[FERMAT, Pierre de (1601-1665)]. DIOPHANTUS of Alexandria (fl. A.D. 250). Arithmeticorum libri sex et de numeris multangulis liber unus. Latin translation by Guilelmus Xylander (Wilhelm Holtzmann, 1532-1576). Edited by Claude Bachet de Mziriac (1581-1638). Commentary by Pierre de Fermat. Toulouse: Bernard Bosc, 1670. 2o (324 x 218 mm). Text in Greek and Latin in double columns, commentary in Latin in single column. A few woodcut text diagrams, 2 engraved head-pieces, one engraved initial, woodcut initials and tailpieces. (Title laid down and browned, occasional faint marginal browning.) Later half calf, gilt spine, marbled boards (joints splitting, spine ends and board edges very worn, boards slightly rubbed). FIRST EDITION OF FERMAT'S THEOREMS RELATING TO NUMBER THEORY, second edition of Bachet's Diophantus. Fermat, a Toulouse parlementaire and amateur mathematician, made important discoveries in analytic geometry and algebra, and prepared the way for the development of differential calculus. Most of his known works, including this book, were published posthumously by his son, Clment-Samuel Fermat (1630-1690). One of Fermat's 48 observations was that he had discovered a "truly marvelous demonstration" of an unproved theorem, but that his margin was too narrow for him to note it down. Mathematicians have since been fascinated by his claim, trying to either find his demonstration or to prove it false. It was only in 1995 that Andrew Wiles, professor of mathematics at Princeton, proved it, albeit using 20th century methods that Fermat could not have used. The exact formula that Fermat discovered remains unknown. Norman 777; Smith, p. 348.