Galileo and Descartes on Copernicanism and the cause of the tides

Galileo and Descartes were on the front lines of the defense of Copernicanism against theological objections that took on special importance during the seventeenth century. Galileo attempted to overcome opposition to Copernicanism within the Catholic Church by offering a demonstration of this theory that appeals to the fact that the double motion of the earth is necessary as a cause of the tides. It turns out, however, that the details of Galileo's tidal theory compromise his demonstration. Far from attempting to provide a demonstration of the earth's motion, Descartes ultimately argued that his system is compatible with the determination of the Church that the earth is at rest. Nonetheless, Descartes's account of the cause of the tides creates difficulty for this argument.     

Galileo and the problem of infinity

During the period before the Greek revolution of 1821, and especially during the years between 1750 and 1821, there were two ways in which European scientific thought was propagated in Greece. The first is traditional. It comes from ancient Greece and, through Byzantium, reaches the period before the Greek revolution. It makes known the thought of Aristotle, Democrititus, and others on ‘natural philosophy’. The second way comes from Europe. The Greek scholars of the period before the Greek revolution, and especially at the end of the eighteenth century, tried to bring to and propagate in Greece the spirit ofthe European Enlightenment, They tried to make known to the Greek people the scientific achievements of Newton, Descartes, Lavoisier, and Laplace. Scientific knowledge is an important weapon against superstition, and Greek students had to learn about science to become free persons in an independent Greek state.     

Galileo and prior philosophy

Galileo claimed inconsistency in the Aristotelian dogma concerning falling bodies and stated that all bodies must fall at the same rate. However, there is an empirical situation where the speeds of falling bodies are proportional to their weights; and even in vacuo all bodies do not fall at the same rate under terrestrial conditions. The reason for the deficiency of Galileo’s reasoning is analyzed, and various physical scenarios are described in which Aristotle’s claim is closer to the truth than is Galileo’s. The purpose is not to reinstate Aristotelian physics at the expense of Galileo and Newton, but rather to provide evidence in support of the verdict that empirical knowledge does not come from prior philosophy.     

Galileo and the problem of concentric circles

In 1892, Eliakim Hastings Moore accepted the task of building a mathematics department at the University of Chicago. Working in close conjuction with the other original department members, Oskar Bolza and Heinrich Maschke, Moore established a stimulating mathematical environment not only at the University of Chicago, but also in the Midwest region and in the United States in general. In 1893, he helped organize an international congress of mathematicians. He followed this in 1896 with the organization of the Midwest Section of the New York City-based American Mathematical Society. He became the first editor-in-chief of the Society's Transactions in 1899, and rose to the presidency of the Society in 1901.     

Some observations of Leonardo,Galileo, Mariotte and others relative to size effect

A letter in which astronomer John Flamsteed expounded his unusual views about the causes of earthquakes survives in a number of drafts and copies. Though it was compiled in response to shocks felt in England in 1692 and Sicily in 1693, its relationship to the wide range of comparable theories current in the later seventeenth century must be considered. Flamsteed's suggestion that an ‘earthquake’ might be an explosion in the air was linked with contemporary thinking about the roles of sulphur and nitre in earthquakes underground, and in combustion, respiration, and other processes. It reveals his concern with subjects other than astronomy and the influence of his continuing contact with members of the Royal Society; it also offers an early example of how seventeenth-century work on sulphur and nitre prepared the way for ‘airquake’ and electrical theories associated with the London earthquake of 1750.