Free Three Scientific Revolutions: How They Transformed Our Conceptions of Reality by Richard H. Schlagel

he had to abjure on his knees before them” (Drake, p. 351). Drake adds that “three cardinals of the ten refused to sign the sentence,” while Cardinal Francesco Barberini, the pope’s nephew who had aided Galileo throughout the trial, “immediately commuted the place of Galileo’s imprisonment at Rome to the Florentine embassy there” (pp. 351–52). Francesco Niccolini, the Tuscan ambassador to Rome, “then undertook to secure a pardon for Galileo from the pope, who refused, but permitted Galileo to be moved to the custody of Archbishop Ascanio Piccolomini, of Siena” (pp. 351–52). Near the end of 1633 he was permitted to be “imprisoned” in his villa at Arcetri where he remained for the rest of his life.
    It was there in the few years remaining to him that he wrote Dialogues Concerning Two New Sciences , his second most famous work, published in 1638. Retaining the same three disputants the four days of dialogue recounts much of his earlier research on motion and on falling objects, but declares “his purpose is to set forth a very new science dealing with a very ancient subject.” 29 He then provides an excellent statement of the scope and originality of his book:
    There is, in nature, perhaps nothing older than motion, concerning which the books written by philosophers are neither few nor small; nevertheless I have discovered by experiment some properties of it which are worth knowing and which have not hitherto been either observed or demonstrated. Some superficial observations have been made, as, for instance, that the free motion of a heavy falling body is continuously accelerated; but to just what extent this acceleration occurs has not yet been announced; for so far as I know, no one has yet pointed out that the distances traversed, during equal intervals of time, by a body falling from rest, stand to one another in the same ratio as the odd numbers beginning with unity. (p. 147)
    Galileo was unaware apparently that the odd number law, which he had experimentally proven in 1604, had been previously formulated by Nicole Oreme in the fourteenth century.
    He continues by describing some additional contributions that he foresees as just the beginning of a whole new world of discoveries.
    It has been observed that missiles and projectiles describe a curved path of some sort; however no one has pointed out the fact that this path is a parabola. But this and other facts, not few in number or less worth knowing, I have succeeded in proving; and what I consider more important, there have been opened up to this vast and most excellent science, of which my work is merely the beginning, ways and means by which other minds more acute than mine will explore its remote corners. (pp. 147–48)
    Rejecting Aristotle’s explanation of projectile motion as requiring a contiguous, continuous mover, he seems to have adopted Jean Buridan’s fourteenth-century explanation that motion is caused by the mover impressing a force or “impetus” on the projectile that continues the motion without the presence of the mover, though he did not anticipate the law of inertia because of the influence of gravity. Some of these contributions were not discoveries of specific laws but refinements of scientific methodology, such as beginning with the simpler aspects of a problem before moving to more complex ones.
    He antedates Newton’s formal method of presentation by dividing his analysis of motion into “Definitions, Axioms, Theorems, and Propositions.” Beginning with the simplest, uniform motion, and then moving to accelerated and unnatural or projectile motions, this is followed by four axioms and six theorems with diagrams to illustrate his reasoning. His method anticipates that of modern science in rejecting a priori or even common-sense definitions in favor of those best “fitting natural phenomena” supported by experimental evidence . The