7th ESHS Conference Prague 2016

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7th International Conference of the European Society for the History of Science The analysis of BAPP will be based on the analysis of the contents, including advertisements, its public as well as the evolution of its membership and geographic distribution nationwide. The BAPP shows that although sharing some characteristics with other coeval Portuguese medical journals, it naturally presents specific features. As the journal of a nationwide professional association by its very nature BAPP was overtly corporative and provides important clues on how the Portuguese medical profession built its power by regulating the profession and thereby establishing the rules for the legal practice of medicine as the Association oversaw the application of legislation; creating benefits and the basis of a doctors’ welfare system; concomitantly, it contributed to building the doctor’s figure as an intellectual leader in Portuguese society from the standpoint of Lisbon’s doctors, as the city was then undergoing the process of becoming the country’s intellectual centre, in addition to being the political and administrative capital. Keywords: medicine, medical press, Association of Portuguese Physicians, liberal monarchy, First Republic 68
Prague, Czech Republic, 22–24 September, 2016 Symposium 67: Algebra, Humanism and Cultural Policies Organizers: Veronica Gavagna (University of Florence, Florence, Italy), Pier Daniele Napolitani (University of Pisa, Pisa, Italy), Sabine Rommevaux-Tani (CNRS - Université Paris Diderot, Paris, France) At first sight, the history of algebra seems to be completely foreign to the so-called Mathematical Humanism as to content, methodology and social environment. Algebra came from the Arabic culture into the Latin West where it found a fertile ground inside the Italian abacus schools, the institutions that provided the education for the growing middle class. Just in this world of cossist algebra, Tartaglia discovered the solving rules for the cubic equation, the first original result of the Western mathematics with respect to the Ancient Greek mathematics. Subsequently, Cardano’s Ars Magna disseminated the rules for solving formulas of cubic and quartic equations all over Europe and furthermore Bombelli "invented" the complex numbers: apparently, algebra was ready for the ‘symbolic’ revolution without any other external suggestion. On the other side, it seemed that the Renaissance Courts, whose political, economic and cultural influence was dominant at that time, promoted only the restoration of Greek Classics. The mathematical humanism encouraged the reawakening and the reinterpretation of the Archimedean tradition: Luca Valerio and Bonaventura Cavalieri’s reworking of the Archimedean geometry of measure brought it to a higher level of abstraction and the humanist Galileo tried to interpret the Book of Nature in Mathematical terms. In the ‘received wisdom’ of the great part of the scientific literature the previous were considered two separated worlds, both from social and intellectual viewpoint, but are we sure this is correct? We propose to focus the discussion mainly on the following points Did the different cultural policies in Europe (especially in Italy and French) have any influence in the flourishing of mathematical humanism? Could the arabic-abachistic algebraic tradition have the possibility of a further autonomous development in the Late Cinquecento? Could we recognize any kind of relationship between Medieval and Renaissance algebra -- seen by practitioners as a problem solving tool – and the restoration of Classics promoted by influential Courts and humanistic circles? What was the role played by Diophantus and Pappus’ translations in the emergence of Viète’s ars analytica? What was the role played by Viete’s logistica speciosa in the creation of new mathematical objects? Could we recognize a kind of influence of scientific institutions or centre of power in the diffusion of symbolic algebra in the Late Renaissance? Did the Renaissance reworking of the Archimedean geometry influence the emergence of a new concept of ‘mathematical object’ (e.g. the curve-equation of Descartes)? Keywords: History of mathematics, History of Algebra, Humanism, Renaissance History On the interaction between algebra and arithmetics in 11th–13th century Arabic mathematics (ID 224) Eleonora Sammarchi (CNRS, UMR 7219 / Univ. Paris Diderot-Paris 7 / Univ. Paris I, Paris, France) When algebra was founded as a theory for second degree equations, arithmetics was still a sort of practice rather than a properly science. The Egyptian mathematician Abu Kamil (9 th cent) prepared the ground for a fruitful interaction between algebra and arithmetics. In his work, arithmetics could be used as a tool in algebra and gave contents to the new discipline. At the same time, many arithmetical 69
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