20190725T090020190725T1145Europe/AmsterdamPractical Mathematics in Early Modern Europe
During the early modern period, the mathematical sciences dramatically upgraded its status. It went from having a secondary role and ancillary status in the mid 16th century, up to be considered the most powerful tool of scientific research by the turn of the 18th century. As recognized by a large historiography, these transformations cannot be accounted for in terms of internal developments. It is necessary to look outside universities and scholarly mathematics, taking into account the broader social context, in particular the role of social practices of arithmetic, geometry and metrology. These provided essential impulses that help explain the momentous conceptual and methodological transformations mathematics went through in early modern Europe. Our hypothesis, based on several case studies, is that a general mathematization of civil life took place. Elementary arithmetic and geometry became ubiquitous for merchants, gaugers, architects, instrument-makers and engineers, with growing impact on education practices and far-reaching epistemological consequences. To track this evolution, one can study the material culture of practical mathematics, i.e. objects closely linked to what people socially do, both in the higher court culture and in the artisan's workshops. New literary forms developed, such as practitioners commonplace books, booklets and other forms of modern teaching material, printed metrological tables and comptes faits to make mathematics readily usable. We hope to show that these widespread practices, backed by social and political authority, help explain the success of mathematical values (of precision, "application" of mathematics, computation and forecasting) and of new mathematical concepts (most notably "arithmetical" ratios and proportionality), a ...
Drift 13, Rm. 003History of Science Society 2019meeting@hssonline.org
During the early modern period, the mathematical sciences dramatically upgraded its status. It went from having a secondary role and ancillary status in the mid 16th century, up to be considered the most powerful tool of scientific research by the turn of the 18th century. As recognized by a large historiography, these transformations cannot be accounted for in terms of internal developments. It is necessary to look outside universities and scholarly mathematics, taking into account the broader social context, in particular the role of social practices of arithmetic, geometry and metrology. These provided essential impulses that help explain the momentous conceptual and methodological transformations mathematics went through in early modern Europe. Our hypothesis, based on several case studies, is that a general mathematization of civil life took place. Elementary arithmetic and geometry became ubiquitous for merchants, gaugers, architects, instrument-makers and engineers, with growing impact on education practices and far-reaching epistemological consequences. To track this evolution, one can study the material culture of practical mathematics, i.e. objects closely linked to what people socially do, both in the higher court culture and in the artisan's workshops. New literary forms developed, such as practitioners commonplace books, booklets and other forms of modern teaching material, printed metrological tables and comptes faits to make mathematics readily usable. We hope to show that these widespread practices, backed by social and political authority, help explain the success of mathematical values (of precision, "application" of mathematics, computation and forecasting) and of new mathematical concepts (most notably "arithmetical" ratios and proportionality), as well as the changing status of early modern mathematical sciences.
Organized by Thomas Morel
Using Euclid in a Practical Context: Claude Richard’s Course on Sectors at the Imperial College (Madrid, ca. 1656)View Abstract Organized SessionMathematics09:00 AM - 09:30 AM (Europe/Amsterdam) 2019/07/25 07:00:00 UTC - 2019/07/25 07:30:00 UTC
Father Claude Richard (Ornans 1589 – Madrid 1664) was professor of mathematics at the Jesuit Imperial College in Madrid (1627-1767) from 1630 until his death. He published Euclides elementorum geometricorum libros tredecim Isidorum et Hypsidem et Recentiores de Corporibus Regularibus, et Procli propositiones geometricas (Antwerp, 1645), and Apollonii Pergaei Conicorum libri IV cum commentariis Claudii Richardi (Antwerp, 1655). Furthermore, the Spanish Royal Academy of History keeps a legacy of eleven manuscript files –titled Mathesis varia– by Richard, together with eighty factitious volumes containing Jesuits’ manuscripts on mathematics and physics. Among these, two draft copies of the course on the construction and use of sectors taught by Richard around 1656 have been identified, one written by Richard himself, the other by one of his students. Richard claimed that the whole practical geometry consisted of the brief and easy use of sectors, an instrument first invented by the Flemish Michel Coignet, he said. However, his “Treatise on the division of the twelve diverse straight lines of sectors, with their practical use in practical geometry, and also the proofs of these divisions and the use” was not only concerned with the brief and easy instrumental practice of geometry. It also insisted on demonstrating the solid Euclidean foundations of this practice, which would justify the numerical consideration of continuous magnitudes as quantities –accepting a margin of error sensorially imperceptible and irrelevant for the purposes of application.
Conceptual Change in Early Modern Practical GeometriesView Abstract Organized SessionMathematics09:30 AM - 10:00 AM (Europe/Amsterdam) 2019/07/25 07:30:00 UTC - 2019/07/25 08:00:00 UTC
As recognized by a growing body of literature, most conceptual and methodological shifts in early modern mathematics cannot be accounted for in terms of internal theoretical developments. On the contrary, this literature suggests, social and institutional contexts and the social practices of arithmetic, geometry, and metrology provide inputs that may explain the momentous transformations mathematics went through in early modern Europe. This paper analyses some 16th-century practical geometry books that contain theoretical innovations — as compared to contemporary authoritative editions of Euclid’s Elements. It pays particular attention to old notions (such as ratio and curve) that were newly defined, to new ideas (such as measure) that were introduced as if they were old ones, and to new methods (such as the use of material instruments) that were legitimized in practical geometry books. By paying attention to them the paper aims to document ways in which mathematical innovations “sneaked in” so to speak into the established, ordinary, authoritative body of mathematical results. The emphasis is not only on documenting new concepts and methods connected to social practices, but also on analyzing how practice and practical tools added legitimacy and authority to new concepts and new methods.
Writing, Drawing, and Preaching Geometry in the Early Modern German MinesView Abstract Organized SessionMathematics10:15 AM - 10:45 AM (Europe/Amsterdam) 2019/07/25 08:15:00 UTC - 2019/07/25 08:45:00 UTC
In the sixteenth and seventeenth centuries, mathematical sciences played an increasingly important role in Western societies. Most historical accounts try to understand how the study of nature came to use mathematical methods and how mathematical concepts and tool became the standard tool for scholars. A more fundamental and yet lesser-known shift happened outside of the scholarly world. Practical mathematics, understood as a set of basic skills in arithmetic and geometry, became ubiquitous in European civic life for officials, engineer and artisans of all kinds. Early modern mines build a perfect case study for this hypothesis, both given their crucial economic importance and since they are considered a crucible of modern technical rationality. I will analyze the growing importance and the public nature of mathematical arts in the German mining states. Scholars observed practitioners and then wrote about geometria subterranea. Numerous sketches were drawn to illustrate the surveying methods that were used. Computing schools and teaching contracts attest of a lively and efficient tradition of practical teaching. Even sermons routinely presented to a general audience the essential features and principles of geometric operations. Surveying was a public practice whose geometrical character would lend gravitas and accuracy to legal decisions. These ubiquitous uses greatly heightened a public recognition of the efficiency of mathematics.
Michael Coignet: A Mathematical Practitioner in 16th Century AntwerpView Abstract Organized SessionMathematics10:45 AM - 11:15 AM (Europe/Amsterdam) 2019/07/25 08:45:00 UTC - 2019/07/25 09:15:00 UTC
Around 1550 Antwerp was a vibrant port. Its many schools catered for the many companies, its Beurs was one of the first stock markets of the world, its printers published books on all subjects. Ships travelled to all parts of Europe, the Baltic, Italy, Scotland, the Azores with merchants dreaming of sailing even further. This optimistic view was shattered by the Iconoclastic Revolt of 1566 and the intransigence of Philip II to make concessions to the protestants. First and foremost among Antwerp’s mathematicians was Michiel Coignet, schoolmaster, winegauger, instrument maker and mathematician to the Archdukes. From the 1570s onwards he kept notes on a variety of mathematical subjects. Parts of these notes written between 1576 and 1603 are preserved in the Bibliothèque Nationale in Paris (Ms Néer 56, Est de Michaelis Coigneti 1576). They give an insight not only in mathematical developments but also in some sociological changes. The manuscript shows the relation between pure and applied mathematics. In this talk we will address these topics.
True Solar Motion, Eccentric Parameters, and Clocks as Mathematical Instruments: Tracking Planetary Theory within the Gears of Renaissance AutomataView Abstract Organized SessionMathematics11:15 AM - 11:45 AM (Europe/Amsterdam) 2019/07/25 09:15:00 UTC - 2019/07/25 09:45:00 UTC
Planetary automata, also called planetary clocks, were expensive and rare masterpieces of technical ingenuity designed to show the subtle motion of the heavenly bodies according to Ptolemaic theory. These automata may justly be considered mathematical instruments for a two-fold reason: they manifest a mechanical transposition of mathematical astronomy, and their conception and design required the mastery of practical geometry and trigonometry. They were almost exclusively the reserve of princes and emperors, and within the history of astronomy notice of about a dozen of them has reached us, of which four from the Renaissance survive (in Paris, Vienna, Kassel, and Dresden). This paper presents new research on these instruments, focusing on the two created under the explicit direction of Landgrave Wilhelm IV of Hesse-Kassel around 1560. Passing from the abstract geometrical models described by Ptolemy to a brass mechanism led Wilhelm, his chief “artifex” Eberhard Baldewein, and the roughly dozen craftsmen working under them to use eccentric axles, epicyclic gears, and cogwheels with deliberately uneven toothing. The research described, part of the ongoing project “Deus ex machina,” aims at deducing certain astronomical parameters implicit in Wilhelm’s mechanisms. In particular, the possibility of deriving parameters for the solar eccentricity will be explored in connection with Wilhelm’s own renowned program of astronomical observation. Could it be that a careful analysis of these machines (and the written sources once accompanying them) allows us to witness in their gearing the birth of a new astronomical theory?
Thomas Morel
