An unpublished autograph by Christiaan Huygens: His letter to David Gregory of 19 January 1694

A letter written by Christiaan Huygens to David Gregory (19 January 1694) is published here for the first time. After an introduction about the contacts between the two correspondents, an annotated English translation of the letter is given. The letter forms part of the wider correspondence about the ‘new calculus’, in which L'Hospital and Leibniz also participated, and gives some new evidence about Huygens's ambivalent attitude towards the new developments. Therefore, two mathematical passages in the letter are discussed separately. An appendix contains the original Latin text.     

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 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.     

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.     

Bartolomeo Telioux and the early history of the thermometer

In the late 1810s and 1820s the Edinburgh phrenologists were largely concerned with trying to establish phrenology as the true science of mind. They challenged the accepted theories about the nature of mind and the brain; in turn, phrenology was attacked by the proponents of Scottish common-sense philosophy and by some medical men. The ensuing debate, which is discussed as an example of conflict between incommensurable world-views, involved a wide range of contentious theological, philosophical, scientific and methodological issues.     

Relativity of motion: From Occam to Galileo

Early observations of the southern celestial sky were reported in many sixteenth-century books and compilations of voyages of discovery. Here we analyse these accounts in order to find out what was really seen and reported by the first navigators. Our analysis had resulted in new interpretations of the phenomena reported by Amerigo Vespucci and Andreas Corsali. Thus, a reassessment of the discovery of the Coalsack Nebula, the Magellanic Clouds, and the Southern Cross can be made. From a comparative review of the observations of the latter constellation as published between 1500 and 1600, we demonstrate that only questionable records found their way to contemporary compilations of voyages of discovery, and that as a result public knowledge about this constellation at the end of the sixteenth century was entirely unreliable. Another problem we discuss is that although the stars of the Southern Cross were the first to be discovered, and were observed again and again by many navigators, it was not until 1678 that their proper positions were found in stellar atlases and star catalogues accessible to astronomers. We explain how negligence of and subsequently confidence in Ptolemy's astronomy by, respectively, the early navigators and cartographers, were at the root of this amazingly long-lasting gap in the knowledge of the southern celestial sky.     

Galilean argumentation and the inauthenticity of the Cigoli letter on painting vs. sculpture

This essay is partly a case study of the role of logic in historiography. It is also partly a test case for the thesis of a Galilean correspondence between aesthetic attitude and scientific thought, advanced by Panofsky, Koyré, and Heilbron. Intrinsically, it is a discussion of the authenticity of the letter to Cigoli dated 26 June 1612, widely attributed to Galileo, containing argumentation about the relative aesthetic merits of painting and sculpture. I undertake a systematic analysis of the letter’s method of argument, comparing and contrasting it with Galileo’s. I argue that the letter does have some Galilean characteristics: critical reasoning; ad hominem argumentation, in the seventeenth-century sense; and appeal to experimentation. However, the letter falls short of the typical Galilean open-mindedness, fair-mindedness, and clarity; crucially, it uses several illative terms which Galileo never uses, and does not use the one he uses most often. The latter features outweigh the former. Moreover, I discuss some aspects of the letter’s substantive content, primarily a theory of vision that disregards the dynamics of perspective and the faculty of binocularity, which Galileo understood and exploited very well. My novel argument vindicates an old judgment of Favaro, who doubted the letter’s authenticity.