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Napier, Fermat, Descartes
In seventeenth century mathematics motion is everywhere. Napier’s definition of the logarithm is based on an exponentially decelerating motion. When...
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Applications of Inversive Geometry
In Chapters 1 and 2 , we studied the properties of linear...
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Relationships between Mathematics and Art in Their Intellectual History - Reflections According to Max Bense
The research on the interpretation of mathematics as part of the sciences of mind, introduced as ‘Geisteswissenschaften’ in the German philosophy,...
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What Happens, from a Historical Point of View, When We Read a Mathematical Text?
The history of mathematics can be read in two ways. On the one hand, unlike the history of physics, it does not proceed by conjectures and...
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Some Problems in the History of Modern Mathematics
In this essay I propose five problems for historians of mathematics that call for new or improved historical treatments of modern mathematics. Many...
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Construction of Hyperbolic Geometry
We have carefully studied the properties of linear fractional transformations on the Euclidean plane; it is now time to look elsewhere. There are...
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Ontology in the History and Philosophy of Mathematical Practice: An Introduction
This very short introduction will first outline how ontological investigations and questions of practice go together. The second section will bring...
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What Happens, from a Historical Point of View, When We Read a Mathematical Text?
The history of mathematics can be read in two ways. On the one hand, unlike the history of physics, it does not proceed by conjectures and...
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Ontology in the History and Philosophy of Mathematical Practice: An Introduction
This very short introduction will first outline how ontological investigations and questions of practice go together. The second section will bring...
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A brief history of points at infinity in geometry
In this chapter we give a brief historical overview of the concept of points at infinity in geometry and the subsequent introduction of homogeneous...
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Transformational Geometry
Section 5.5 presented background information for Pieri’s use of transformational methods in his pioneering axiomatization of projective geometry,...
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The History and Philosophy of Mathematical Practice: From Origins to Natural Historians/Philosophers – A Conversation
In this chapter, the authors engage in a dialogue on what constitutes mathematical practice from pre-Socratic Greeks onto the advent of natural...
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Pieri and Projective Geometry
Projective geometry can be described as the geometry of the straightedge, in comparison with Euclid’s geometry of straightedge and compass.
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A Brief History of Elliptic Functions
This chapter sketches the historical development of elliptic functions.
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History of Knot Theory from Gauss to Jones
In 1867, Lord Kelvin, motivated by Tait’s method of producing vortex smoke rings, came up with the vortex atom theory. He hypothesized that atoms...
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The History and Philosophy of Mathematical Practice: From Origins to Natural Historians/Philosophers: A Conversation
In this chapter, the authors engage in a dialogue on what constitutes mathematical practice from pre-Socratic Greeks onto the advent of natural...
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The Ghost and the Spirit of Pythagoras
This chapter introduces the concept of radical Pythagorean mathematics, as part of mathematical modernism, which emerged around 1900 and extends to...
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Real Analytic Plane Geometry
Among the few choices of systems of axioms to construct a geometric model of the plane (for example, via Euclid or Hilbert) we take the least...
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Carnot’s theory of transversals and its applications by Servois and Brianchon: the awakening of synthetic geometry in France
In this paper we discuss in some depth the main theorems pertaining to Carnot’s theory of transversals, their initial reception by Servois, and the...
