John of Palermo

(fl. Palermo, Sicily, 1221- 1240)

translation of scientific works.

John of Palermo, translator from Arabic to Latin, worked at the court of Emperor Frederick II. Little is known of his life. He was designated as Frederick’s “philosopher” by the well- known mathematician Leonardo Fibonacci in the introduction to the latter’s Flos. John is also mentioned in the introduction to Fibonacci’s Liber quadratorum (dated 1225). He appears to be identical with the Johannes de Panormo mentioned in diplomatic documents of Frederick II ranging in date from 1221 to 1240.

The only known work by John of Palermo is a Latin translation of an Arabic tract on the hyperbola entitled, in Latin, De duabus lineis semper approximantibus sibi invicem et nunquam concurrentibus. The original Arabic may be related to a work by Ibn al-Haytham of similar title. The tract consists of five propositions. Its overall objective is to show that the hyperbola and one of its asymptotes have the desired relationship between a straight line and a curve that always, on extension, come closer together but never meet. That is, its purpose is to demonstrate the asymptotic property of the hyperbola. The author makes free use of Apollonius’ Conics but does not use Apollonius’special parameter, the latus rectum; rather, he employs the fundamental axial property to which Archimedes was accustomed to refer. The De duabus lineis was one of the few works available in Latin in the Middle Ages that treated conic sections in a nonoptical context. A somewhat later Latin treatise entitled De sectione conica orthogona, quae parabola dicitur shares three propositions with the De duabus lineis. A version of the De sectione conica was published in 1548 and both tracts appear to have influenced a variety of authors, including Johann Werner, De elementis conicis (Nuremberg, 1522); Oronce Fine, De speculo ustorio (Paris, 1551); Jacques Peletier, Commentarii tres (Basel, 1563); and Francesco Barozzi, Geometricum problema tredecim modis demonstratum (Venice, 1586).

BIBLIOGRAPHY

The text and an English translation of the De duabus lineis, and a collection of references to John of Palermo, are in M. Clagett, “A Medieval Latin Translation of a Short Arabic Tract on the Hyperbola,” in Osiris,11 (1954), 359-385. Since the appearance of this text, which was based on the earliest and best MS, Oxford, Bodl., D’ Orville 70, 61v, three further MSS have been discovered: Paris, B. N. lat. 7434, 79v-8lr (colophon missing); and Vienna, Nationalbibliothek 5176, 143v-146r (colophon missing), and 5277, 276v-277r (proem, proofs of propositions I-IV, and colophon missing), The text will be republished and related to the sixteenth-century authors in volume IV of M. Clagett, Archimedes in the Middle Ages.

The De section conica orthogona, quae parabola dicitur was published in an altered version by Antonius Gongava Gaviensis in an ed. of Ptolemy’s Quadripatitum (Louvain, 1548). For a comparison of this printed text with a sixteenth-century MS, Verona, Bibl. Capitolare, cod. 206, lr-8v, see J. L. Heiberg and E. Wiedemann, “Eine arabische bische Schrift ü ber die Parabel und parabolische Hohlspiegel” in Bibliotheca mathematic, 3rd ser., 11 (19101911), 193208. There is a further copy of this work in Regiomontanus’ hand: Vienna, Nationalbibliothek 5258, 27r-38v. Other copies are in Oxford, Bodl., Canon. Misc 480, 47r-54r, 15c; and Florence, Bibl. Laur. Medic. Ashb. 957, 95r-110v, 15-16c. In both of these the tract is attributed to Roger Bacon.

On the work of Ibn alphen; Haytham that may be related to De duabus lineis, see F. Woepcke, L’ algè bre d’Omar al-Khîyyami (Pairs, 1851), pp. 73ff.; and L. Leclerc. Histoire de la mé dencine arabe, I (Pairs, 1876), 515. Wospcke transates the title given by Ibn al-Haytham (through Ibn abi Usaibia) as “18. Mé moire sur la ré futation de la dé monstration que l’ hyperbole et ses deux asymptotes s’ approchent indé finiment l’ une des autres, sans dependant jamais se rencontrer”.

M. Clagett