PAPPUS OF ALEXANDRIA

PAPPUS OF ALEXANDRIA flourished about the end of either the 3d or the 4th century A.D. Which of these dates is the more probable it is difficult to determine, owing to conflicting evidence, but recent opinion inclines to the former. Suidas states that Pappus was a contemporary of Theon, thus placing him towards the end of the 4th century, and ascribes several treatises to him. These treatises have not survived, and the only work by which Pappus is now known, his Mathematical Collection, receives no mention from Suidas. This work consisted of eight books, the first and the earlier part of the second of which are lost, and its interest is mainly, though not exclusively, historical. From what remains of the second book, it is conjectured that the first two books were arithmetical. The third book explains some of the methods for the duplication of the cube, treats of the progressions and the five regular polyhedra. The fourth book discusses the figure called the arbelos ('a shoemaker's knife'), the spiral of Archimedes, the conchoid of Nicomedes, and the quadratrix of Dinostratus. The fifth book contains some theorems regarding isoperimetrical figures plane and solid, and a short account of the semi-regular solids of Archimedes. The sixth book comments on some of the works of Theodosius, Aristarchus of Samos, and Euclid. From the seventh book, which is the longest and most valuable of the Collection, is derived a large part of our knowledge of Greek geometry. Many of the writings here analysed are no longer extant, and it is on the indications (in the notable instance of Euclid's Porisms, the very obscure indications) which Pappus gives of the object or the contents of them that the geometers of the 17th and 18th centuries relied for their restorations of these writings. The eighth book is devoted mainly to mechanics. The mathematical interest of the Collection does not equal the historical, but several of the books contain important theorems, the discovery of which is probably due to Pappus himself. One of these has been long associated with the name of Guldinus (1577-1643). Some others have received a brilliant development from the mathematicians of modern times. The last six books of the Mathematical Collection were translated into Latin by Commandinus, an Italian geometer, and were published in 1588; another edition appeared in 1660. Fragments of the Greek text have been printed at various times in England, France, and Germany, but the only complete edition is that of Fridericus Hultsch, Pappi Alexandrini Collectionis quæ supersunt (3 vols. Berlin, 1876-78).