VIVIANI (ViNesNrio,) a celebMted Italian mathematician, was born at Flo rence, in 1621, some say-1622. He was a disciple of the illustrious Galileo, and lived with him from the 17th to the 20th year of his age. After the death of his great master, he passed two or three years more in prosecuting geometrical studies without interruption, and in this time it was that he formed the design of his Restoration of Aristeus. This ancient geometrician, who was contemporary with Euclid, had composed five books of prob lems, " De Locis Solidis," the bare' pro positions of which were collected by Pappus, but the books are entirely lost ; which Viviani undertook to restore by the force of his genius.
He broke this work off before it was finished, in order to apply himself to ano ther of the same kind, which was, to re store the fifth book of Apollonius's "Co nic Sections." While he was engaged in this, Borelli found, in the library of the Grand Duke of Tuscany, an Arabic M. S. with a Latin incription, importing that it, contained the eight books of Apohlonius's Conic Sections ; of which the eighth was not found to be there. He carried this MS. to Rome, in order to translate it with the assistance of a professor of the oriental languages. So unwilling, how ever, was Viviani to lose the fruits of his labours, that he refused to receive the smallest account from Borelli on the sub ject.
At length he finished the work, and published it in 1659, with the title " De Maxim's et Minimis geometries di vinatio in quintum conicorum Apollonii Pergxi." He was called by the state to undertake an operation of great import viz, to prevent the innundations of the 'fiber, in which Cassini and he were employed for some length of time. On account of his great talents he' received a pension from Louis XIV. In 1666 he was honoured by the Grand Duke with the title of the first mathematician. He resolved three problems which had been proposed to all the mathematicians of Europe. Li 1669 he was chosen to fill, in the Royal Academy of Sciences, a place among the eight foreign associates. This circumstance, so honourable to his repu tation, gave new vigour to his exertions, and he published three books of the " Di vination upon Aristeus," in 1701, which he dedicated to the King of Fiance. Vi viani -acquired a good fortune, which he laid out in building a magnificent house at Florence ; here he placed a bust of Galileo, with several inscriptions in ho nour of that great man. He died in 1703, aged 81.