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This paper examines how a certain threshing machine was developed and improved by Jobst Heinrich Voigt and Gottfried Wilhelm Leibniz between 1699 and 1700. While this machine was based on various mechanical principles and instruments, including the pinned drum mechanism first noted by Georg Philipp Harsdörffer, it was later reconceptualized as a 'mathematical' machine. I claim that such a positioning was not unique to this machine, but part of a wider movement during the 18th century that considered various artisanal instruments as mathematical, as well as agricultural and artisanal knowledge as scientific. Examining the development and subsequent reception of this machine, I show that during the first decades of the 18th century these conceptions gave rise to a double image of this machine, and hence of agricultural knowledge in general: on the one hand, this machine was considered as more efficient and productive (while still in need of improvement); on the other hand, it was viewed, either implicitly or explicitly, as something that should be studied by mathematicians, thus reflecting a changing image of mathematics., Competing Interests: Declaration of competing interest No competing interests to declare., (Copyright © 2024 Elsevier Ltd. All rights reserved.)

In 1887 Helmholtz discussed the foundations of measurement in science as a last contribution to his philosophy of knowledge. This essay borrowed from earlier debates on the foundations of mathematics (Grassmann/Du Bois), on the possibility of quantitative psychology (Fechner/Kries, Wundt/Zeller), and on the meaning of temperature measurement (Maxwell,Mach.). Late nineteenth-century scrutinisers of the foundations of mathematics (Dedekind, Cantor, Frege, Russell) made little of Helmholtz's essay. Yet it inspired two mathematicians with an eye on physics (Poincaré and Hölder), and a few philosopher-physicists (Mach, Duhem,Campbell). The aim of the present paper is to situate Helmholtz's contribution in this complex array of nineteenth-century philosophies of number, quantity, and measurement., (2003 Published by Elsevier Ltd.)