On 29 April 2015, four beacons were deployed onto an ice island in the Strait of Belle Isle to record positional data. The ice island later broke up into many fragments, four of which were tracked by the beacons. The relative influences of wind drag, current drag, Coriolis force, sea surface height gradient and sea-ice force on the drift of the tracked ice island fragments were analyzed. Using atmospheric and oceanic model outputs, the sea-ice force was calculated as the residual of the fragments' net forces and the sum of all other forces. This was compared against the force obtained through ice concentration-dependent relationships when sea ice was present. The sea-ice forces calculated from the residual approach and concentration-dependent relationships were significant only when sea ice was present at medium-high concentrations in the vicinity of the ice island fragments. The forces from ocean currents and sea surface tilt contributed the most to the drift of the ice island fragments. Wind, however, played a minimal role in the total force governing the drift of the four ice island fragments, and Coriolis force was significant when the fragments were drifting at higher speeds.

In the first part of chapter 2 of book II of the Physics Aristotle addresses the issue of the difference between mathematics and physics. In the course of his discussion he says some things about astronomy and the ‘ ‘ more physical branches of mathematics”. In this paper I discuss historical issues concerning the text, translation, and interpretation of the passage, focusing on two cruxes, ( I ) the first reference to astronomy at 193b25–26 and ( II ) the reference to the more physical branches at 194a7–8. In section I, I criticize Ross’s interpretation of the passage and point out that his alteration of ( I ) has no warrant in the Greek manuscripts. In the next three sections I treat three other interpretations, all of which depart from Ross's: in section II that of Simplicius, which I commend; in section III that of Thomas Aquinas, which is importantly influenced by a mistranslation of ( II ), and in section IV that of Ibn Rushd, which is based on an Arabic text corresponding to that printed by Ross. In the concluding section of the paper I describe the modern history of the Greek text of our passage and translations of it from the early twelfth century until the appearance of Ross's text in 1936.

Argument

In this paper I offer some reflections on the thirty-second proposition of Book I of Euclid’s Elements, the assertion that the three interior angles of a triangle are equal to two right angles, reflections relating to the character of the theorem and the reasoning involved in it, and especially on its historical background. I reject a common view according to which there was at some time a petitio principii in the theory of parallels and argue that certain kinds of skepticism about Proclus’ historical reports are excessive. The evidence we have makes it reasonable to suppose that the so-called common notions were made explicit in the earlier fourth century BCE and the postulates, including the parallel postulate, somewhat later than that. On the other hand, it seems clear that some proof of I,32 was available by the mid-fifth century. I attempt to describe what such a proof would have been like and reflect on its significance for our understanding of early Greek geometry.

In his critical study of Speusippus Leonardo Tarán (T.) expounds an interpretation of a considerable part of the controversial books M and N of Aristotle's Metaphysics. In this essay I want to consider three aspects of the interpretation, the account of Plato's ‘ideal numbers’ (section I), the account of Speusippus’ mathematical ontology (section II), and the account of the principles of that ontology (section III). T. builds his interpretation squarely on the work of Harold Cherniss (C.), to whom I will also refer. I concentrate on T. because he has brought the ideas in which I am interested together and given them a concise formulation; he is also meticulous in indicating the secondary sources with which he agrees or disagrees, so that anyone interested in pursuing particular points can do so easily by consulting his book.