- 国際文化学研究 : 神戸大学国際文化学部紀要 (ISSN:13405217)
- vol.25, pp.65-106, 2006-01
Arabic Mathematics has been characterized as algebra. Compared with this, Arabic geometry had not influence on the later mathematics, and has not been studied so much. However without this geometry, no solution of cubic equations has not completed in Arabic mathematics. We sketch here the synopsis of the geometrical works of Abu Sahl al-Quhl (second half of the tenth century), "one of the most eminent mathematicians in Iraq", and investigate the origin and development of his geometrical ideas. Thirty three mathematical works are attributed to him, and almost of them are geometrical. His ideas were from Archimedes, Euclid and Apollonius. The opus magnum of the last one is indispensable for al-Quhl's works, and in the field of conic sections he contributed much. He completed the lacuna of the Greek mathematics, and developed it further. For showing this aspect four treatises are presented with partial translations. "On Tangent Circles" investigated Apollonian circle problems further, and "On the Trisection of Angle" solved the famous problem by Apollonian conic sections. "On the Motion" was a unique treatise in Arabic mathematics, for it dealt with infinity which had been avoided in Greek mathematics. "On the Perfect Compass (an instrument to draw conies by continuous moving)" gave an idea on the new classification of curves, which anticipates the seventeenth-century European mathematics. The problems and method which he used seems to be analytical and purely Greek, and he might be called as the last Greek-style mathematician. The atmosphere where he studied shows that Arabic science developed under a kind of patronage, and the manuscripts containing his treatises shows that Greek geometry was well established at his times. In conclusion, geometry flourished in Arabic world of the tenth century, and its results were over the Greek ones, and might be compared to the early modern mathematics in Europe.