GALILEI, GALILEO (b. Pisa, Italy, 15 February 1564; d. Arcetri, Italy, 8 January 1642), physics, astronomy.

    in which the double motion of the earth was invoked to account for the periodic disturbance of its water. The first notation concerning this theory occurs in the notebooks of Sarpi in 1595. Galileo wrote a treatise on it early in 1616, and wished to make it the central theme of his Copernican Dialogue of 1632, considering the tides to offer a compelling argument for the double motion of the earth.

It was also in 1597 that Galileo began the production—for sale—of a mathematical instrument, the sector or proportional compass. The idea for this instrument probably came to him from Guidobaldo, whose knowledge of it may in turn have been derived from Michel Coignet. Galileo transformed it from a simple device of limited use to an elaborate calculating instrument of varied uses and of great practical utility by adding to it a number of supplementary scales. He employed a skilled artisan to produce it (and other mathematical instruments) in his own workshop and wrote a treatise on its use for engineers and military men.

During his residence at Padua, Galileo took a Venetian mistress named Marina Gamba, by whom he had two daughters and a son. The elder daughter, Virginia, who was born in 1600, later became Galileo's chief solace in life. The vivacity of her mind and the sensitivity of her spirit—as well as her many impositions on her father's good nature—are evident in the letters that Galileo received and treasured. Both she and her sister Livia were entered in a nunnery near Florence at an early age, Virginia taking the name Maria Celeste. Livia, who took the name Arcangela, was of a peevish disposition and frail health. The son, Vincenzio, was later legitimized. After periods of estrangement from his father, Vincenzio became reconciled with him in his last years but did not long survive him. Marina Gamba remained at Venice when Galileo returned to Florence, and shortly afterward she married.

Early Work on Free Fall.

Toward the end of 1602, Galileo wrote to Guidobaldo concerning the motions of pendulums and the descent of bodies along the arcs and chords of circles. His deep interest in phenomena of acceleration appears to date from this time. The correct law of falling bodies, but with a false assumption behind it, is embodied in a letter to Sarpi in 1604. Associated with the letter is a fragment, separately preserved, containing an attempted proof of the correct law from the false assumption. No clue is given as to the source of Galileo's knowledge of the law that the ratios of spaces traversed from rest in free fall are as those of the squares of the elapsed times. The law is algebraically derivable from the medieval mean-degree theorem known as the Merton rule, but Galileo's false assumption in 1604 contradicts the specific association of speed and time that is always found in medieval derivations of that theorem. Moreover, Galileo's faulty demonstration invoked no single instantaneous velocity as a mean or representative value; instead, it proceeded by comparison of ratios between infinite sets of instantaneously varying velocities. It is probable either that he observed a rough 1, 3, 5, ... progression of spaces traversed along inclined planes in equal times and assumed this to be exact, or that he reasoned (as Christian Huygens later did) that only the oddnumber rule of spaces would preserve the ratios unchanged for arbitrary changes of the unit time. From this fact, the times-squared law follows immediately. Galileo's derivation of it from the correct definition of uniform acceleration followed only at a considerably later date.

The appearance of a supernova in 1604 led to disputes about the Aristotelian idea of the incorruptibility of the heavens, in which Galileo took an active part. He delivered three lectures to overflow crowds at Padua and prepared to publish an astronomical work; he did not do so, however, and only a short fragment of the manuscript survives. Lodovico delle Colombe, who published a theory of new stars at Florence, suspected Galileo of having written a pseudonymous attack on him, and it is certain that Galileo's ideas are reflected in still another pseudonymous work, published in rustic dialect at Padua in 1605, which ridiculed the professors of philosophy. In 1606, however, Galileo's attention was diverted from this dispute by the plagiarism of his proportional compass by Simon Mayr (or Marius, in the Latinized form used for publication), a German then at Padua, and Mayr's pupil Baldassar Capra. Galileo had privately printed a small edition of his treatise on the use of the compass in that year; Mayr and Capra produced a Latin book on the construction and use of the same instrument, claiming that Galileo had stolen it from them. Mayr had returned to Germany, so Galileo brought his action against Capra. The book was suppressed and Capra was expelled from the university. In the following year Galileo published a full account of the case in his first publicly circulated printed work, the Difesa ... contro alle calunnie & imposture di Baldessar Capra.

Early in 1609, Galileo began the composition of a systematic treatise on motion in which his studies of inclined planes and of pendulums were to be integrated under the law of acceleration, known to him at least since 1604. In the composition of his treatise, he became aware that there was something wrong with his attempted derivation of 1604, which had