Astronomers have always considered the motion of the Moon as highly complicated, and this motion is decisive in determining the circumstances of such critical celestial phenomena as eclipses. Table-makers devoted much ingenuity in trying to find ways to present it in tabular form. In the late Middle Ages, double argument tables provided a smart and compact solution to address this problem satisfactorily, and many tables of this kind were compiled by both Christian and Jewish astronomers. This paper presents multiple examples (...) of the diversity of approaches adopted by compilers of tables who used this powerful tool, and brings to light intellectual interactions among them that are otherwise hidden from view. (shrink)

In this paper, we analyze the astronomical tables for 1340 by Immanuel ben Jacob Bonfils who flourished 1340–1365, based on four Hebrew manuscripts. We discuss the relation of these tables principally with those of al-Battānī, Abraham Bar Ḥiyya, and Levi ben Gerson, as well as with Bonfils’s better known tables, called Six Wings. An unusual feature of this set of tables is that there are two kinds of mean motion tables, one arranged for Julian years from 1340 to 1380, months, (...) days, hours, and minutes of an hour, and the other arranged in the Hebrew calendar for the times of conjunctions and oppositions of the Sun and the Moon only, with subtables for 19-year cycles, single years in a 19-year cycle, and months. The latter arrangement is found in Bonfils’s Six Wings for solar and lunar motions only, whereas in his Tables for 1340, this arrangement applies to all planets. Notably absent are tables for the trigonometric functions, etc., that are generally found in such sets of astronomical tables. (shrink)

In 1675, Burchard de Volder became the first university physics professor to introduce the demonstration of experiments into his lectures and to create a special university classroom, The Leiden Physics Theatre, for this specific purpose. This is surprising for two reasons: first, early pre-Newtonian experiment is commonly associated with Italy and England, and second, de Volder is committed to Cartesian philosophy, including the view that knowledge gathered through the senses is subject to doubt, while that deducted from first principles is (...) certain. On the surface, it is curious that such a man would bring experiments to university physics. After all, in demonstrating experiments to his students, he was teaching them through their senses, not reason. However, if we consider the institutional context of de Volder’s teaching, we come to see de Volder’s Cartesian experimentalism as representative of a certain form of pre-Newtonian Dutch Cartesian science, as well as part of a larger tradition of teaching through observation at the University of Leiden. Considering de Volder’s institutional context will help us see that de Volder’s experimentalism was not in spite of his Cartesianism, but motivated by it. This paper will describe de Volder’s physics curriculum, the Theatre in which it was taught and how his work predates similar efforts in other European Universities. The second part will consider three aspects of the culture at the University of Leiden: a tradition of teaching through observation, a particular reception of Cartesianism, and an eclectic approach to the New Philosophy. The concluding portion shows how de Volder would have understood his enterprise in Cartesian terms. (shrink)