Almagest

The models with eccentricities and radius, and the calculation formula underlying in the 10 planetary longitude tables in the Qizheng Tuibu (1477), have been completely outlined. Ptolemaic planetary theory has been applied in the compilation of these tables with slightly revision of the parameters and variables. The first equation (aequatio centri) for the superior planets in the relative tables in the Qizheng Tuibu is the same as q(cm) in Almagest. The values for the first equation for Venus are the same as the solar equation of the center in the Qizheng Tuibu. The model of the first equation for Mercury has the same as Ptolemaic eccentricity but with different radius. The variable for proportion of Saturn is the mean argument of center, of Jupiter, Mars and Venus is the true argument of center, of Mercury is a particular one. The variable for the second equation (aequatio argumenti) p is the true argument of anomaly, different from Ptolemaic selection of the mean argument of anomaly p(am). The same 10 tables from 47^v to 52^r of the Sanjufīnī Zīj (1366), without the columns for q(n+1)-q(n), p(n+1)-p(n) in the Qizheng Tuibu, have been explained.

During Kepler’s time the ephemerides of the longitude of Mars were mainly calculated using the Alfonsine and the Prutenic tables. The error in the prediction of the longitudes was usually about 2 degrees for both, but in some critical situations, it could reach 5 degrees (in singular catastrophic events, as Owen Gingerich labeled them). Kepler’s Rudolphine tables diminish the error to just minutes of arc. Kepler introduced three novelties, all improving Mars’ predictions: 1) he made the orbits elliptical (first law), 2) he replaced the equant point by the area law (second law), and, finally 3) he bisected the orbit of the Earth. James Voelkel and Gingerich analyzed the degree of responsibility that each of Kepler’s novelties has in the improvement of the predictions of Mars’ longitude and suggest that while around 0.5 degree of the error is solved introducing the first two laws, the remaining around 4.5 degrees disappear once you introduce the bisection of the orbit of the Earth. In this paper I will argue that the distribution of the responsibility is actually different: while 0.5 degree must be attributed to the first two laws, only another 0.5 must be attributed to the bisection of the eccentricity of the Earth, and the remaining around 4 degrees are due to an error in the longitude of the apogee. There is evidence that Tycho and Longomontanus had a correct value of the longitude of the apogee before Kepler’s arrival to work with them in Prague. Therefore, it was Tycho and not Kepler who solved the main part of the catastrophe of Mars, even if not the most difficult one.

Nous nous intéressons dans cet article à un épisode de la vie scientifique française de la deuxième moitié de la décennie 1720, à savoir le rejet par l’Académie Royale des Sciences d’un mémoire de la Société Royale des Sciences de Montpellier, écrit à l’issue de la grande aurore boréale de 1726 par François de Plantade, proposant un système basé sur le principe de la circulation de la matière magnétique proche de celui défendu par Edmund Halley, occasionnant une crise institutionnelle sérieuse entre les deux sociétés. Un autre système, proposé par Jean-Jacques Dortous de Mairan au nom de l’Académie parisienne et d’essence profondément cartésienne, est alors en cours d’élaboration, et sera publié au début de la décennie suivante. Nous suggérons que les arguments communiqués à Plantade par différents interlocuteurs parisiens pour justifier le rejet de son mémoire masquent une motivation d’ordre « politique », dans le contexte de pénétration du newtonianisme perçu comme une menace. Nous replaçons cet épisode dans la périodisation proposée par John Bennett Shank de l’escalade du conflit opposant cartésiens et newtoniens dans la première moitié du XVIIIe siècle.

From the middle of the 18^th century on, the central authority in Vienna strove to increase its control over education in the Habsburg lands, attempting to introduce a series of reforms in university education in order to modernize the curricula in lower and higher educational institutions, institutions in which the influence of the Jesuits was predominant until the Society of Jesus’s suppression by the Pope in 1773. A consequence of these reforms was that the teaching of mathematics changed significantly in Habsburg territories between circa 1750 and 1784.

In this paper, we shall survey the content and structure of the course in Elementary Mathematics at the Charles-Ferdinand University in Prague. The teaching of mathematics at this college, which is fairly well documented, represents a fruitful case study for assessing the circulation of modern ideas in mathematical teaching. These ideas were promoted by contemporary authors like Christian Wolff or Nicolas Louis de la Caille, and were assimilated by the local scholarly community.

Since the present study represents no more than a preliminary exploration, our survey will cover only the period running from circa 1750 up to the year 1784. The terminus a quo here marks the publication of the first compendia written by a Jesuit professor from Prague and the terminus ad quem marks the end of Latin as the language of higher education. The switch to German as the official language of teaching introduced important changes, such as the adoption of new German textbooks and the end of Jesuit cultural hegemony even in scientific writings.

F. Longo Auricchio, G. Indelli, G. Leone, G. Del Mastro, La Villa dei Papiri. Una residenza antica e la sua biblioteca (Henk Kubbinga)

Iraklis Katsaloulis, The Prediction of Earthquakes in Greece: Science, politics and public sphere (Η πρόβλεψη των σεισμών στην Ελλάδα: Επιστήμη, πολιτική και δημόσια σφαίρα) (Kostas Tampakis)