Volume Basic Euclidean Geometry by Rothe Franz (15 results)

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Taschenbuch. Condition: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - The present second volume starts with Euclidean geometry, and the text gets a more educational and even more elementary flavour. Here I start with Thales theorem about the angle in a semicircle, and continue with Euclid's related theorems about angles in a circle.The most simple parts of the Euclidean geometry are given in detail, as well as the later parts about similarity, and finally area in Euclidean geometry with the theorem of Pythagoras and trigonometry, and the measurement of the circle. Too, the lens equation from geometrical optics is treated.In several sections is recalled the strictly modern view of the first volume, beginning with Hilbert's axioms from the Foundations of Geometry. After some discussion of logic and axioms in general, we go on with a short section about incidence geometries in two dimensions.The theorems from neutral geometry which have been proved in the first volume and are needed again, are cited.The relation of analytic and synthetic geometry is treated on Hilbert's rigorous account.…

Taschenbuch. Condition: Neu. Volume II | Basic Euclidean Geometry | Franz Rothe | Taschenbuch | A Course in Old and New Geometry | Englisch | 2025 | Franz Rothe | EAN 9798231094943 | Verantwortliche Person für die EU: Libri GmbH, Europaallee 1, 36244 Bad Hersfeld, gpsr[at]libri[dot]de | Anbieter: preigu Print on Demand. …

Buch. Condition: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - The present first volume begins with Hilbert's axioms from the emph{Foundations of Geometry}.After some discussion of logic and axioms in general, incidence geometries, especially the finite ones, and affine and projective geometry in two and three dimensions are treated. As in Hilbert's system, there follow sections about the axioms of order, and congruence in neutral geometry, the axioms of measurement and of completeness, and deviating from Hilbert, about circles.The insight of independence of the parallel axiom leaves many open roads to pursue,but the desire to develop a natural as well as completely axiomatic system remains. In this context, the classification of Hilbert planes into three types,---as semi-euclidean, semi-elliptic or semi-hyperbolic, known as the uniformity theorem is a important step beyond Euclid. A further step is the introduction of the axiom of the unbounded opening of an angle. In the spirit of Hilbert, a completely axiomatic theory of area in neutral geometry is set up, before branching into the cases of Euclidean, or semi-hyperbolic, or semi-elliptic geometry.Finally, the attention has to focus of Euclidean geometry. The text gets a more educational and even more elementary flavor. Here I start with Thales theorem about the angle in a semicircle, and continue with Euclid's related theorems about angles in a circle.The most simple parts of the Euclidean geometry are given in detail, as well as the later parts about similarity, and area in Euclidean geometry with the theorem of Pythagoras andtrigonometry, and finally the measurement of the circle.…

Taschenbuch. Condition: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - The present first volume begins with Hilbert's axioms from the emph{Foundations of Geometry}.After some discussion of logic and axioms in general, incidence geometries, especially the finite ones, and affine and projective geometry in two and three dimensions are treated. As in Hilbert's system, there follow sections about the axioms of order, and congruence in neutral geometry, the axioms of measurement and of completeness, and deviating from Hilbert, about circles.The insight of independence of the parallel axiom leaves many open roads to pursue,but the desire to develop a natural as well as completely axiomatic system remains. In this context, the classification of Hilbert planes into three types,---as semi-euclidean, semi-elliptic or semi-hyperbolic, known as the uniformity theorem is a important step beyond Euclid. A further step is the introduction of the axiom of the unbounded opening of an angle. In the spirit of Hilbert, a completely axiomatic theory of area in neutral geometry is set up, before branching into the cases of Euclidean, or semi-hyperbolic, or semi-elliptic geometry.Finally, the attention has to focus of Euclidean geometry. The text gets a more educational and even more elementary flavor. Here I start with Thales theorem about the angle in a semicircle, and continue with Euclid's related theorems about angles in a circle.The most simple parts of the Euclidean geometry are given in detail, as well as the later parts about similarity, and area in Euclidean geometry with the theorem of Pythagoras andtrigonometry, and finally the measurement of the circle.…