Gregorie, Descartes, Kepler, and the Law of Refraction (original) (raw)

Kepler's near discovery of the sine law: A qualitative computational model

this paper we cannot go into the history of optics, but will give a detailed account of Kepler's study of refraction based on his Ad Vitellionern paralipomena of 1604. Thanks to his diligent reporting style Kepler's writings are grateful objects of study and allow us to reconstruct his path of reasoning in detail. But we will first critically review a previous model of the discovery of the sine law of refraction

Physico-mathematics and the search for causes in Descartes’ optics—1619–1637

Synthese, 2011

One of the chief concerns of the young Descartes was with what he, and others, termed "physico-mathematics". This signalled a questioning of the Scholastic Aristotelian view of the mixed mathematical sciences as subordinate to natural philosophy, non explanatory, and merely instrumental. Somehow, the mixed mathematical disciplines were now to become intimately related to natural philosophical issues of matter and cause. That is, they were to become more 'physicalised', more closely intertwined with natural philosophising, regardless of which species of natural philosophy one advocated. A curious, shortlived yet portentous epistemological conceit lay at the core of Descartes' physicomathematics-the belief that solid geometrical results in the mixed mathematical sciences literally offered windows into the realm of natural philosophical causation-that in such cases one could literally "see the causes". Optics took pride of place within Descartes' physico-mathematics project, because he believed it offered unique possibilities for the successful vision of causes. This paper traces Descartes' early physico-mathematical program in optics, its origins, pitfalls and its successes, which were crucial in providing Descartes resources for his later work in systematic natural philosophy. It explores how Descartes exploited his discovery of the law of refraction of light-an achievement well within the bounds of traditional mixed mathematical optics-in order to derive-in the manner of physico-mathematics-causal knowledge about light, and indeed insight about the principles of a "dynamics" that would provide the laws of corpuscular motion and tendency to motion in his natural philosophical system. [467]

Physico-Mathematics and the Search for Causes in Descartes'

Synthese , 2012

The properties and the nature of light: the study of Newton's work and the teaching of optics

Science and Education, 2005

The history of science shows that for each scientific issue there may be more than one models that are simultaneously accepted by the scientific community. One such case concerns the wave and corpuscular models of light. Newton claimed that he had proved some properties of light based on a set of minimal assumptions, without any commitments to any one of the two models. This set of assumptions constitutes the geometrical model of light as a set of rays propagating in space. We discuss this model and the historical reasons for which it had the head-primacy amongst the relevant models. We argue that this model is indispensable in structuring the curriculum in Optics and attempt to validate it epistemologically. Finally, we discuss an approach for alleviating the implicit assumptions that students make on the nature of light and the subsequent interference of geometrical optics in teaching the properties of light related to its wave-like nature.

Studies on James Gregorie (1638 - 1675)

"As a general conclusion this dissertation suggests that the mathematical and optical contributions of James Gregorie, Isaac Barrow and Isaac Newton are more closely related to one another than it is usually acknowledged. The first chapter contains a narrative of Gregorie's life and works. Evidence on Gregorie's life within 17th-century Scottish universities, his involvement in setting up the St Andrews observatory, his activities in the early 1670's as leader of a Scottish network of mathematical virtuosi, and his juvenile astrological concerns is here produced for the first time. Gregorie's correspondence with Newton is studied. It is argued that John Collins, representing the world of practical mathematicians, was a source of motivations for some of Gregorie's mathematical discoveries, and that Gregorie's attempts to publicize his contributions failed because of institutional practices characteristic of the early Royal Society. The second chapter studies Gregorie's contributions to optics, including a description of a hitherto unpublished manuscript. A major center of interest is the origins of the notion of geometrical optical image, which are shown to have been influenced by the philosophical empiricism. I argue that Gregorie, Barrow, and Newton produced a methodological revolution in geometrical optics. The new optical science sought experimental confirmation for its basic notions and results and thus provided a direct methodological antecedent to Newton's Principia. The third chapter studies Gregorie's work on "Taylor" expansions and his analytical method of tangents, which has passed unnoticed so far. It appears that Gregorie's work is a substantial counter-example to the standard thesis that geometry and algebra were opposed forces in 17th-century mathematics. The last chapter studies and translates an unpublished mathematical manuscript featuring results similar to those in section 1 of Newton's Principia. Placing the contributions of Newton and Gregorie in the context of 17th-century discussions on indivisibles, l argue that Gregorie and Newton were idiosyncratic in their rejection of indivisibles. Research on the manuscripts of James Gregorie and David Gregory shows that David's Geometria practica is actually James's, and that David's optical book heavily borrows from James's optical manuscript."

1 Newtonian Optics in the Eighteenth Century: Discussing the Nature of Science

2015

Despite the difficulty of precisely describing the nature of science, there is a widespread agreement concerning the necessity of incorporating into curricula some notions about how the scientific activity operates. Studying the history of conceptual development and the process of acceptance of scientific ideas by the scientific community may help teachers to incorporate valuable concepts on the nature of science in science teaching. Shortly afterwards the publication of the book Opticks, by Isaac Newton, in 1704, there appears a number of popular lectures and published works presenting the content of this book, attempting to make it suitable for the general public. These published works and popular lectures, however, did not discuss some conceptual problems in Newton’s book. The present paper analyses the development and acceptance process of Newtonian optics during the eighteenth century in Europe, and emphasizes some aspects of nature of science that can be learnt by the study of...

Gregorie, Descartes, Kepler, and the Law of Refraction (original) (raw)

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