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Plato of Tivoli

PLATO OF TIVOLI

(fl. Barcelona, first half of twelfth century)

mathematics, astronomy, astrology, medicine [?].

Presumably an Italian, Plato is known only through his work, at least part of which was produced at Barcelona between 1132 and 1146. He was one of the first scientist-scholars active in the Iberian Peninsula to provide the Latin West with some of the works of Greek authors as transmitted of elaborated in Arabic and Hebrew and with works originally written in those languages; he was the first to edit Ptolemy in Latin and to help in the translation of the most important Hebrew treatise on geometry. His name appears only as a translator from the Arabic and Hebrew—or, better, as an editor of translations made in collaboration with the Jewish mathematician and polymath Abraham bar Ḥiyya ha-Nasi (Savasorda). It is impossible to determine to what extent the translations ascribed to Plato alone or to both men reflect Plato’s linguistic and scientific knowledge finds the Latin rendering exact and clear. In the introductions to two translations Plato says that he was prompted by selective interests: he preferred al-Battānī to Ptolemy because al-Battānī was less verbose, and Ibn al-Ṣaffär to many other authors on the astrolabe because he was more reliable and scientific He was a friend of at least one other translator of Arabic scientific literature, John, son of David, to whom he dedicated his translation of the work on the astrolabe. In the middle of the thirteenth century Plato was mentioned as an eminent Christian mathematician by the author of the Summa Philosophie wrongly ascribed to Robert Grosseteste. His influence as a translator and editor is shown by the use of his versions by Leonardo Fibonacci and Albertus Magnus, by the relatively large number of manuscripts of his texts still surviving, and by the number of printed editions of some of them produced in the late fifteenth and sixteenth centuries.

The four truly scientific works—two mathematical and two astronomical—that in manuscripts or printed editions carry the name of Plato of Tivoli, with of without the name of Abraham bar Ḥiyya, as a translator are the following:

1. The Liber Embadorum (“Book of Areas,” or “Practical Geometry”) of Savasorda, identified by Steinschneider as the Ḥibbur ha-meshiḥah we-ha-tish-boretof Abraham bar Ḥiyya, translated from the Hebrew in 1145 [the manuscripts give the right astronomical equivalent of this date but the wrong Hegira year, 510/1116 instead of 540/1145] and preserved in at least five manuscripts.

2. The Sphericaby Theodosius of Bithynia, translated from the Greco-Arabic version of Ḥunayn ibn Ishäāq or of Qusṭā ibn Lūqā and extant in eleven manuscripts and four early editions.

3. Al-Battāni’s al-Zij (“Astronomical Treatise”), or De motu stellarum, in ten manuscripts and two editions.

4. The De usu astrolabii of Abu’l-Qāsim Maslama (Ibn al-Sạffār), in three manuscripts-quite convincing linguistic reasons have been given by M. Clagett to confirm a suggestion (based on the place of this text in the three existing manuscripts) that Plato is the author of the Latin translation from the Arabic of Archimedes’In quadratum [for Quadratura?] circuli, or De mensura circuli.

The translations from the Arabic of seven other works (five astrological, one geomantical, and one medical [now lost]) are ascribed to Plato, with or without Abraham bar Ḥiyya, in the manuscripts.

1. Ptolemy’s Quadripartitum, translated in 1138 and preserved in nine manuscripts and five editions.

2. The Iudicia Almansoris, which is the Centum(or Centumquinquaginta) propositiones or Captula (Stellarum) by, or dedicated to, one al-Manṣaur (or by ar-Razi [?]), translated in 1136 and preserved in over forty manuscripts and a dozen printed editions.

3. TheDe electionibus horarum of Ali ibn Aḥmad al-Imrani, translated in 1133 or 1134 and extant in eighteen manuscripts.

4. The De nativitatibus or De iudiciis nativitatum of Abu Ali al-Khayaṭ, translated in 1136 and preserved in nine manuscripts.

5. The De revolutionibus nativitatum by Abū Bakr al-Ḥasan (Albubather), preserved in one manuscripts.

6. The Questiones geomantce or Liber Arenalis scientie by “Alfakini, son of Abizarch” or “son of Abraham,” probably translated in 1135 and preserved in two printed editions and one manuscript (copied from the earlier edition [?]).

7. A De pulsibus et urinis by “Aeneas” (Ḥunayn ibn Isḥāq [?]), now lost.

A translation of an anonymous Commentary an the Tabula Smaragdica, extant in one manuscript, has been tentatively attributed to Plato by its recent editors.

The translation of Abraham bar Ḥiyya’s Geometry (Liber embadorum) contributed much to both the structure and the contents of Leonardo Fibonacci’s Practica geometriae.In particular it was the first work to introduce into the Latin study of mathematics the solutions of quadratic equations and, with Theodosius’ it furthered the development of trigonometry. As late as 1819, Plato of Tivoli’s translation of al-Battāni’s al-Zij was the basis for Delambre’s detailed study of that work.

BIBLIOGRAPHY

I. Original Works. Printed eds. of the works cited in text are Abraham bar Ḥiyya, Liber embadorum, M. Curtze, ed., in Urkunden zur Geschichte der Mathematik im Mittelalter und der Renaissance, I which is vol. XII of Abhandlugen zur Geschichute der Mathematischen Wissenscheafen (Leipzig, 1902), 10–182, with German trans. On fcing pages; Theodosius of Bithynis, Spherica(Venice, 1518; Vienna, 1529; Messina, 1558); al-Battani, De motu stellarum (Nuremberg, 1537; Bologna, 1645), both eds. with additooins and notes by Regiomontanus; Archimedes, In quadrum circuli, Marshall Clagett, ed., in “The De Mensurs circuli,” in Osiris, 10 (1952), 599–605, and in Clagett’s Archimeds in the Middle Ages,I(Madison, Wis., 1964), 20–26, with English trans. on opposite pages_see also 691–708 for for a selective index of geometrical terms that includes those used in this trans; Ptolemy, Quadripartitum (Venice, 1484, 1493; Basel, 1551); Iudicia Almansoris (Venice, 1484, 1492; Basel, 1533; Ulm, 1641, 1647); al-Imarani, De electionibusm horarum, partyly edited by J. M. Millas-Vallicrosa in Las traducciones rientales . . . (see below),328–339;Questiones geomantice(Verona, 1687, 1705); and Commentary on the Tabuta Smaragdica, R. Steeie and D. W. Singer, eds., in Proceedings of the Royal Society of Medicine, Hist. sec., 21 (1928), 41–57.

No printed eds. are known to exists of De usu astrolabii, De iudiciis nativitatum, De revolutionibus nativiatatum, and De pulsibus et urinis.

No complete list of MSS containing the translations ascribed to Plato of Tivoli has been published, but many are mentioned in L. Thorndike and P. Kibre, A Catalog of Incipits of Medicaeval Scientific Works in Latin, rev. ed. (Cambridge, Mass., 1963), see index, col. 1889. See also the works of Boncompagni, Carmody, Haskins, Millás-Vallicrosa, Sarton, and Steinschneider cited below.

II. Secondary Literature. The four essential works dealing with Plato of Tivoli are F. J. Carmody, Arabic Astronomical and Astrological Sciences in Latin Translation: A Critical Bibliography (Berkeley-Los Angels, 1956), see inde,192; C. H. Haskins, Studies in History of Mediaeval Science (Cambridge, Mass., 1927), 9–11; G. Sarton, Introdution to the History of Science, II, pt. i (Balt8imore, 1931), 177–179; and M. Steinschneider, Die Europaischen Ubersertzungen aus dem Arabischen bis Mitte des 17ten Jahrhunderts(1904–1905; Graz, 1956), 62–66.

Further information is in the introdutions to the modern eds. of Plato’s works and in B. Boncompagni, “Delle versioni fatte da platone Triburtino,” in Atti dell’ Accademia pontificia dei Nuovi Lincei, 4 (1851), 249–286; J.A. von Braunmuhl, Vorlesungen über die Geschichte der Trigonometrie I (Leipzig, 1900), 48–50; C. H. Haskins, “The translations of Hugo Sanctallensis” in Romanic Review2 (1911), 2, a note on the date of the Liber embadorum; J. M. Millas-Vallicrosa, Assaig d’historia de les idees fisiques i mathematiques a la Catalunya medieval I (Barcelona, 1931), 29 ff., on the De usu astrolabii; Las traducciones orientales enm los manuscritos de la Bibliotheca cateral de Toledo (Madrid, 1942); and Estudios sobre historic de la cinecia espanoloa (Barcelona, 1949), 219 ff., “La obra enciclopedica de Abraham bar Ḥiyya” C. A. Nallino’ ed. of al-Battani, Opus astronomic um (De motustellarum) Arabic text and new Latin trans., I (Milan, 1903), 1-lvi; M. Steinschneider, “Abraham Judaeus: Savasorda und Ibn Esra . . .,” in Zeitschrift für Mathematic12 (1867), 1–44, important for the relationship between Plato and Abraham, for the authorship of the Indicia Almansoris and for al-Imrani’ De electionibus horarum; L. Thorndike, A History of Magic and Experimental Science, II (London, 1923), esp. 82–83; and P. Ver Eecke’ introduction to his French trans.of Theodosius of Bithynia’ Spherica (Bruges, 1926; repr. Paris, 1959), xxxv–xli, on trhe Latin printed eds., on the use made of them, and on Regiomontanus.

Lorenzo Minio-Paluello

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