GALILEI, the famous mathematician and astronomer, was the son of a Florentine nobleman, and born in the year 1564. He had from his infancy a strong inclination to philosophy and the mathematics; and made prodigious progress in these sciences. In 1592, he was chosen professor of mathematics at Padua; and during his abode there he invented, it is said, the telescope; or, according to others, improved that instrument, so as to make it fit for astronomical observations: (See ASTRONOMY, No. 27.) In 1611, Cosmo II. grand duke of Tuscany sent for him to Pisa, where he made him professor of mathematics with a handsome salary, and soon after inviting him to Florence, gave him the office and title of principal philosopher and mathematician to his highness.

He had been but a few years at Florence, before he was convinced by sad experience, that Aristotle's doctrine, however ill grounded, was held too sacred to be called in question. Having observed some solar spots in 1612, he printed that discovery the following year at Rome; in which, and in some other pieces, he ventured to assert the truth of the Copernican system, and brought several new arguments to confirm it. For these he was cited before the inquisition; and after some months imprisonment, was released upon a simple promise, that he would renounce his heretical opinions, and not defend them by word or writing. But having afterwards, in 1632, published at Florence his "Dialogues of the two greatest systems of the world, the Ptolemaic and Copernican," he was again cited before the inquisition, and committed to the prison of that ecclesiastical court at Rome. In June 22d N. S. that year, the congregation convened: and in his presence pronounced sentence against him and his books, obliging him to abjure his errors in the most solemn manner; committed him to the prison of their office during pleasure; and enjoined him, as a saving penance, for three years to come, to repeat once a-week the seven penitential psalms: referring to themselves, however, the power of moderating, changing, or taking away altogether or in part, the above-mentioned punish Galileo lived ten years after this, seven of which were employed in making still further discoveries with his telescope. But by the continual application to that instrument, added to the damage he received in his flight from the nocturnal air, his eyes grew gradually weaker, till he became totally blind in 1639. He bore this calamity with patience and resignation, worthy of a great philosopher. The loss neither broke his spirit, nor hindered the course of his studies. He supplied the defect by constant meditation: whereby he prepared a large quantity of materials, and began to dictate his own conceptions; when, by a ditterm of three months continuance, wailing away by degrees, he expired at Arcetti near Florence, in January 1642, N.S. in the 78th year of his age.

Among various useful inventions of which Galileo was the author, is that of the simple pendulum, which he had made use of in his astronomical experiments. He had thoughts of applying it to clocks; but did not execute it: the glory of that invention was reserved for Vincenzo his son, who made the experiment at Venice in 1649; and M. Huygens afterwards carried this invention to perfection. He wrote a great number of treatises, several of which were published in a collection by Signor Mendelli, under the title of L'opera di Galileo Galilei Lynceo. Some of these, with others of his pieces, were translated into English and published by Thomas Salibury, Esq. in his mathematical collections, &c. in two volumes folio. A volume also of his letters to several learned men, and solutions of several problems, were printed at Bologna in quarto. Besides these, he wrote many others, which were unfortunately lost through his wife's devotion; who, solicited by her confessor, gave him leave to peruse her husband's manuscripts; of which he tore and took away as many as he said were not fit to be published.