Session Chair: Sumner Braund (History of Science Museum, University of Oxford, UK)
Making & doing: reflections on the mathematical cultures of 16th-century instruments
Author: Samuel Gessner
Co-Author: Michael Korey
Jim Bennett left a legacy that continues to influence and inspire museum professionals, cataloguers, science communicators, instrument experts, and many others. For instrument historians alone there are multiple levels of inspiration for the further study of the history and context of the rich corpus of the material heritage of science. Picking up on one, this paper foregrounds Jim’s analysis of 16th-century mathematical instruments. Without doing justice to Jim’s nuanced approach, we might simplify his stance to the statement that such instruments were not as much for ‘knowing’ as for ‘doing’ (1998, 2003). This paper will present a florilegium of early modern mathematical instruments whose functions seem clear, but not the context of their use or intended purpose. These include examples from our own work: a gearwork-driven equatorium conceived by Nicolaus Valerius (1564) and the Circles of Proportion produced by Elias Allen (c. 1630). The catchphrase ‘knowing and doing’ offers a fruitful perspective to solve some open puzzles about them. Following Jim’s understanding that instruments embody specific mathematical cultures helps with this task. Indeed, a large share of mathematical instruments produced and preserved from the 16th century are referred to today, perhaps somewhat euphemistically, as ‘compendia.’ As such, instruments give expression to a collection of knowledge areas, problems, and operations that were once seen as belonging to the repertoire of a single mathematical practitioner and hence coherent, albeit today classified in separate disciplines. Read as historical sources in this way, can instruments serve to sound out the contours of the past mathematical cultures from which they emerged?
Galileo’s Telescope Reassessed: Overlooked Documents and Material Analysis of Item No. MG-2428.
Author: Giorgio Strano
Museo Galileo in Florence owns the only three surviving items connected to Galileo Galilei’s activity as an optician: two complete telescopes and a broken objective lens.
In 2023, in the exigency of making a new and philologically reliable replica of Item No. MG-2428 — i.e. the telescope made by Galileo for the Grand Duke of Tuscany Cosimo II de’ Medici —, the original instrument has been removed from its showcase, partly dismounted, measured and inspected also with the aid of an endoscope. If nothing new has emerged about the optical components — which were thoroughly analyzed in the 1990s by the National Institute of Applied Optics in Arcetri, Firenze —, a number of remarkable facts re-delineate the telescope’s overall structure and story.
On the one hand, two recently published documents indicate the provenance of the telescope tubes designed by Galileo. On the other hand, the material examination of Item No. MG-2428 outlines that the intrinsic structure of such tubes is different from the current interpretation. Finally, in addition to the information already available on the non-originality of this telescope’s ocular lens — which was loose in its housing, then lost, and finally replaced by the end of the 19th century — some historical documents (old pictures) and material elements (puzzling inconsistencies with the expected structure) indicate that the instrument underwent some dramatic modifications in the time lapse between 1860 and 1970.
Johann Friedrich Penther (1693–1749) and his book “Praxis Geometriae”
Author: Petra Svatek
This lecture analyses the book “Praxis Geometriae”, which was written by the German mathematician Johann Friedrich Penther (1693-1749). It deals with surveying instruments and their practical application in the field and thus offers an important teaching aid for cartographers in the production of maps. It was first published in 1732, at a time when surveying was experiencing an enormous boom in large parts of Europe, both in military and in private cartography.
After a brief biography of Penther, the presentation offers a critical analysis of the content of the frontispiece, which contains an allegorical depiction of geometry, the preface and the main text. Which sources did Penther use, how is the methodical procedure for drawing a map explained and how can his explanations be categorised in relation to the works of other authors who also published books on surveying at the same time?
The last part of the lecture is dedicated to the extensively illustrated appendix. Penther shows fictitious and real maps and plans, measuring instruments (compass, astrolabe, quadrant, etc.) and trigonometric figures. Using examples, he explains, among other things, the method of vertical and horizontal measurement and the realisation of the measurement results in a map. While the fictitious maps only show a few details and are used exclusively for learning the surveying method, the map of the German county of Stolberg illustrates the fine art of mapmaking with position and area signatures in a slightly hilly landscape, which was reproduced with hatchings.
Instruments and conflicting views on precision in the late 18th century.
Author: Jan Tapdrup
The late 18th century witnessed considerable disciplinary displacements between natural-/experimental philosophy and practical mathematics. At the same time, the attitude toward measurement and what was meant by precision changed significantly, as can be seen in both literature and instruments.
The diversity and range of the changed attitudes to quantification, precision, and the use of instruments, to what Bernard le Bovier de Fontenelle earlier had termed l'esprit géometrique has been pointed out in The Quantifying Spirit in the Eighteenth Century, edited by Heilbron, Frängsmyr, and Rider (1990).
In this paper, I will firstly address, assess, and qualify the thesis in this book that the later 18th century saw a rapid increase in the range and intensity of application of mathematical methods by looking at the three collections belonging respectively to Jean Antoine Nollet (France), Adam Wilhelm Hauch (Denmark), and Antoine Laurent Lavoisier (France).
I will look at specific instruments and the relative number of instruments in the collections that may be regarded as precision instruments. Supplemented by an analysis of literary sources, I intend to examine to what extent the application of mathematical methods is reflected in scientific instrument collections and how. Secondly, I hope to show how the concept of precision developed epistemologically during this period.
