Three Generations: From Tartaglia to Galileo
To follow the evolution of the concepts that finally led to the correct formulation of the laws of motion would require several thick volumes. We have, therefore, chosen to report a few last episodes in this long chain of events. In the 16th century Nicol
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1. Stroke over s
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n reading the last chapter, anyone who has had any contact with classical mechanics will have noticed that there is only a slight difference between Aristotle’s Second Law of Dynamics and that of Newton. In Aristotle’s version, force is proportional to mass and velocity, whereas in Newton’s version it is proportional to mass and acceleration. If, in agreement with the present notation, we denote velocity by s’ (derivative of distance with respect to time), and acceleration by s’’ (second derivative of distance with respect to time), then this difference is reduced to only one stroke over s. But, in fact, the difference is enormous. Between Aristotle and Newton a long evolutionary chain extends. To add this little stroke over s, new concepts had to be elaborated, many problems posed, some of them solved, others left open (but always aiming for solutions), and many calculations had to be done. This long process of trial and error finally led to the invention of calculus. A complex set of interactions between various levels of conceptual, physical, mathematical, and even theological ideas at last produced the result, the foundation of classical mechanics, the starting point of modern science. To illustrate this arduous path, let us focus on its last phase, when mechanical investigations, still strongly embedded in a philosophical context, made a heroic effort to overcome conceptual inertia and adapt themselves to empirical data.
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Chapter 11
2. Science and Artillery As we remember, the prehistory of the science of motion goes back to Zeno’s problem of the flying arrow. Unfortunately, however, as time passes applications of science become more and more dangerous. In the first half of the 16th century Nicolo Tartaglia studied the motion of cannonballs and substantially contributed to the more efficient use of artillery. He initially had scruples about whether he should publish his discoveries since “it would be a most blameworthy thing to teach Christians how they could better slaughter one another.”1 However, when in 1537 the Turkish invasion was imminent, his scruples evaporated, and his work Nova scientia was published. It certainly deserves an honorable mention in the history of mechanics. Alexander Koyré was thinking precisely about this work when he wrote that sciences are usually born from false theories.2 Tartaglia’s theory was false, but the way he posed the problem marked a new chapter in the science of motion. Tartaglia does not try to free himself from the burden of Aristotelian doctrine. He seems to accept it without any discussion, and does not enter into subtle analyses of natural places and the nature of motion; instead, he struggles to find some quantitative and geometric characteristics of motion. His work is not simply one more treatise de motu, but the beginning of a new approach, nova scientia, indeed. Tartaglia does not avoid practical conclusions referring to the accuracy of artillery fire but, in general, he keeps his analyses on an abstract level. Any artificially made ma
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