To Explain the World: The Discovery of Modern Science Read Online Free PDF Page B

proportional to the amount in the account increases exponentially with time (though if the interest rate is low it takes a long time to see this). The first person to guess that the increase in the speed of a falling body is proportional to the time elapsed seems to have been the sixteenth-century Dominican friar Domingo de Soto, 16 about two centuries after Oresme.
    From the mid-fourteenth to the mid-fifteenth century Europe was harried by catastrophe. The Hundred Years’ War between England and France drained England and devastated France. The church underwent a schism, with a pope in Rome and another in Avignon. The Black Death destroyed a large fraction of the population everywhere.
    Perhaps as a result of the Hundred Years’ War, the center of scientific work shifted eastward in this period, from France and England to Germany and Italy. The two regions were spanned in the career of Nicholas of Cusa. Born around 1401 in the town of Kues on the Moselle in Germany, he died in 1464 in the Umbrian province of Italy. Nicholas was educated at both Heidelberg and Padua, becoming a canon lawyer, a diplomat, and after 1448 acardinal. His writing shows the continuing medieval difficulty of separating natural science from theology and philosophy. Nicholas wrote in vague terms about a moving Earth and a world without limits, but with no use of mathematics. Though he was later cited by Kepler and Descartes, it is hard to see how they could have learned anything from him.
    The late Middle Ages also show a continuation of the Arab separation of professional mathematical astronomers, who used the Ptolemaic system, and physician-philosophers, followers of Aristotle. Among the fifteenth-century astronomers, mostly in Germany, were Georg von Peurbach and his pupil Johann Müller of Königsberg (Regiomontanus), who together continued and extended the Ptolemaic theory of epicycles. * Copernicus later made much use of the Epitome of the Almagest of Regiomontanus. The physicians included Alessandro Achillini (1463–1512) of Bologna and Girolamo Fracastoro of Verona (1478–1553), both educated at Padua, at the time a stronghold of Aristotelianism.
    Fracastoro gave an interestingly biased account of the conflict: 17
You are well aware that those who make profession of astronomy have always found it extremely difficult to account for the appearances presented by the planets. For there are two ways of accounting for them: the one proceeds by means of those spheres called homocentric, the other by means of so-called eccentric spheres [epicycles]. Each of these methods has its dangers, each its stumbling blocks. Those who employ homocentric spheres never manage to arrive at an explanation of phenomena. Those who use eccentric spheres do, it is true, seem toexplain the phenomena more adequately, but their conception of these divine bodies is erroneous, one might almost say impious, for they ascribe positions and shapes to them that are not fit for the heavens. We know that, among the ancients, Eudoxus and Callippus were misled many times by these difficulties. Hipparchus was among the first who chose rather to admit eccentric spheres than to be found wanting by the phenomena. Ptolemy followed him, and soon practically all astronomers were won over by Ptolemy. But against these astronomers, or at least, against the hypothesis of eccentrics, the whole of philosophy has raised continuing protest. What am I saying? Philosophy? Nature and the celestial spheres themselves protest unceasingly. Until now, no philosopher has ever been found who would allow that these monstrous spheres exist among the divine and perfect bodies.
    To be fair, observations were not all on the side of Ptolemy against Aristotle. One of the failings of the Aristotelian system of homocentric spheres, which as we have seen had been noted around AD 200 by Sosigenes, is that it puts the planets always at the same distance from the Earth, in contradiction with the fact that the