Abstract
This chapter covers some of the concepts and properties that arise when infinitesimal notions are introduced in the geometry theory. The hyperreal space is shown to have a practical and rich application in geometry. A few theorems and proofs are examined. Also as an important part of this work, some algebraic geometry is developed using hyperreal vectors. This is a definitional approach used to formalize notions from the traditional GTP methods and to verify their basic axioms. We start with a brief review of non-Archimedean geometry.
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© 2001 Springer-Verlag London
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Fleuriot, J. (2001). Infinitesimal and Analytic Geometry. In: A Combination of Geometry Theorem Proving and Nonstandard Analysis with Application to Newton’s Principia. Distinguished Dissertations. Springer, London. https://doi.org/10.1007/978-0-85729-329-9_4
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DOI: https://doi.org/10.1007/978-0-85729-329-9_4
Publisher Name: Springer, London
Print ISBN: 978-1-4471-1041-5
Online ISBN: 978-0-85729-329-9
eBook Packages: Springer Book Archive