ABSTRACT
The writings of Archimedes on infinitesimals appear in a paradoxical light from the 9th century on. The history of infinitesimal geometry, notably the part that treats areas and volumes, surfaces and solid curves, has one distinctive characteristic. Except for complete translations of The Measurement of the Circle and On the Sphere and Cylinder, very few of his works were known in Arabic. The fundamental issue is to discover how the two works, were received in the world of Arabic mathematics. Indeed, their reception plays a part in determining the characteristics that distinguish Arabic Archimedeans. The earliest known text of Archimedean mathematics in Arabic is the philosopher and mathematician Abu Ishaq al-Kindi's. The use of pointwise transformations by the successors of the Banu Musa, like Thabit ibn Qurra, his grandson Ibrahim ibn Sinan, and many others, has its origin in the works of Ban Musa. The structure of Ibn al-Haytham's treatise on The Measurement of the Paraboloid is simple but significant.
