Non-Euclidean Geometry: A Critical and Historical Study of Its Development (1912)

Non-Euclidean Geometry is a history of the alternate geometries that have emerged since the rejection of Euclids parallel postulate. Italian mathematician ROBERTO BONOLA (18741911) begins by surveying efforts by Greek, Arab, and Renaissance mathematicians to close the gap in Euclids axiom. Then, starting with the 17th century, as mathematicians began to question whether it was actually possible to prove Euclids postulate, he examines non-Euclidean predecessors Saccheri, Lambert, Legendre, W. Bolyai, Wachter, and Thibaut, and non-Euclidean founders Gauss, Schweikart, Taurinus, Lobachevski, and J. Bolyai. He concludes with a look at later developments in non-Euclidean geometry. Including five appendices and an index of authors, Bonolas Non-Euclidean Geometry is a useful reference guide for students of mathematical history.