Historians of seventeenth-century science have frequently asserted that Kepler's laws of planetary motion were largely ignored between the time of their first publication and the publication of Newton's Principia . In fact, however, they were more widely known and accepted than has been generally recognized.Kepler's ideas were, indeed, rather slow in establishing themselves, and until about 1630 there are few references to them in the literature of the time. But from then onwards, interest in them increased fairly rapidly. In particular, (...) the principle of elliptical orbits had been accepted by most of the leading astronomers in France before 1645 and in England by about 1655. It also received quite strong support in Holland.The second law had a more chequered history. It was enunciated in its exact form by a few writers and was used in practice by some others without being explicitly formulated, but the majority, especially after 1645, preferred one or another of several variant forms which were easier to use but only approximately correct. The third law attracted less interest than the others, chiefly perhaps because it had no satisfactory theoretical basis, but it was correctly stated by at least six writers during the period under review.Between about 1630 and 1650 Kepler's Epitome Astronomiae Copernicanae was probably the most widely read work on theoretical astronomy in northern and western Europe, while his Rudolphine Tables, which were based upon the first two laws, were regarded by the majority of astronomers as the most accurate planetary tables available.Kepler's work certainly did not receive all the recognition it deserved, but the extent to which it was neglected has been much exaggerated. (shrink)

The paper is an introduction to and an annotated translation of De quantitatibus, a mathematical manuscript by Johannes Kepler. Conceived as a philosophical treatise, the text collects, orders, and interprets the Aristotelian passages relevant to mathematics. Kepler thought of De quantitatibus as an introduction to Dasypodius's textbook, but by choosing the Aristotelian context, he distances himself from the tradition to which Dasypodius belonged. Dasypodius's works on mathematics, like Ramus's, were within the genre developed after the rediscovery of Proclus's commentary on (...) Euclid. Instead, Kepler took a position following the Aristotelian humanism of Schegk. While the dating of De quantitatibus is still uncertain, it is likely that Kepler wrote it not too long after his education in Tübingen, where he received instruction in natural philosophy under the influence of Schegk. In De quantitatibus, Kepler also exhibits some original views on mathematics within this humanist Aristotelian context. (shrink)

A major intellectual shift between Copernicus and the mid-17th century was the rejection of Aristotelian assertions concerning the relationship of mathematics to physical nature. Aristotle asserted that “The minute accuracy of mathematics is not to be demanded in all cases, but only in the case of things which have no matter. Therefore its method is not that of natural science; for presumably all nature has matter.” Thus, he pulled out the rug from under the feet of the aspiration to a (...) mathematically based natural sciences, asserting that: “And at the same time not even this is true, that mensuration deals with perceptible and perishable magnitudes; for then it would have perished, when they perished. And astronomy also cannot be dealing with perceptible magnitudes nor with this heaven above us. For neither are perceptible lines such lines as the geometer speaks of, nor are the movement and complex orbits in the heaven like those which astronomy treats, nor have geometrical points the same nature as the actual stars.”. (shrink)