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

    Arcetri, in the hills above Florence. It was probably on the occasion of his departure from Siena that he uttered the celebrated phrase “Eppur si muove,” apocryphally said to have been muttered as he rose to his feet after abjuring on his knees before the Cardinals Inquisitors in Rome. The celebrated phrase, long considered legendary, was ultimately discovered on a fanciful portrait of Galileo in prison, executed about 1640 by Murillo or one of his pupils at Madrid, where the archbishop's brother was stationed as a military officer.

Galileo was particularly anxious to return to Florence to be near his elder daughter. But she died shortly after his return, in April 1634, following a brief illness. For a time, Galileo lost all interest in his work and in life itself. But the unfinished work on motion again absorbed his attention, and within a year it was virtually finished. Now another problem faced him: the printing of any of his books, old or new, had been forbidden by the Congregation of the Index. A manuscript copy was nevertheless smuggled out to France, and the Elzevirs at Leiden undertook to print it. By the time it was issued, in 1638, Galileo had become completely blind.

Two New Sciences.

The title of his final work, Discourses and Mathematical Demonstrations Concerning Two New Sciences (generally known in English by the last three words), hardly conveys a clear idea of its organization and contents. The two sciences with which the book principally deals are the engineering science of strength of materials and the mathematical science of kinematics. The first, as Galileo presents it, is founded on the law of the lever; breaking strength is treated as a branch of statics. The second has its basis in the assumption of uniformity and simplicity in nature, complemented by certain dynamic assumptions. Galileo is clearly uncomfortable about the necessity of borrowing anything from mechanics in his mathematical treatment of motion. A supplementary justification for that procedure was dictated later by the blind Galileo for inclusion in future editions.

Of the four dialogues contained in the book, the last two are devoted to the treatment of uniform and accelerated motion and the discussion of parabolic trajectories. The first two deal with problems related to the constitution of matter; the nature of mathematics; the place of experiment and reason in science; the weight of air; the nature of sound; the speed of light; and other fragmentary comments on physics as a whole. Thus Galileo's Two New Sciences underlies modern physics not only because it contains the elements of the mathematical treatment of motion, but also because most of the problems that came rather quickly to be seen as problems amenable to physical experiment and mathematical analysis were gathered together in this book with suggestive discussions of their possible solution. Philosophical considerations as such were minimized.

The book opens with the observation that practical mechanics affords a vast field for investigation. Shipbuilders know that large frameworks must be strongly supported lest they break of their own weight, while small frameworks are in no such danger. But if mathematics underlies physics, why should geometrically similar figures behave differently by reason of size alone? In this way the subject of strength of materials is introduced. The virtual lever is made the basis of a theory of fracture, without consideration of compression or stress; we can see at once the inadequacy of the theory and its value as a starting point for correct analysis. Galileo's attention turns next to the problem of cohesion. It seems to him that matter consists of finite indivisible parts, parti quante, while at the same time the analysis of matter must, by its mathematical nature, involve infinitesimals, parti non quante. He does not conceal—but rather stresses—the resulting paradoxes. An inability to solve them (as he saw it) must not cause us to despair of understanding what we can. Galileo regards the concepts of “greater than,” “less than,” and “equal to” as simply not applicable to infinite multitudes; he illustrates this by putting the natural numbers and their squares in one-to-one correspondence.

Galileo had composed a treatise on continuous quantity (now lost) as early as 1609 and had devoted much further study to the subject. Bonaventura Cavalieri, who took his start from Galileo's analysis, importuned him to publish that work in order that Cavalieri might proceed with the publication of his own Geometry by Indivisibles. But Galileo's interest in pure mathematics was always overshadowed by his concern with physics, and all that is known of his analysis of the continuum is to be found among his digressions when discussing physical problems.

Galileo's parti non quante seem to account for his curious physical treatment of vacua. His attention had been directed to failure of suction pumps and siphons for columns of water beyond a fixed height. He accounted for this by treating water as a material having its own limited tensile strength, on the analogy of rope or copper wire, which will break of its own weight if sufficiently long. The cohesion of matter seemed to him best explained by the existence of minute vacua. Not only did he fail to suggest the weight of air as an explanation of the siphon phenomena, but he rejected that explanation when it was clearly offered to him in a letter by G. B. Baliani.