Gersonideana Bilbiographia > Part Two: Works by Gersonides

VII. Science

Astronomy and Astrology | Mathematics | Logic

A. Astronomy and Astrology
NOTE: Wars of the Lord, TreatiseV, part I constitutes Gersonides’ Astronomy and is sometimes referred to as such in the literature on Gersonides.
1. Barker, Peter and Bernard R. Goldstein, “The Role of Comets in the Copernican Revolution,” Studies in the History an Philosophy of Science 19 (1988): 299-319.
Gersonides’ cometary theory and observations are put in the context of other such medieval reports.
2. Beaujouan, Guy. “Les orientations de la science latine au d?but du XIVe si?cle,” Gad Freudenthal (ed.), Studies on Gersonides—A Fourteenth-Century Jewish philosopher-Scientist (Leiden: Brill, 1992): 71-80.
3. Curtze, Maximilian. “Die Abhandlung des Levi ben Gerson ueber Trigonometrie und den Jacobstab,” Bibliotheca Mathematica (n.s.) 12 (1898): 97-112.
Contains a German translation (from the Latin) of portions of Gersonides’ De sinibus, chordis, et arcubus, one of the first European writings on trigonometry (this text is part of Wars of the Lord V. I) and material on Gersonides’ Jacob staff.
4. Duhem, Pierre. Le syst?me du monde (Paris: Hermann, 1954), Vol. 4, pp. 38-41 and Vol. 5, pp. 201-29.
A brief account of Gersonides’ astonomy, astrology, and philosophy.
5. Freudenthal, Gad. “Levi ben Gershom as a Scientist: Physics, Astrology, and Eschatology,” Proceedings of the Tenth World Congress of Jewish Studies, Division C, Vol. 1: Jewish Thought and Literature (Jerusalem: World Congress of Jewish Studies, 1990): 65-72.
Shows that Gersonides’ astrology “was founded on the best contemporary science;” Gersonides’ “vision of mankind as influenced by the his eschatological views.”
6. Goldstein, Bernard R. “Preliminary Remarks on Levi ben Gersoni’s Contributions to Astronomy,” Proceedings of the Israel Academy of Sciences and Humanities 3 (1969): 239-54. Also published in Hebrew: “Al Terumato shel R. Levi ben Gershom le-Astronomiyah,” Divrei ha-Aqademiyah Ha-Le‘umit ha-Yisraelit le-Mada‘im 4 (1970): 174-85.
A brief account of Gersonides’ astonomy, emphasizing his discussions of astronomical instruments and theories.
7. Goldstein, Bernard R. “Some Medieval Reports of Venus and Mercury Transits,” Centaurus 14 (1969): 49-59. Reprinted in Goldstein, Theory and Observation in Ancient and medieval Astronomy (London: Variorum Reprints, 1985).
P. 54: a translation of a passage from Wars V.i, chapt. 133, discussing a Venus transit reported by Averroes.
8. Goldstein, Bernard R. Al-Bitruji: On the Principles of Astronomy, Vol. 1 (New Haven: Yale University Press, 1971).
Pp. 40-43 contain a discussion of criticisms of al-Bitruji’s astronomical models which appear in Wars V.i, chapts.
40-41.
9. Goldstein, Bernard R. “Theory and observation in Medieval Astronomy,” Isis 63 (1972): 39-47. Reprinted in Goldstein,
Theory and Observation in Ancient and Medieval Astronomy (London: Variorum Reprints, 1985).
Goldstein presents Gersonides’ unusual view (by medieval standards) that astronomical theories should be tested by observation and that where agreement between observation and theory is poor, the theory should be discarded.
10. Goldstein, Bernard R. “Levi ben Gerson’s Preliminary Lunar Model,” Centaurus 18 (1974): 275-88. Reprinted in Goldstein, Theory and Observation in Ancient and Medieval Astronomy (London: Variorum Reprints, 1985).
An account of Gersonides’ preliminary lunar model, which he later replaced.
11. Goldstein, Bernard R. The Astronomical Tables of Levi ben Gerson (= Transactions of the Connecticut Academy of Arts and Sciences, Vol. 45) (Hamden, Conn.: Archon Books, 1974).
An edition, with commentary, of all trigonometrical and astronomical tables, in Wars V.i, published for the first time.
12. Goldstein, Bernard R. “Levi ben Gerson’s Analysis of Precession,” Journal for the History of Astronomy 6 (1975): 31-41. Reprinted in Goldstein, Theory and Observation in Ancient and Medieval Philsophy (London:
Variorum Reprints, 1985).
Translation, with commentary, of Wars V. i, chapt. 61, concerning Gersonides’ derivation of precession by comparing his own observations with those in Ptolemy’s Almagest.
13. Goldstein, Bernard R. “Astronomical and Astrological Themes in the Philosophical Works of Levi ben Gerson,” Archives internationales d’histoire des sciences 26 (1976):221-24. Reprinted in Goldstein, Theory and Observation in Ancient and Medieval Astronomy (London: Vasriorum Reprints, 1985).
A brief account of Gersonides’ views on astronomy, astrology, and miracles in the Bible.
14. Goldstein, Bernard R. “Levi ben Gerson: On Instrumental Errors and the Transversal Scale,” Journal for the History of Astronomy 8 (1977): 102-112.
An account of Wars V. i, chapt. 12 in which Gersonides applies the transversal scale to the astrolabe, and discusses the errors in taking stellar altitudes with this instrument.
15. Goldstein, Bernard R. “Medieval Observations of Solar and Lunar Eclipses,” Archives internationales d’histoire des sciences 29 (1979): 101-56. Reprinted in Goldstein, Theory and Observation in Ancient and Medieval Astronomy (London: Variorum Reprints, 1985).
A translation, with commentary, of Wars V.1, chapts. 80 and 100, in which are described Gersonides’ observations and analyses of four solar and six lunar eclipses.
16. Goldstein, Bernard R. “The Status of Models in Ancient and Medieval Astronomy,” Centaurus 24 (1980):132-47.
Gersonides’ attitude towards astronomical models is placed in the context of the views expressed by ancient and medieval astronomers.
17. Goldstein, Bernard R. “Star Lists in Hebrew,” Centaurus 28 (1985): 185-208.
The relationship of Gersonides’ short list of stars to other such lists in Hebrew and Arabic.
18. Goldstein, Bernard R. “Levi ben Gerson’s Theory of Planetary Distances,” Centaurus 29 (1986): 272-313.
Translation, with commentary, of Wars V.i, chapts. 130 and 131, concerning a new theory of planetary distances. The notion of a “fluid” layer between the planetary spherical shells allows for much greater distances than those in tolemy’s Planetary Hypotheses.
19. Goldstein, Bernard R. “Preliminary Remarks on Levi ben Gerson’t Cosmology,” David Novak and Norbert Samuelson (eds.), Creation and the End of Days: Judaism and Scientific Cosmology (Lanham, MD.: University Press of America, 1986): 261-76.
A translation, with commentary, of Wars V.i, chapt. 29, concerning the order of the planetary spheres.
20. Goldstein, Bernard R. “A New Set of Fourteenth-Century Planetary Observations,” Proceedings of the American Philsophical Society 132 (1988): 371-99.
A translation, with commentary, of Wars V.i, chapts. 46, 109, 113, 117, and 122, which texts include forty five planetary observations, a very extensive list by medieval standards.
21. Goldstein, Bernard R. “Galileo’s Account of Astonomical Miracles in the Bible: A Confusion of Sources,” Nuncius 5 (1990): 3-16.
An account of Gersonides’ discussion of astronomical miracles in the Bible in the context of other ancient and medieval discussions of them.
22. Godstein, Bernard R. and David Pingree, Levi ben Gerson’s Prognostication for the Conjunction of 1345 in Translations of the American philosophical Society Vol. 80, part 6 (1990). 60 pp.
Editions of the Hebrew and Latin versions, with translations, of Gersonides’ only known astrological treatise. A commentary includes discussions of the astronomical computations in this text, and of its relationship to astrological history, particularly the theory reported by Abraham ibn Ezra. It is also argued that Iohannes de Muris (fl. Ca. 1320-1350) alluded to this treatise in his own discussion of the astrological meaning of this planetary conjucntion. The date of Gersonides’ death (April 20, 1344) is reported in the colophon to the Latin version of this text (and nowhere else).
23. Goldstein, Bernard R. “Levi ben Gerson: On Astronomy and Physical Experiments,” in S. Unguru (ed.), Cosmology and Astronomy, 1300-1700: Tension and Accomodation (= Boston Studies in the Philosophy of Science, vol. 126) (Dordrecht: Kluwer, 1991): 75-82.
Consideration of Gersonides’ experiment for locating the center of vision in the eye and his experiment for explaining the size and shape of the image seen with the camera obscura’ similarities to Kepler’s discussion of the same topics are noted.
24. Goldstein, Bernard R. “Levi ben Gerson’s Astrology in Historical Perspective,” G Dahan (ed.), Gersonide en son temps (Louvain:Peeters, 1991): 287-300.
25. Goldstein, Bernard R. “Levi ben Gerson’s Contributions to Astronomy,” Gad Freudenthal (ed.), Studies on Gersonides—A Fourteenth –Century Jewish Philosopher-Scientist (Leiden: Brill, 1992): 3-19.
26. Guenther, Siegmund. “Die erste Anwendung des Jakobsstabes zur geographischen Ortsbestimmung,” Bibliotheca Mathematica (n.s.) 4 (1890): 73-80.
27. Hugonnard-Roche, Henri. “Probl?mes m?thodologiques dans l’astrpmp,oe ai d?but du XIVe si?cle,” Gad Freudenthal (ed.), Studies on Gersonides—A Fourteenth-Century Jewish Philosopher-Scientist (Leiden: Brill, 1992): 55-70.
28. Langermann, Y. Tzvi. “An Unknown Astronomical Treatise by Levi ben Gershom,” Kiryat Sefer 59 (1984), p. 636 (Hebrew).
This treatise, Hug ha-Shamayim, describes an astronomical instrument, the armillary sphere, distinct from the Jacob Staff’ also includes a short star list for 1325 (on which see Bernard R. Goldstein, “Star Lists in Hebrew,” Centaurus 28 (1095): 185-208, pp. 199-202).
29. Mancha, Jos? Luis. “Egidius of Baisiu’s Theory of Pinhole Images,” Archive for History of Exact Sciences 40 (2989): 1-36.
On pp. 29-31 Mancha compares Gersonides’ study of pinhole images in Wars V.i with that of his contemporary Egidius in a text published here for the first time. Mancha also notes that the two latin versions of Wars V.i differ only slightly and were composed by the same translator, Pertrus of Alexandria, and not by two independent translators as has sometimes been supposed.
30. Mancha, Jos? Luis. “The Latin Translation of Levi ben Gerson’s Astronomy,” Gad Freudenthal (ed.), Studies on Gersonids: A Fourteenth-Century Jewish Philosopher-Scientist (Leiden: Brill, 1992):21-46.
31. Marx, Alexander. “The Scientific Work of Some Outstading Medieval Jewish Scholars,” Israel Davidson (ed.), Essays and Studies in Memory of Linda R. Miller (New York: Jewish Theological Seminary, 1938): 117-170.
Overview of Gersonides’ mathematics and astronomy on pp. 153-60.
32. Poulle, Emmanuel. “L’astronomie latine au XIVe si?cle,” G. Dahan (ed.), Gersonide en son temps (Louvain: Peeters, 1991): 253-64.
33. Roche, J.J. “The Radius Astronomicus in England,” Annals of Science 38 (1981): 1-32.
Pp. 3-9 on Gersonides’ astronomical invention, the Jacob Staff.
34. Romano, David. “L’apport arabe dans l’oeuvre scientifique de Gersonide,” G. Dahan (ed.), Gersonideen son temps (Louvain:Peeters, 1991): 265-85.
35. Sarton, George. Introduction to the History of Science, Vol. III, pt. 1 (Washington: Carnegie Institute, 1947).
Pp. 594-607, give an overview, now largely outdated, of Gersonides’ scientific work.
36. Sezgin, Fuat. Geschichte des arabischen Schrifttums, Band 6: Astronomie (Leiden: Brill, 1978).
Sezgin, pp. 53ff., places Gersonides among medieval critics of Ptolemy, and relates his work to treatises written in Arabic.
37. Steinschneider, Moritz. “Levi ben Gerson und der Baculus Jacobi,” Bibliotheca Mathematica 4 (1890), p, 107. Reprinted in Steinschneider’s Gesammelte Schriften, Vol. I (Berlin, 1925), p. 270.
38. Thorndike, Lynn. A History of Magic and Experimental Science, Vol. III (New York: Columbia University Press, 1934).
A discussion, on pp. 303-11, of Gersonides’ astrological treatise based on the Latin manuscripts.


B. Mathematics
1. Carlebach, Joseph. Lewi ben Gerson als Mathematiker (Berlin: J. Lamm, 1910). Reprint: Miriam Gillis Carlebach (ed.), Joseph Carlebach: Ausgewaehlte Schriften, Vol. Two (Hildesheim: Georg Olms, 1982): 713-952.
Contains: biographical study of Gersonides, the Latin (and only surviving)text of Gersonides’ De numeris harmonicis, and German translation of selections from Gersonides’ Ma‘aseh Hoshev.
2. Chemla, Karine and Serge Pahaut, “Remarques sur les ouvrages math?matiques de Gersonide,” Gad Freudenthal (ed.), Studies on Gersonides—A Fourteenth-Century Jewish Philosopher-Scientist (Leiden: Brill, 1922): 149-191.
3. Curtze, Maximilian. “Die Abhandlung des Levi ben Gerson ueber Trigonometrie und den Jacobstab,” Bibliotheca Mathematica (n.s.) 12 (1898): 97-112.
Contains a German translation (from the Latin) of Gersonides’ De sinibus, chordis, et arcubus, one of the first European writings on trigonometry. This text is part of Wars of the Lord V.i.
4. Curtze, Maximilian. “Urkunden zur Geschichte der Trigonometrie im christlichen Mittelalter,” Bibiliotheca Mathematica (3rd series) 1 (1900): 321-416.
Further portions of De sinibus…translated into German.
5. Curtze, Maximilien. “Die Dunkelkammer,” Himmel und Erde 13 (1901): 225-36.
Contains a German translation of portions of De sinibus…
6. Espenshade, Pamela. “A Text on Trigonometry by Levi ben Gerson,” The Mathematics Teacher 60 (1967): 628-37.
Portions of De sinibus… translated into English.
7. Lange, Gerson. Sefer Maassei Chosceb. Die Praxis des Rechners. Ein hebraeisch-arithmetisches Werk des Levi ben Gerschom aus dem Jahre 1321 (Frankfurt am Main: Louis Golde, 1909).
Edition of Ma‘aseh Hoshev with German traslation, preceded by a 14 page introduction.
8.L?vy, Tony. “Gersonide, commentateur d’Euclide: Traduction annot?e de ses gloses sur les El?ments,” Gad Freudenthal (ed.), Studies on Gersonides—A Fourteenth-Century Jewish Philosopher-Scientist (Leiden:
Brill, 1992): 83-147.
9. Lindberg, David C. “The Theory of Pinhole Images in the Fourteenth Century,” Archive for History of the Exact Sciences 6 (1970): 299-328.
10. Mancha, Jos? Luis. “Egidius of Baisiu’s Theory of Pinhole Images,” Archive for History of the Exact Sciences 40 (1989): 1-36.
Gersonides’ contributions to optical theory are compared with other medieval writings on the subject, pp. 29-31.
11. Marx, Alexander. “The Scientific Work of Some Outstanding Medieval Jewish Scholars,” Israel Davidson (ed.), Essays and Studies in Memory of Linda R. Miller (New York: Jewish Theological Seminary, 1938): 117-170.
Overview of Gersonides’ mathematics and astronomy on pp. 153-60.
12. Polski, Joseph. “Fragment of the Commentaries [in Hebrew] on Euclid Concerning Parallel Lines,” Istoriko-matematitcheskie Issledovaniya [= Historico-Mathematical Researches] 11 (1958): 763-82 (Russian).
Russian translation of Gersonides on Euclid’s fifth (parallel) postulate’ cf. Rosenfeld, 1958 and 1976 and Pont, 1986 (all in this section).
13. Pont, Jean-Claude. L’Aventure des parall?les. Histoire de la g?om?trie non euclidienne: Pr?curseurs et attard?s (Bern/Frankfurt/New York: Peter Lang, 1986).
Pp. 188-91 give a brief account of Gersonides’ attempts to prove Euclid’s fifth (parallel) postulate, following Rosenfeld, 1958. Cf. also Rosenfeld, 1976.
14. Rabinovitch, Nachum L. “Rabbi Levi ben Gershon and the Origins of Mathematical Induction,” Archive for History of Exact Sciences 6 (1970): 237-48.
Survey of Gersonides’ contributions to mathematics and argument that Gersonides is the earliest known mathematician to have used the technique of mathematical induction in a systematic and self-conscious fashion.
15. Rabinovitch, Nachum L. Probability and Statistical Inference in Ancient and Medieval Jewish Literature (Toronto: University of Toronto Press, 1973): index, s.v., “Levi ben Gershon.”
16. Rabinovitch, Nachum L. “Early Antecedents of Error Theory,” Archive for History of Exact Sciences 13 (1974):
348-58.
Gersonides’ anticipation of Galileo’s error theory; contains discussions of Gersonides’ commentaries to Proverbs 19:28, 16:13-14, and 27:23.
17. Rosenfeld, B.A. “The Proofs of Euclid’s Fifth Postulate by the Mathematicians Ibn al-Haitham and Gersonides,” Istorikomatematitcheskie Issledovaniya [= Historico-Mathematical Researches] 11(1958: 733-90 (Russian).
18. Rosenfeld, B.A. Istoria Neevklidovoi Geometrii (Moscow:Nauka, 1976) (Publication of the Russian Academy of Sciences, Institute for the History of Nature and Technology) (Russian). English translation: A History of Non-Eculidean Geometry. Evoloution of the Concept of a Geometric Space, translated by A. Shenitzer, with the assistance of A. Grant (New York: Springer Verlag, 1988).
Pp. 86-91 of the Russian and pp. 109-12 of the English present a brief account of Gersonides’ attempt to prove Euclid’s fifth (parallel) postulate, noting similarities to analogous attempts by Arab mathematicians.
19. Sarfatti, Gad B. Mathematical Terminology in Hebrew Scientific Literature in the Middle Ages (Jerusalem: Magnes, 1968) (Hebrew).
Pp. 220-30 on Gersonides’ mathematical usages; includes a detailed decription of Ma‘aseh Hoshev. Gersonides’ mathematical terminology is shown not to be original, testifying to the existence of a received terminology; this received terminology is shown to be permeated with Arabisms.
20. Sarton, George. Introduction to the History of Science, Vol. III, pt. 1 (Washington: Carnegie Institute, 1947).
Pp. 594-607, give an overview, now largely outdated, of Gersonides’ scientific work.
21. Sezgin, Fuat. Geschichte des arabischen Schrifttums, Band 5: Mathematik (Leiden: Brill, 1974).
On pp. 56-60 Gersonides’ contributions to trigonometry and to the study of Euclid’s parallel postulate are noted.
22. Steinschneider, Moritz. Mathematik bei den Juden, (Berlin/Leipzig, 1893-99; Frankfurt, 1901; Hildesheim: George Olms, 1964).
Pp. 129-33 on Gersonides’ mathematical works.
23. Werner, Eric and Isaiah Sonne. “The Philosophy and Theory of Music in Judeo-Arabic Literature” (Second Installment), Appendix II:” Concerning the Treatise De numeris harmonicis by Gersonides,” HUCA 17 (1942-43): 564-72.
A study of De numeris harmonicis in the context of musical theory.
24. Werner, Eric. “The Mathematical Foundation of Philippe de Vitri’s Ars nova,” Journal of the American Musicological Society 9 (1956): 128-32.
The importance of Gerosnides’ De numeris harmonicis for the history of music theory.


C. Logic
1. Bertola, Ermenegildo. “Levi ben Gerson e la logica Arabo-Giudaica,” Pier Lombardo 5 (1961): 55-68. Reprinted in Bertola, Il Pensiero Ebraico: Studi e Ricerche (Padova: Cedam, 1972).
Pp. 337-59 on Gersonides.
2. Manekin, Charles. “Preliminary Observations on Gersonides’ Logical Writings,” PAAJR 52 (1985): 85-113.
Comprehensive description of Gersonides’ logical writings.
3. Manekin, Bezalel (Charles). “The Book Sha‘arei Zedeq and its Attribution to Gersonides,” Alei Sefer 14 (1987): 55-58 (Hebrew).
The Author demonstrates that it is very unlikely that Gersonides is the author of Sha‘arei Zedeq, a commentary on the thirteen hermeneutical principles of halakhic exegesis.
4. Manekin, Charles. “Problems of ‘Plenitude’ in Maimonides and Gersonides,” Ruth Link-Salinger et al. (eds.), A Straight Path—Studies in Medieval Philosophy and Culture: Essays in Honor of Arthur Hyman (Washington: Catholic University of America Press, 1988): 183-94.
Maimonides and Gersonides both accept the principle of plenitude (“no genuine possibility can remain forever unrealized”), but they restrict its application and in two cases anticipate problems of logic raised by modern interpreters of Aristotle.
5. Manekin, Charles. “Logic and Science in Gersonides,” Knowledge and the Sciences in Medieval Philosophy. Proceedings of the Eighth International Congress of Medieval Philosophy (S.I.E.P.M), Helsinki 24-29 August 1987 (Helsinki, 1990), Vol. II: 565-73.
6. Manekin, Charles. The Logic of Gersonides: A Translation of the Sefer ha-Heqqesh ha-Yashar (Book of the Correct Syllogism) (Dordrecht: Kluwer, 1992) (New Synthese Historical Library no. 40).
7. Rosenberg, Shalom. “Logic and Ontology in Jewish Philosophy in the Fourteenth Century,” Ph. D. Dissertation (Hebrew University, 1973) (Hebrew).
Pp. 25-28, 78-81, and 214-35 contain references to Gersonides’ contributions to logic.
8. Sinyor, Alan David. “Gersonides on the Categories,” Ph.D. Diss. (Cambridge University, 1989).
A study of Gersnoides’ supercommentary on Averroes’ Middle Commentary on Aristotle’s Categories. This dissertation seeks to evaluate the supercommentary insofar as it relates to Gersnoides’ mature philosophical views as expressed in Wars of the Lord. For Gersonides, the Categories is not a part of logic, but a pre-scientific study of the extra-mental world which is prior to logic proper; doctrines discussed include the relation of substance to accident, the locus of differentia in the categorical scheme; the definition of place and its relation to space; and the nature of number. The dissertation includes a working translation of the supercommentary.