Almagest

This work analyzes the phase correlation of the three lunar cycles and the Exeligmos/(Saros) Cycle, after the study of the chapter “About Exeligmos” in “Introduction to the Phenomena” by Geminus. As Geminus reports, each Exeligmos Cycle began on very specific and rare dates, when the Moon was positioned at the starting points of the three lunar cycles: New Moon (Synodic), at Apogee (Anomalistic), and at the Node (Draconic). The extremely large duration of the Annular Solar eclipse occurred on December 22, 178 BC (Saros series 58) marks the start of the “Prominent Saros Cycle Apokatastasis”. The next day, December 23, 178 BC, the Winter Solstice occurred. During these two neighboring dates, the celebration of the religious festival of Isia started in Egypt and Hellenistic Greece. Based on the analysis of the specific position of the Mechanism’s Parapegma events, December 22/23 178 BC appears as the ideal starting date, i.e. functional and representative, in order to calibrate the initial position of the Mechanism’s pointers.

The models with Northern and Southern limits for the superior planets, inclination and slant for the inferior planets, and the calculation formula underlying in the five planetary latitude tables in the Qizheng Tuibu (1477), have been completely outlined. Ptolemaic planetary latitude theory has been applied in the compilation of these tables with slight revision of the parameters and variables, which are implicitly given in the Sanjufīnī Zīj. The planetary latitude tables for five planets in the Qizheng Tuibu are double-argument tables in which the true centrum κ and the true anomaly av are selected as variables. For the superior planets: the Northern latitude β = c5 (κ) × c3 (av)/60, if κ∈[0°, 90°], [270°, 360°]; the Southern latitude - β = c5 (κ) × c4 (av)/60, if κ∈[90°, 270°]. For the inferior planets: Inclination > 0°, if av∈[90°, 270°]; Inclination ˂ 0°, if κ∈[0°, 90°], [270°, 360°]; Slant > 0°, if av∈[0°, 180°]; Slant ˂ 0°, if av∈[180°, 360°]. The latitude of Venus, β = β1 + β2 + β3 = Inclination × cos (κ + 90°) + Slant × cos κ + 0;13° × cos2κ. The latitude of Mercury, if κ∈[0°, 90°] or [270°, 360°], β = β1 + β2 + β3 = Inclination × cos (κ + 270°) + 0.9 × Slant × cos (κ + 180°) - 0;45° × cos2κ; if κ∈[90°, 270°], β = β1 + β2 + β3= Inclination × cos (κ + 270°) + 1.1 × Slant × cos (κ + 180°) - 0;45° × cos2κ. The possible scribal and calculation errors in the above five tables could be revised and corrected.

The intercultural and scholarly interactions among the integral parts of the vast mosaic of Ottoman population that stretched over three continents, namely South East Europe, Asia Minor, Caucasus, the Levant, North Africa, part of the Gulf countries, Hejaz and Yemen, are still undiscovered sites waiting for interdisciplinary and multidisciplinary research. This diverse mosaic of population consisted of various communities of different ethnic and religious backgrounds, e.g. Turks, Arabs, Greeks, Armenians, Jews, Albanians, Hungarians, Serbs, Croatians and Bosnians. Today, thanks to the publication of the eighteen volumes of the History of Ottoman Scientific Literature and the two volumes of The Ottoman Scientific Heritage, we are better equipped to discover, study and explain aspects of these intercultural and scholarly interactions. There are two main categories to be observed in these uncharted waters, the first interaction is among three Islamic languages (Turkish, Arabic and Persian), while the second includes translations from other languages to Turkish and Arabic. In this second category, we observe two subgroups, the first subgroup contains translations from Ancient Greek and Latin to Arabic and Turkish; the second subgroup features a vast number of translations from modern European languages to Turkish and Arabic.

Meanwhile the ethnic backgrounds of scholars from different religious communities e.g., Muslim, Orthodox Greek, Orthodox Armenian, Jews, provides insights into the different processes of interaction among scholars, the production and exchange of knowledge, and the movement of ideas during the six-century long history of the Ottoman Empire. This is certainly an unexplored field of research waiting for the cooperation of modern scholars with diverse training.

Cette étude s’appuie sur des journaux d’observations originaux et examine les raisons et la manière dont les observations météorologiques se mettent en place au sein d’un observatoire à l’époque moderne en examinant le cas de l’Observatoire de Paris dans ses premières décennies de fonctionnement. Il montre l’existence de causes multiples à l’origine de tels relevés, étudie les pratiques, recense les instruments, pose la question de l’appartenance de la météorologie aux sciences de l’observatoire à cette époque. Ces causes sont spécifiques à l’histoire même de l’institution, relèvent de demandes du pouvoir, s’inscrivent dans des recherches scientifiques de l’époque, physique et astronomique. L’observatoire apparaît en météorologie comme un lieu édictant normes et pratiques, au centre de réseaux d’observations, un bâtiment-instrument au même titre qu’il l’est pour l’astronomie.

Nous analysons les tenants et les aboutissants du débat scientifique très intense qui s’est tenu dans la communauté savante européenne au tournant du XVIIIe siècle autour du paradoxe que représentait, pour ceux qui voyaient dans la montée des vapeurs et des exhalaisons et leur résolution en pluie la cause première des variations du baromètre, le fait que le baromètre soit généralement bas quand le ciel est chargé de nuages et le temps à la pluie, et au contraire plutôt haut quand le temps est beau et le ciel clair. Nous donnons les éléments du contexte de la pensée de l’époque en la matière, détaillons les idées alors dominantes sur le lien entre pluie et pression de l’air, présentons les observations confortant les partisans des vapeurs et de la pluie comme cause première des variations du baromètre, ainsi que leur propositions, expériences de laboratoire à l’appui, pour résoudre le paradoxe.

The enlargement of scientific literacy in 19th-20th century Europe involved both new components of educational systems (primary schools and technical/vocational schools), and vulgarization of the sciences. We reconstruct the design of an intuitive, natural geometry curriculum by Jules Dalseme (1845-1904), who became professor of Mathematics at the Paris educational institution for prospective primary school teachers Ecole Normale de la Seine in 1872. Dalseme’s educational outlook is rooted in his engineering education (Ecole Polytechnique) and reflects the interplay between Euclidean geometry and practical geometry for the arts and crafts. He took advantage of the concrete and reasoned geometry put forward by the engineer Edouard Lagout (1820-1884) to train workers (but also for general primary education), inspired by the activities in the construction yard. Geometry was a path for the initiation to science, as well as useful knowledge for the arts and crafts: old and new purposes of elementary schools emerge in Dalseme’s textbooks for elementary school as crucial aspects for developing a mathematics for the multitude in the late modern age in Europe. His contribution is part of a more general trend going beyond numeracy and measure recipes in school mathematics and aimed to educate “reasoning citizens” and to help the nation social and economic progress.