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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.