Inertia as a theorem in Galileo’s Discorsi
Júlio C. R. de Vasconcelos
Universidade Estadual de Feira de Santana
Bahia. Brazil
Contrary to widely held beliefs, it could be said that there is no principle of inertia in Galileo’s Discorsi (Two New Sciences) on the grounds that although one can find a first conception of the law of inertia in this masterpiece, this conception does not act in the Discorsi as a principle or as any kind of demonstrative tool, except inside a "scholium", in which Galileo argues, in mathematical terms and through two different "ways", for the truth of the so-called "double-distance rule".
Galileo’s conception of inertia appears only in the second of these "ways"; the first of them, however, is the most important one as Galileo tries to relate the mentioned rule to the development of the second "new science", based upon just one principle, which is not a principle of inertia.
Given that Galileo himself, subsequently to that scholium, mentions twice the double-distance rule as obtained "ex demonstratis", it is probably safe to say that this rule works as a theorem of inertia in the Discorsi. It is this theorem, instead of any law of inertia, that is used for demonstration in Galileo’s science of motion, especially in its projectile theory. Last but not least, the theorem also provides a definition for instant speed in a fall and a measure for horizontal speed in a projectile motion.
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