (Acerbi et~al. 2010, 64), recapitulating and confirming on this point Mogenet’s previous remarks about the nature of this work (Mogenet 1956). Tihon (1992, 123–4) remarks that the Great Commentary might be classified in the same category and reflects the incomplete state of the text; on this point see also (Jones 1999b, 169–170). Pingree (1994, 80f) proposes interpreting a set of scholia to the Vat. Gr. 1594 in the same sense.
- 29.
Tihon (1976–1977, 51–2).
- 30.
- 31.
- 32.
- 33.
One famous case is the controversy about the attribution of the so-called Prolegomena to the Almagest, once attributed by Mogenet to Eutocius of Ascalon, then attributed by Knorr to a certain Arcadius. For an updated discussion, see (Acerbi et~al. 2010, 65–6).
- 34.
Tihon (1992, 137).
- 35.
Tihon (1973, 103–8).
- 36.
For convenience I differentiate the various parts of the present introduction by letters [a], [b]. The translations of the prefaces to the Little and Great Commentary on the Handy Tables are proposed in an appendix: they will occasionally serve as points of comparison in the course of my commentary.
- 37.
Akroatai. The term, for which we here keep a literal translation, is all too easily translated as ‘student’. This translation is not illegitimate in one sense, but it tends to impose a modern notion on a series of ancient terms, each of which carry specific nuances, as we shall see.
- 38.
Teknon, which literally means ‘child’ or ‘my child’ but which is very often used in a metaphorical way to designate a distinguished student. See Pappus of Alexandria’s similar address to Hermodoros at the beginning of book VII of his Mathematical Collection ‘hermôdore teknon’ (634.3).
- 39.
‘Mathematical composition’ is for mathematikê syntaxis, the traditional name for the Almagest.
- 40.
The expression used is hypomnêmatismos, which strongly recalls the verb by which Ptolemy himself characterizes his enterprise at Alm. I.8.6–16. The verb is used at other places in the Almagest (Alm. I.159.20, II.206.7, 338.22, 608.8).
- 41.
Askêsis tôn astronomountôn; the notion is recalled slightly later in Theon’s commentary on the very first words of the Almagest by the mention of “ho ton astronomein epaggellomenon”, namely “the one who pretends to practice astronomy” (in Alm 319.13).
- 42.
Hê protropê tôn stoicheioumenôn.
- 43.
Philalêthôs kai zêtêtikôs, these typical qualifiers appear not infrequently in Ptolemy and belong to the group of terms by which he designates the ‘legitimate philosophers’, that is, those who follow a legitimate method in their inquiry. Hipparchus and Hipparchus’s methods, in particular, are often credited with similar epithets or adverbs: zêtêtikos, philalêthos, gnêsios. In the present case the expression seems to be directly borrowed from a remark by Ptolemy within this complex theory of the movement of the moon about the corrections needed on previous models (Alm. I.328.4: book 4, ch. 9).
- 44.
The term used is hupomnêmatistoi, in correspondence with the expression used above for Theon’s own enterprise.
- 45.
Mellontes hapanta grammikôs apodeiknuein, which is an almost literal quotation of the concluding sentence, in book I, on the transition between the exposition of the ‘general conceptions’ and the ‘particular demonstrations’: Ptolemy says that before the first demonstration, he must make an abridged presentation of the theory of chords in a circle, and he adds “hapax ge mellontes hekasta grammikôs apodeiknuein”, that is, “and for this we shall demonstrate once and for all each thing geometrically” (Alm. I.31.5 H). Thus, ‘each thing’ (hekasta) has become ‘all things’ (hapanta) and, of course, the sentence taken out of its context appears to be much more general than it is in reality.
- 46.
psiloi ephodoi, which is also the expression used in the introductory sentences of Theon’s Little commentary on the Handy Tables (see the translation in appendix): there he says that he shall only present the mere procedures of calculation, without presenting any demonstration that might justify them.
- 47.
The term used is again hupomnêmatismos, and the whole formula strongly reminds one of the similar formulas used by Ptolemy and that are often associated with the idea of length (e.g., Alm I. 159.19–21).
- 48.
Lit. “Dio to stoicheiôdê“: it is unclear, whether Theon refers to the ‘elementary character’ of the first book of the syntaxis itself, or to the style of his own explanation. The ambiguity might be voluntary.
- 49.
This is a literal excerpt from the final remarks of Ptolemy’s explanations about the basic purpose and structure of the Almagest (Alm.I 7.25–8.16), in which he explains that for the sake of brevity, he will only present what the ancients had sufficiently investigated (êkribômena) and that he will only rework that that were “not generally determinated or not as usefully as it was possible <to do>”.
- 50.
This is again an allusion to the passage in book IV, in which Ptolemy explains what the attitude should be of those who correct the ancients’ determinations. Alm. I. 328.8–11.
- 51.
Again taken from the same passage in book 4, Alm. 328.11.
- 52.
See part I. Pingree 1994, 78 is of a different opinion: “Those students who studied the Almagest under [Pappus’s and Theon’s tutelage] were interested primarily in learning the details of Ptolemy’s mathematical models, and no practical motive such as the practice of astrology.” Pingree’s justification for maintaining a strict division between the two putative kinds of publics is that “Astrologers operated with far less sophisticated material ; at best they learned how to manipulate the Handy Tables, a skill also taught by Theon” (ibid.) Personally I find Pingree’s interpretation far less compelling than Jones’s better documented one (cf. part I); moreover, the preface to Theon’s Little Commentary leaves no ambiguity on the fact that he would expect one, in principle at least, to understand the geometrical proofs of the Almagest.
- 53.
Bernard (2010a).
- 54.
For a useful synthesis on the practice of ancient astrology in the Ancient Greco-Roman world, see (Barton 1994).
- 55.
- 56.
Ibid.
- 57.
As pointed out by François Charette (personal communication), to check this would require, in principle at least, having philological or papyrological evidence for an organized curriculum leading from more elementary (?) treatises, like the Elements or the treatise included in the domain of ‘little astronomy’, to more advanced studies like that of the Almagest.
- 58.
See, for example, in Alm. 452.14–458.8 (on ‘sexagesimal parts’) or 458.9–462 or 579.11–580 (on multiplication and division). Cf. the summary of similar passages in the Prolegomena, (Acerbi et~al. 2010, 57–59).
- 59.
Namely, the explanations given in chapters 2 to 5 of the Almagest, in which the main hypotheses of the treatise are presented. Theon’s commentary on this relatively short part of the Almagest runs (in Rome’s edition) to more than a hundred pages (in Alm. 334–447)!
- 60.
For a typical example of ‘Theonine’ digression, see his long commentary, drawn from Zenodorus, of Alm. 13.16–19: it runs to some 40 pages.
- 61.
A typical example is Theon’s presentation of what we know as Menelaus’s theorem, in Alm. 539.17–539.25 and (Rome 1936, 538 n. 2).
- 62.
Here the translation is more legitimate, since the expression used by Theon explicitly refers to “those who come to us so as to learn such a subject matter” (see Appendix 2 and the note).
- 63.
Again a transparent allusion to the Almagest’s wording.
- 64.
Cuomo (2000).
- 65.
- 66.
Bernard (2003a, 132 and 133 n. 197).
- 67.
- 68.
Peri tou akouein = De Audiendo, 42d–43f.
- 69.
It is probably not by chance that part [c] of Theon’s preface looks so much like a promotional self-advertisement, meant to attract students to him. In the ‘liberalised’ context evoked by Jones (ibid. 157: the Greco-Roman astrologer as an ‘independent professional’), one had to compete for students. Organized fights to attract students to the ‘courts’ of renowned sophists, in Eunapus’s time, were not uncommon. Cf. note 66 above.
- 70.
In Eucl. 84.8–23.
- 71.
See, for example, in Alm. 329.19–330.2. This preliminary knowledge might also be interpreted in light of the ancient practice, which was formalized in late Neoplatonist circles, of introducing introductory (‘isagogical’) remarks (prolegomena) situating the contents of the treatise studied in a larger context. See (Mansfeld 1994, 1998).
- 72.
An interesting and classical example of the use of books within technical studies is Galen, who frequently makes explicit the way he would consult books, especially the various versions of Hippocrates’s writings, and compose his own texts. On this see (Andorlini 2000).
- 73.
- 74.
Tihon (1976–1977, 50–52).
- 75.
- 76.
Vit. Procl. 26.21-27.37 Saffrey.
- 77.
This should not, of course, exclude the possibility that preliminary notes were written down as a preparation for the course. Festugières (1950, 34–47) discusses the meaning of hypomnêmatismos as a term describing the unedited notes taken for an oral course (dialexis, homilia). His remarks confirm that the edited version would be an a posteriori production.
- 78.
We might compare with the way by which D. Barbaro, in the Renaissance period, included one letter from Antonio Maria Pazzi (Gessner 2010). However, in this case as in Pappus’s, the reference to Pazzi is explicit in Barbaro’s text, while there is no such reference to any student or collaborator in Theon.
- 79.
- 80.
in Alm. 398.6–399-8. This faulty demonstration is discussed in Knorr (1996).
- 81.
See Peri itou akouein 39d–40f, 41–43 Belles Lettres, especially 40c: “For it is the easiest thing in the world to find fault with one’s neighbor, and also a useless and inane proceeding unless it be applied in some way to correcting [pros tina diorthôsin] or avoiding similar faults.” (transl. Lacus Curtius, Loeb Library 1927; parenthesis added).
- 82.
Even in the case of the Great Commentary, which looks more like an incomplete work (Tihon 1991) this remains a very difficult task.
- 83.
In his introduction to the collective volume ‘les lieux de savoirs’ (Jacob 2007, 23).
- 84.
See the references signaled by Jacob in this note 1, ibid. p. 23.
- 85.
Bernard (2003a, 132).
- 86.
Sluiter (1999, 203).
- 87.
Jones (1999b, 168).
- 88.
These allusions are indicated, in our translation given above (part II) by underlined dots.
- 89.
Translation Toomer. The verb should be translated in a better manner, but it is not my purpose here to discuss this point. For the same reason, I will not propose here a uniform translation of the term, that I am incapable of giving at the present moment.
- 90.
An other occurrence with very close meaning and almost the same wording is found in book X, Alm. II 338.20.
- 91.
Alm. II 206.7–8.
- 92.
Alm. II. 608.2–10.
- 93.
On this question, I refer the reader to J. Feke’s forthcoming paper (Feke 2012).
- 94.
in Alm. 325.1–17.
- 95.
In Alm. 325.4–5.
- 96.
In Alm. 325.7–13.
- 97.
In Alm. 325.14–17.
- 98.
See note 45.
- 99.
I have developed this argument in the chapter devoted to Pappus, Theon and Hypatia in Bernard (2010b, 426–9).
- 100.
For the very same reason, I would nuance Jones’s elliptic judgment that “neither Pappus nor Theon shows much interest in or understanding of the large scale plan of the Almagest” (Jones 1999b, 165). One might of course always contest that a given commentator really understood the structure of such a complex treatise; but Theon, at least, certainly pays the utmost attention to the whole structure of the treatise and constantly, if not obsessively, reminds the reader of this. This might be regarded as an amplification of Ptolemy’s own concern for the overall structure of his progression.
- 101.
Theon in fact uses formulae like ‘in order to make this clear…’ and therefore calls to the value of saphêneia, clarity, which is typical of many treatises from late antiquity. Remarkably, Theon does not put forward this value in this introduction, as if it was not really at stake for him. What seems really important for him is to supply proofs where it is possible to do so – even in places in which this might appear useless (cf. part [c] above).
- 102.
Such a reading was suggested, in one or our workshops, by Fabio Acerbi commenting on the interesting passage devoted, in Theon, to useful rules for the memorization of the so-called Menenalus theorem (cf. note 61 above).
- 103.
Mogenet and Tihon (1985). This edition includes a French translation of the text.
- 104.
Lit. logikê ephodos. ‘Ephodos’ refers to the action of following something step by step, like a calculation in the present case.
- 105.
Here the verb employed is, as in the introduction of the Almagest and of Theon’s commentary on the latter (cf. note 40), hypomnêmatisasthai.
- 106.
The privilege of having ‘launched’ the issue is awarded to Eulalius and Origenes, and the treatise is first presented as a response to it, then Theon adds his own opinion and approval of the project.
- 107.
In the context of the study of the Almagest and the Handy Tables, such an expression cannot but have a very heavy weight: it directly refers to the ‘mathematical theôria’ to which Ptolemy explains that he devotes himself in Alm. I 6.21–23.
- 108.
En tois mathêmasi, which might be understood in a looser way: in their studies. Tihon: ‘dans les sciences’.
- 109.
Pragmateia tês syntaxeôs.
- 110.
Hypothesis has to be understood here in the ‘Ptolemaic’ sense, as the kinematic-geometrical basis from which the tabular computations are established and justified.
- 111.
Lit. dia tês aitiôdous didaskalias, that is a ‘quasi-causal’ teaching. This is probably a double allusion, first to the “knowledge of the causes” thanks to which errors might be corrected in a table (see below the end of the same sentence); and second, to the fact that understanding the computational method and its geometrical basis really amounts to understanding the true movements of the stars: Ptolemy insists heavily on this aspect in book III of the Almagest when he introduces the basic purpose of building a table of mean motion and anomaly for the irregular movement of the sun, see Alm. I 208.15–27, book 3, ch.2; at the same time, the Almagest is not a work on the physics of the Heavens, so that this might only be qualified of ‘quasi-causal’, as Theon has it.
- 112.
The Greek ekthesis is frequently used by Ptolemy in various and interconnected meanings, from the presentation of a complement argument to the bare outlook of tables. The meaning here can only be the way to present the tables, that is, how and why they should be constructed (cf. the title of II.6, II.8 or II.13 in the Almagest).
- 113.
Scholia.
- 114.
Lit. ‘of such a quality’, têlikouta.
- 115.
This is probably a discrete allusion to Ptolemy’s self promotion as striving for a quasi divine disposition of the soul, as a consequence of his choice of studying the movements of Heavenly bodies through mathematics. This opposition mortal / divine is well reflected in the famous epigram sometimes attributed to Ptolemy and that is indeed present in several copies of the Almagest: “Well do I know that I am mortal, a creature of one day. // But if my mind follows the winding paths of the stars// Then my feet no longer rest on earth, but standing by // Zeus himself I take my fill of ambrosia, the divine dish.” The Greek Anthology, transl. Patton, Cambridge MA: Harvard Univ. Press, 1916, repr 1960, vol.3, book IX, epigram 577, p. 321.
- 116.
Tihon (1978).
- 117.
Psêphoria tôn asterôn, the notion of ‘calculation’/psêphophoria is used frequently by Ptolemy and always only to position the sun, moon or planets through specific tables; the notion is therefore intrinsically related to the use of Tables. It might almost be translated as ‘algorithmic procedure using tables or series of tables’.
- 118.
This alludes to the Great Commentary.
- 119.
Lit. Mathêsis tês toioutês didaskalias, <they come> for the learning what is thus taught.
- 120.
Lit. psiloi ephodoi. See note 46.
References
References to Ancient Texts
Alm. Claudii Ptolemaei Opera quae extant omnia. Syntaxis mathematica I. Libros I-VI (1898) II. Libros VII.-XIII. (1903), ed. Heiberg. Leipzig: Teubner.
Cam. 1538. Camerarius’s edition of Theon of Alexandria’s commentary on the Almagest. In Claudii Ptolemæi Magnæ constructionis, id est perfectæ cœlestium motuum pertractionis lib. XIII [Ed. Simon Grynaeus]. Theonis Alexandrini in eosdem commentariorum lib. XI [cura Joachimi Camerarii]. Basel: Johan Walder.
GC Great Commentary of Theon of Alexandria on the Handy Tables. The reference is to Tihon’s edition (Tihon 1993), pages and line numbers.
In Alm. Commentary of Theon of Alexandria on the Almagest. The reference is to Rome’s edition (Rome 1936), pages and lines numbers.
In Eucl. Proclus diadochi in Primum Euclidis Elementorum Librum commentarii, ed. Godfried Friedlein. Leipzig: Teubner, 1873 (rééd. Georg Olms 1967).
LC Little Commentary of Theon of Alexandria on the Handy Tables. The reference is to Tihon’s edition (Tihon 1978), pages and line numbers.
Vit. Procl. Marinus de Néapolis, Proclus ou Sur le Bonheur = Vita Procli. 2002. Text edited, translated and annotated by H.D. Saffrey and A.P. Segonds. Paris: Belles Lettres.
Modern Studies
Acerbi, F., N. Vinel, and B. Vitrac. 2010. Les ‘Prolégomènes à l’Almageste’. Une édition à partir des manuscrits les plus anciens. Introduction générale-Parties I–III. Sciamvs 11: 53–210.
Andorlini, I. 2000. Codici papiracei di medicina con scoli e commento. In Le commentaire, entre innovation et tradition, dir. M.O. Goulet-Cazé, 37–52. Paris: Vrin.
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Bernard, A. 2003a. Sophistic aspects of Pappus’s collection. Archive for the History of Exact Sciences 57(2): 93–150.
Bernard, A. 2003b. Ancient rhetoric and Greek mathematics: A response to a modern historiographical dilemma. Science in Context 16(3): 391–412.
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Feke, J. 2012. Ptolemy’s defence of theoretical philosophy. Apeiron 45(1): 61–90.
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Gessner, S. 2010. Bons procédés entre érudits. Un mésolabe pour l’édition de l’Architecture de Vitruve (1567). Revue de Synthèse 131(4): 523–541.
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Mansfeld, J. 1994. Prolegomena. Questions to be settled before the study of an author, or a text. Leiden: Brill.
Mansfeld, J. 1998. Prolegomena mathematica. From Apollonius of perga to the late neoplatonists. Leiden: Brill.
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Appendix: The Prefaces to Theon’s Commentaries on the Handy Tables
Appendix: The Prefaces to Theon’s Commentaries on the Handy Tables
1. Theon’s preface to his ‘Great Commentary’ on the Handy Tables, on the basis of the Mogenet and Tihon edition and translation of it.Footnote 103
[a] Of Theon of Alexandria, <memorandum on the Handy Tables of Ptolemy, first part>
[b] Since you have assigned us the task of going through in detail into the reasoned methodFootnote 104 of the treatise of the Handy Tables, my companions Eulalius and Origenes, I have tried to write down a memorandumFootnote 105 by proceeding as far as possible in the most exacting way, for we alsoFootnote 106 thought it would add not a small contribution to the 
Footnote 107; thus, I have undertaken the teaching of the proposed subject matter in five books, so that 
in mathematicsFootnote 108 might be able to follow, and closely following the treatise of the Syntaxis.Footnote 109 In this way, indeed, what is received in each of the hypothesesFootnote 110 will be more easily remembered by them.
[c1] We will <thus> teach, through quasi-causal teaching,Footnote 111 the expositionFootnote 112 of the Handy Tables and the reason of the <underlying> calculations, so that, each time we have any doubt about a writing mistake in the numbers that are disposed in the tables, we might easily correct them by the knowledge of the causes;
[c2] furthermore, we will also make comparisons, wherever the disposition of the tables presented <in the Handy Tables> or the explanations given in the same treatise differ from what is explained in the Composition, since he <i.e. Ptolemy> has arranged them according to their own respective treatment;
[c3] and 
, we have considered it was superfluous, on one hand, to complete it with geometrical procedures that we could already explain in a sufficiently clear manner by discourse alone, since we have already explained these procedures in a more geometrical manner once and for all in our remarksFootnote 113 on the Composition; but, on the other hand, wherever the subject matter was not suitable for such<verbal> explanations, we have presented them <i.e., the geometrical arguments> in such a way, that they might be more easily understood.
[d] As for you, my companions, if anything has escaped my attention on such important matters,Footnote 114
,Footnote 115 I beg your comprehension for no equivalent treatment, before us, has reached us.
2. Theon’s preface of his ‘Little Commentary’ on the Handy Tables, on the basis of the text edited and translated (in French) by Anne Tihon.Footnote 116
Of Theon of Alexandria, on the Handy Tables.
The more reasoned method <leading> the calculation of <the positions of> starsFootnote 117 through the Handy Tables, Epiphanios my boy, has been provided by us in the five books of another treatise.Footnote 118 But since, as far as the latter is concerned, most of those who come to us so as to learn such subject matterFootnote 119 do not only happen to be unable to follow competently the multiplications or divisions of numbers, but also to be completely uninitiated in geometrical demonstrations, we have tried for them also to make a commentary as far as possible more methodical, presenting the bare proceduresFootnote 120 so that the presentation of this subject matter might appear more clearly to them.
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Bernard, A. (2014). In What Sense Did Theon’s Commentary on the Almagest Have a Didactic Purpose?. In: Bernard, A., Proust, C. (eds) Scientific Sources and Teaching Contexts Throughout History: Problems and Perspectives. Boston Studies in the Philosophy and History of Science, vol 301. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-5122-4_5
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