Book Review: Euclid's Book on Divisions of Figures (περὶ διαιρέσεωυ βιβλίου)

David Eugene Smith
1916 Bulletin of the American Mathematical Society  
Euclid's Book on Divisions of Figures {irepl hiaipéaecov /3c/3\(ov) 9 with a restoration based on Woepcke's text and on the Practica Geometrioe of Leonardo Pisano. By RAYMOND CLARE ARCHIBALD. Cambridge, Eng., University Press, 1915. ix+88pp. OF the nine works attributed to Euclid the "Elements" is, of course, by far the most important and the most widely known. The "Data" is known to us through the TOTTOÇ avaXvófievos of Pappus, as stated in the Commandino edition of 1660, page 241; the
more » ... " was restored by Chasles, and earlier by Robert Simson; the "Optics" was known to earlier scholars through Theon, and has recently appeared in a modern edition through the labors of Heiberg; the "Phenomena" is nearly complete and was edited by Menge; the "Conies" is lost, except as part of it may have been embodied in the works of Apollonius; and the "Pseudaria" and "Surface Loci" are known only through fragments. The ninth work, entitled "On Divisions" (of figures), was for a long time known only through references by Proclus, but in 1570 it appeared in print under the editorship of John Dee and Federico (sometimes printed Federigo) Commandino in Latin translation from the Arabic. In 1851 Woepcke found an Arabic manuscript of the work at Paris, and this was published in translation in the Journal Asiatique. It seems that John Dee, when he visited Commandino at Urbino in 1563, gave to the latter a Latin manuscript of the work as translated into Arabic by one Muhammed Bagdedinus, and this together with an Italian version was published seven years later. An English translation appeared in London in 1660 and again in 1661. David Gregory included the Latin text in his edition of Euclid in 1703 with the statement: "Joannes Dee Londinensis, cum Librum de Divisionibus superficierum, Machometo Bagdedino (qui floruisse creditur seculo Christi decimo) vulgo adscriptum, ex Arabico (uti credo, licet hoc expresse non dicat) in Latinum verteret." As to the conjectured date of "Machometo Bagdedino" it may be said in
doi:10.1090/s0002-9904-1916-02836-9 fatcat:awnlvexq45gk7fmkgjzzquzcum