Pierre Maurice Marie Duhem Alan Aversa Galileo’s Precursors Translation of Studies on Leonardo da Vinci (vol. 3)∗ June 29, 2018 Springer ∗Duhem (1906) To my wife, who made this translation possible, to the Blessed Virgin Mother, and to the Holy Trinity, Who makes all things possible Foreword Note on the Translation Everything translated from the original French of Duhem (1906). Additions in [brackets] belong to the translator. Alan Aversa June 29, 2018 ix Acknowledgements The translator would like to thank Gery and Rebecca Aversa for helping to make this work open access. xi Preface To the third series of our Studies on Leonardo da Vinci, we give a subtitle: Galileo’s Parisian Precursors. This subtitle announces the idea of which our previous stud- ies had already discovered a few aspects and which our new researches place in full light. The Science of mechanics inaugurated by Galileo—by his followers, by his disciples Baliani, Torricelli, Descartes, Beeckman, Gassendi—is not a creation; modern intelligence did not produce it from the very start and from all the pieces which reading the art of Archimedes of applying geometry to natural effects had re- vealed to it. Galileo and his contemporaries used the mathematical skill acquired in the trade of the geometers of Antiquity to clarify and develop a mechanical Science of which the Christian Middle Ages had posed the principles and the most essential propositions. The physicists who taught in the 14th century at the University of Paris had designed this Mechanics by taking observation as their guide; they had sub- stituted it for the Dynamics of Aristotle, convinced of its ineffectualness to “save the phenomena.” At the time of the Renaissance, the superstitious archaism, where the wit of the Humanists and the Averroist routine of a retrograde Scholasticism are complacent, rejected this doctrine of the “Moderns.” The reaction was strong, particularly in Italy, against the Dynamics of the “Parisians,” in favour of the in- admissible dynamics of the Stagirite. But, despite stubborn resistance, the Parisian tradition found, outside schools as well as in Universities, masters and scholars to maintain and develop it. It is of this Parisian tradition that Galileo and his followers were heirs. When we see the science of Galileo triumph over the obstinate Peripateti- cism of Gremonini, we believe, uninformed in the history of human thought, that we are witnessing the victory of the young modern Science over the medieval Philoso- phy, obstinate in its psittacism; in truth, we behold the long-prepared triumph of the science that was born in Paris in the 14th century on the doctrines of Aristotle and Averroes, revived by the Italian Renaissance. No movement can perdure if it is not maintained by the continuous action of a motive power, directly and immediately applied to the mobile. This is the axiom on which the whole Dynamics of Aristotle rests. According to this principle, the Stagirite wants to apply to the arrow that continues to fly after leaving the bow a motive power which carries it; he believes this power xiii xiv Preface is found in the disturbed air; it is the air, hit by the hand or by the ballistic machine, which supports and guides the projectile. This assumption, which seems to push its improbability even to ridicule, seems to have been admitted almost unanimously by the physicists of Antiquity; one of them spoke out clearly against it, and he, in the last years of Greek philosophy, is, by his Christian faith, almost separated from this Philosophy; we have named John of Alexandria, nicknamed Philoponus. After showing what was unacceptable in the Peripatetician theory of the motion of projectiles, John Philoponus declares that the arrow continues to move without any mover applied to it, because the rope of the bow has created an energy that plays the role of the motive force. The last thinkers of Greece and even Arab philosophers failed to mention the doc- trine of this John the Christian, for whom Simplicius or Averroes had only sarcasm. The Christian Middle Ages, taken by the naïve admiration which inspired the peri- patetic Science when it was revealed, shared first, with respect to the assumption of Philoponus, the disdain of the Greek and Arab commentators; St. Thomas Aquinas only mentions it to warn those it could seduce. But following the condemnations in 1277 by the Bishop of Paris, Étienne Tem- pier, against a group of theses that supported “Aristotle and those of his suite,” a great movement emerges, which will release the Christian thought from the yoke of Peripateticism and Neoplatonism and produce what the archaism of the Renaissance called the Science of the “Moderns.” William of Ockham attacks, with his customary vivacity, the theory of the mo- tion of projectiles proposed by Aristotle; he is content, besides, to simply destroy without building anything; but his critics, with some followers of Duns Scotus, re- store the honor of the doctrine of John Philoponus; energy, the motive force of which he had spoken, reappears under the name of impetus. This hypothesis of the impe- tus, impressed in the projectile by the hand or by the machine which lauched it, is seized upon by a secular master of the Faculty of Arts in Paris, a physicist of genius; Jean Buridan, toward the middle of the 14th century, takes it as the foundation of a Dynamics with which “all the phenemena agree.” The role that the impetus plays in the Dynamics of Buridan is very exactly what Galileo will assign to the impeto or momento; Descartes to the quantité de mouve- ment; and finally Leibniz to the living force. So exact is this correspondance that, for explaining in his Academic Lessons the Dynamics of Galileo, Torricelli will often take up the reasoning and almost the very words of Buridan. This impetus, which would remain unchanged within the projectile if it were not incessantly destroyed by the resistance of the medium and by the action of grav- ity contrary to the movement, Buridan takes, at equal speed, as proportional to the amount of primary matter that the body contains; he conceived this quantity and de- scribed in terms almost identical to those which Newton will use to define mass. At equal mass the impetus is as much greater as the speed is greater; prudently, Buridan refrains from further clarifying the relationship between the size of the impetus and its speed; more daringly, Galileo and Descartes would agree that this relationship is reduced to a proportionality; they will also obtain an erroneous assessment of the impeto and momentum which Leibniz will have to rectify. Preface xv Like the resistance of the medium, gravity reduces constantly and eventually de- stroys the impetus of a mobile that is launched upward, because such a movement is contrary to the natural tendancy of this gravity; but in a mobile that falls, the move- ment is in line with the trendancy of gravity; the impetus also must be constantly increasing, and the speed, in the course of the movement, must grow constantly. This is, according to Buridan, the explanation of the acceleration observed in the fall of a body, an acceleration that the science of Aristotle already knew, but for which the Hellenic commentators of the Stagirite, Arabs or Christians, had given unacceptable reasons. This Dynamics expressed by Jean Buridan presents in a purely qualitative but always exact way the truths that the notions of live force and work allow us to for- mulate in quantitative language. The philosopher of Béthune is not alone in professing this Dynamics; his most brilliant disciples, Albert of Saxony and Nicole Oresme, adopt it and teach it; the French writings of Oresme make it known even to those who are not clerics. When no resistant medium and when no natural tendancy analogous to gravity is opposed to movement, the impetus maintains an invariable intensity; the mobile to which a movement of translation or rotation is applied continues to move with constant speed indefinitely. It is in this form that the law of inertia presents itself to the mind of Buridan; it is in this same form that Galileo will receive it From this law of inertia, Buridan draws a corollary, the novelty of which we must now admire. If the celestial orbs move eternally with a constant speed, it is, according to the axiom of the dynamics of Aristotle, because each of them is subject to an eternal mover of immutable power; the philosophy of the Stagirite requires that such a mover is an intelligence separate from matter. The study of the motive intelligences of the celestial orbs is not only the culmination of Peripatetic Metaphysics; it is the central doctrine around which all the Neoplatonic Metaphysics of the Greeks and of the Arabs revolve, and the Scholastics of the 13th century do not hesitate to receive, into their Christian systems, this legacy of pagan theologies. Now, Buridan has the audacity to write these lines: From the creation world, God has moved the heavens with movements identical to those which currently move them; he impressed on them then an impetus by which they continue to be moved uniformly; these impetus, indeed, meeting no contrary resistance, are never destroyed nor weakened… According to this conception, it is not necessary to pose the existence of intelligences that move celestial bodies in an appropriate manner. Buridan stated this thought in various circumstances; Albert of Saxony explains it in turn; and Nicole Oresme, to formulate it, finds this comparison: “Except for violence, it is in no way similar to when a man has made a clock i and lets it go to be moved by itself.” If one wanted, by a precise line, to separate the reigns of the ancient Science of the reign of modern Science, it would have to be drawn, we believe, at the moment when Jean Buridan developed this theory, at the moment when one stopped looking at the stars as moved by divine beings and when it has been admitted that the celestial and sublunary movements depend on the same mechanics.