Almagest

L’anneau astronomique de Philippes est un cadran solaire portable de hauteur de petites dimensions qui est utilisable pour quatre lieux (Vienne, Rome, Rhodes, Alexandrie). Daté du début du IV^e siècle de notre ère, c’est le seul exemplaire connu de ce type, à l’heure actuelle, datant de l’Antiquité. Alors que l’on croyait jusque dans les années 1980 que ce type d’instrument avait été inventé à l’extrême fin du Moyen âge ou au tout début de la Renaissance, sa découverte a confirmé que les cadrans portables antiques, dont l’ensemble du corpus représente aujourd’hui une trentaine d’exemplaires, sont très élaborés. On se propose ici pour la première fois d’étudier le fonctionnement de cet anneau astronomique et d’estimer sa précision.

The astronomical ring of Philippi is a small portable altitude-based sundial that can be used for four locations (Vienna, Rome, Rhodes, Alexandria). Dated at the beginning of the 4th century AD, it is the only sample of this type known at present dating from Antiquity. While it was believed until the 1980s that this type of instrument had been invented at the very end of the Middle Ages or at the very beginning of the Renaissance, its discovery confirmed that ancient portable sundials, which the whole corpus today represents about thirty samples, are very elaborated. We propose here for the first time to study the operation of this astronomical ring and to estimate its precision.

The astronomical calendar Qizheng Tuibu, issued in 1477 in China, has played a very important role in the scientific exchanges and cooperation between the Mediaeval Islamic and the Chinese astronomers and has been used for the predictions of the solar and lunar eclipses for more than 270 years. The Ptolemaic model for the motion of the Sun has been introduced in the Qizheng Tuibu with the double eccentricity of 0.0351295, and to the other two imperial calendars of the early period of the Qing Dynasty (1644-1911), Xiyang Xinfa Lishu (1645) with 0.03584 and Yuzhi Lixiang Kaocheng (1724) with 0.0358416. The model for the motion of the Moon in Almagest has been applied in the Qizheng Tuibu with different underlying parameters, and the maximum values for the equation of Center, the equation of Anomaly, Increment, Proportion and the Lunar latitude are different from that of the Ptolemaic tradition, Maragha and Samarkand Observatories.

Nicolaus Mulerius (1564-1630) was nominated in 1614 at the newly created University of Groningen as professor of Mathematics and Medical Science. His favorite topic concerned “mathematics” which, in practice, implied astronomy. In due course he published a textbook of astronomy (1616) and a new edition of Copernicus’ epochal De revolutionibus, the third since 1543 and the first annotated version (1617). Defending Copernicus at the new University -that is: at a University meant to produce ministers for the Reformed Church and therefore bound to the word if not the letter of the Bible- required quite some diplomatic skills. So Mulerius took care to have his new edition of Copernicus prefaced by the founder of the University, Ubbo Emmius, a beacon of Calvinist orthodoxy, while inventing various ways to subtly manifest his predilection without being “unmasked”. This attitude may be called “honorable dissimulation”. There was indeed all reason to be careful since -well-paying- theology students, not only Dutch Calvinists but also Lutherans from the German lands, constituted the core of the University’s population. As a matter of fact, in sticking to the letter of the Bible the Groningen theologians did not give way to their Roman-Catholic colleagues of the Curia in Rome. Mulerius’ “honorable dissimulation” is all the more remarkable. The discovery of a unique copy of the auction sale catalog of Mulerius’ private library (1646) made it possible, in this connection, to shed a more revealing light on his astronomical stance.

Mathematical History, mainly the History of Mathematics in Brazil has substantiated the proposition addressed in the present study, namely: conducting a historical-mathematical investigation about Vector Calculus introduction in Brazil. A brief historical contextualization about Vector Calculus emergence and development, as well as about the important features of it and their contributions to the formalization and adoption of the globally valid system is herein performed. This subject was firstly introduced in Brazil by Professor Theodoro Augusto Ramos (1895-1935) as a discipline in the Engineering courses at Polytechnic School of Sao Paulo, back in 1926. This theme opened room for two publications, one of them was written in Portuguese (1927) and the second one was written in French (1930) and published by a renown French publisher at the time. Back in the 1920s and 30s, this theme was a novelty in Brazil; however, other publications about the same subject have emerged around the country − this finding evidenced Brazilian researchers’ interest in it. Therefore, the aim of the present research is to contribute to fulfill the remaining gaps in the history of mathematics in Brazil.

This work, which comes from a specialist, not in the history of science, but in the history of language and translation, proposes to present the corpus of published translations of European scientific works as well as their place in the translation phenomenon of the Neo-Hellenic Enlightenment. It focuses in the translated languages, and address some questions and examples concerning scientific terminology. During the Neo-Hellenic Enlightenment, translations multiplied in general and, in particular, in the field of sciences. The scientific books that were published were for the most translations, synopses, paraphrases or compilations of Western works, especially “Modern”. Translations were made from original works written in Latin, French and other European languages. At the same time, problems arose concerning the language of translations and terminology. Greek scholars oscillated between the learned language and the common language used by translators who desired to be understood by a large audience, while the translation of terms raised many questions. Translations of scientific books were usually faithful to the original; in some cases translators took some liberties, which consisted in abbreviating chapters, adding additional details and comments or footnotes. In order to enrich Greek language, the translators rejected terms of foreign origin and look for Greek correspondents, drawn from “the rich ancestral reserve”, or proposed the creation of neologisms in accordance with the nature of the Greek language.

Ce travail, qui vient d’un spécialiste, non de l’histoire des sciences, mais de l’histoire de la langue et de la traduction, se propose de présenter le corpus des traductions éditées des œuvres scientifiques européennes ainsi que leur place dans le phénomène de traduction de l’époque des Lumières néohelléniques ; il s’intéressera plus particulièrement aux langues traduites, et il abordera quelques questions et exemples concernant la terminologie scientifique. Au cours des Lumières néohelléniques les traductions se multiplient en général et, en particulier, dans le domaine des sciences. Les livres scientifiques qui sont édités sont dans leur majorité des traductions, des abrégés, des paraphrases ou des compilations des ouvrages occidentaux, surtout « modernes ». Les traductions sont réalisées à partir des œuvres originales écrites en latin, en français et en d’autres langues européennes. Dans le même temps, des problèmes se posent en ce qui concerne la langue des traductions et la terminologie. Les érudits grecs oscillent entre la langue savante et la langue commune, utilisée par les traducteurs qui désirent d’être compris d’un large public, tandis que la traduction des termes soulève de nombreuses questions. Les traductions des livres scientifiques sont d’ordinaire fidèles à l’original ; dans certains cas elles prennent quelques libertés qui consistent en l’abréviation de chapitres, l’ajout de précisions supplémentaires et de commentaires ou de notes de bas de page. Afin d’enrichir la langue, les traducteurs refusent les termes d’origine étrangère et recherchent des correspondants grecs, puisés dans « la riche réserve ancestrale », ou proposent la création de néologismes en accord avec la nature de la langue grecque.