scholarly journals The book as instrument: craft and technique in early modern practical mathematics

BJHS Themes ◽  
2020 ◽  
Vol 5 ◽  
pp. 111-129
Author(s):  
Boris Jardine
Keyword(s):  
Early Modern ◽  
Mathematical Practice ◽  
Care Needs ◽  
Practical Mathematics ◽  
Extract Information

AbstractEarly modern books about mathematical instruments are typically well illustrated and contain detailed instructions on how to make and use the tools they describe. Readers approached these texts with a desire to extract information – and sometimes even to extract illustrations which could be repurposed as working instruments. To focus on practical approaches to these texts is to bring the category of ‘making’ to the fore. But here care needs to be taken about who could make what, about the rhetoric of craft, and about the technique of working with diagrams and images. I argue that we should read claims about making instruments cautiously, but that, conversely, we should be inquisitive and open-minded when it comes to the potential uses of printed diagrams in acquiring skill and knowledge: these could be worked on directly, or cut out or copied and turned into working instruments. Books were sites of mathematical practice, and in certain disciplines this was central to learning through doing.

A Priority and Application: Philosophy of Mathematics in the Modern Period

2009 ◽  
Author(s):  
Lisa Shabel
Keyword(s):  
Early Modern ◽  
Mathematical Reasoning ◽  
Philosophy Of Mathematics ◽  
Mathematical Practice ◽  
Natural World ◽  
Pure Mathematics ◽  
Philosophical Account ◽  
Mathematical Ontology ◽  
To Come ◽  
Modern Mathematics

The state of modern mathematical practice called for a modern philosopher of mathematics to answer two interrelated questions. Given that mathematical ontology includes quantifiable empirical objects, how to explain the paradigmatic features of pure mathematical reasoning: universality, certainty, necessity. And, without giving up the special status of pure mathematical reasoning, how to explain the ability of pure mathematics to come into contact with and describe the empirically accessible natural world. The first question comes to a demand for apriority: a viable philosophical account of early modern mathematics must explain the apriority of mathematical reasoning. The second question comes to a demand for applicability: a viable philosophical account of early modern mathematics must explain the applicability of mathematical reasoning. This article begins by providing a brief account of a relevant aspect of early modern mathematical practice, in order to situate philosophers in their historical and mathematical context.

Jacques Rohault and Cartesian Experimentalism

2019 ◽  
pp. 387-401
Author(s):  
Mihnea Dobre
Keyword(s):  
Early Modern ◽  
Intellectual Development ◽  
Natural Philosophy ◽  
Early Modern Period ◽  
Modern Period ◽  
Fresh Perspective ◽  
Practical Mathematics ◽  
One Year ◽  
Mature Work ◽  
Early Activity

This chapter explores the intellectual development of Jacques Rohault—although not considered one of the leading figures of the early modern period, well known among historians of science. It attempts to evaluate Rohault’s Cartesianism and to present it in a more nuanced manner than it is usually illustrated in the literature. Focusing on his mature work, published only one year before his death in 1672, but also referring to his earlier activities in Paris and to the publication of his posthumous works, the chapter argues that his “Cartesianism” came rather late in his thinking, while his early activity concerns mathematics and mechanics. The reading endorsed in this chapter opens a fresh perspective on Rohault’s experimentalism, suggesting a transition from practical mathematics to Cartesian natural philosophy.

Johannes Kepler and the Exploration of the Weight of Substances in the Long Sixteenth Century

2020 ◽  
Vol 25 (4) ◽  
pp. 328-359
Author(s):  
Cesare Pastorino
Keyword(s):  
Sixteenth Century ◽  
Specific Gravity ◽  
Early Modern ◽  
Experimental Research ◽  
Francis Bacon ◽  
Johannes Kepler ◽  
History Of ◽  
Practical Mathematics ◽  
Natural Philosophers ◽  
Extensive List

Abstract Numerous early modern experimentalists, including Galileo Galilei, Francis Bacon and Thomas Harriot, viewed one seemingly humble principle – that at a given volume, different substances can be identified by their particular weight, or specific gravity – as a fundamental key to the understanding of nature in general. Johannes Kepler’s Messekunst Archimedis of 1616 contains a striking summary of the experimental research on specific gravities in the long sixteenth-century. Counting himself amongst an extensive list of authors interested in this problem, Kepler mentions not only natural philosophers or mathematicians interested in Archimedes. His account surprisingly includes humanists, instrument makers, antiquarians and assayers. Received histories of specific gravities often focus on antecedents of modern disciplinary concepts and methodologies, where instead, Kepler’s account suggests the existence of a heterogeneous group of early modern experts involved in experiments on the quantification of matter, at the intersection between the history of science, practical mathematics and the humanities.

Geometry in Context in the Sixteenth Century: the View From the Museum

2002 ◽  
Vol 7 (3) ◽  
pp. 214-230 ◽  
Author(s):  
Jim Bennett
Keyword(s):  
Sixteenth Century ◽  
Natural Philosophy ◽  
Mathematical Practice ◽  
Historical Significance ◽  
Practical Mathematics

AbstractThis paper examines the discrepancy between the attitudes of many historians of mathematics to sixteenth-century geometry and those of museum curators and others interested in practical mathematics and in instruments. It argues for the need to treat past mathematical practice, not in relation to timeless criteria of mathematical worth, but according to the agenda of the period. Three examples of geometrical activity (cartography, surveying and warfare) are used to illustrate this, and two particular contexts (the wider world of human affairs and the discipline of natural philosophy) are presented in which mathematical practice localised in the sixteenth century takes on a special historical significance.

scholarly journals Alligation Alternate and the Composition of Medicines: Arithmetic and Medicine in Early Modern England

2005 ◽  
Vol 49 (3) ◽  
pp. 299-320 ◽  
Author(s):  
Alvan Bregman
Keyword(s):  
Seventeenth Century ◽  
Early Modern ◽  
Early Modern Period ◽  
Early Modern England ◽  
Medical Applications ◽  
Modern Period ◽  
Practical Mathematics ◽  
Set Up ◽  
Mathematical Literature

Practical mathematics in the early modern period was applied to such fields as astronomy and navigation; cartography and surveying; engineering and military arts, including gunnery; and especially banking and mercantile trade. Those who have written about practical mathematics make no mention of medical applications in their surveys, although there were many cases where physicians set up as mathematical practitioners. This article examines medical applications found in practical mathematical literature up to the end of the seventeenth century in England.

The Senses of Mixed Mathematics

2018 ◽  
Author(s):  
Richard Oosterhoff
Keyword(s):  
Early Modern ◽  
Mathematical Practice ◽  
Sensory Experience ◽  
Cutting Edge ◽  
Close Attention ◽  
Renaissance Mathematics ◽  
The Senses

How did engagement with the new printed book reshape early modern disciplines? This chapter considers the rapidly changing area of Renaissance mathematics, focusing on two ‘mixed’ mathematical disciplines, cosmography and music. In cosmography, the new paratexts transformed a medieval standby, Sacrobosco’s Sphere, into a cutting-edge handbook that taught students the procedures of calculation. In music, Lefèvre’s sensory experience of sound prompted him to adopt new geometrical tools to solve old arithmetical problems. In both cases, a close attention to the roles of visualization, touch, and hearing in mathematical practice prompted a distinctive approach to the printed page, shifting the very structures of the mathematical disciplines. The underlying mental habits such books were intended to inculcate can be traced through the margins of Beatus Rhenanus’ mathematical books.

The Heavens Inscribed: the instrumental poetry of the Virgin in early modern France

2008 ◽  
Vol 42 (2) ◽  
pp. 161-185 ◽  
Author(s):  
MICHAEL WINTROUB
Keyword(s):  
Early Modern ◽  
Natural Philosophy ◽  
Early Modern Period ◽  
Virgin Mary ◽  
Specialized Knowledge ◽  
Early Modern France ◽  
Disciplinary Boundaries ◽  
Modern France ◽  
The Status ◽  
Practical Mathematics

AbstractThe expert in the early modern period was frequently looked upon with suspicion. Though expertise was associated with specialized knowledge and skill, it was also associated with cunning, deception and social climbing. Indeed, such knowledge threatened well-defined and time-honoured social and disciplinary boundaries. This was certainly the case with practical mathematics, which was considered by many to be an inferior grade of knowledge, especially when compared with natural philosophy and theology. This spawned numerous attempts to elevate the status of practical mathematics and to lend legitimacy to its practitioners. This article focuses on one such attempt, that of an early sixteenth-century French cosmographer–explorer–poet named Pierre Crignon. Crignon participated in voyages of exploration and was renowned as a cosmographer and navigator, but his contemporaries perhaps best knew him as a poet. The paper examines how Crignon attempted to bring together and legitimate the disparate forms of his expertise as a navigator, cosmographer, humanist poet and theologian through the multivalent medium of his poetry, and in particular through a poem comparing the Virgin Mary to the astrolabe.

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