Toward a Foundation: The Ex Mechanicis Proof of the Law of Chords

  • Jochen Büttner
Part of the Boston Studies in the Philosophy and History of Science book series (BSPS, volume 335)


In a letter to Guidobaldo del Monte written in November 1602, Galileo mentioned having found a proof for the so-called law of chords, i.e. the statement that fall along any chord inscribed in the same circle and sharing either its apex or nadir is completed in equal time. The proof alluded to in the letter is identified with one of the proofs Galileo provided for this proposition in the Discorsi. It is set apart from all other proofs regarding naturally accelerated motion contained in the Discorsi in that it makes a dynamical argument. This chapter reconstructs and discusses in great detail the sequence of steps by which in 1602 Galileo initially established the dynamical argument forming the basis of this proof. Contrary to the widely accepted opinion that Galileo constructed this argument while still holding the assumption characteristic of his older De Motu Antiquiora that motion along inclined planes is in principle uniform, it is thus shown that the argument was constructed only after he had come to accept that falling motion was naturally accelerated. It is, moreover, demonstrated that Galileo was already aware of the law of chords when he first constructed a dynamical argument in support of it. The new proof could be considered to rest on fundamental principles and Galileo indeed earmarked it as being intended to replace a proof of the same proposition he had constructed earlier. The way in which Galileo may have come to accept the law of chords as a heuristic in the first place is discussed.


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© Springer Nature B.V. 2019

Authors and Affiliations

  • Jochen Büttner
    • 1
  1. 1.Max Planck Institute for the History of ScienceBerlinGermany

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