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2019
The curves known as conic sections, the ellipse, hyperbola, and parabola, were investigated intensely in Greek mathematics. The most famous work on the subject was the Conics, in eight books by Apollonius of Perga, but conics were also studied earlier by Euclid and Archimedes, among others. Conic sections were important not only for purely mathematical
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The curves known as conic sections, the ellipse, hyperbola, and parabola, were investigated intensely in Greek mathematics. The most famous work on the subject was the Conics, in eight books by Apollonius of Perga, but conics were also studied earlier by Euclid and Archimedes, among others. Conic sections were important not only for purely mathematical
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General Relativity and Gravitation, 1983
A classification of the possible types of the relative orbits of realistic binary stars in the post-Newtonian approximation of general relativity is presented. Definitions of the relativistic conic sections and their elements are proposed, generalizing the corresponding ones of classical celestial mechanics. The results are compared and contrasted with
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A classification of the possible types of the relative orbits of realistic binary stars in the post-Newtonian approximation of general relativity is presented. Definitions of the relativistic conic sections and their elements are proposed, generalizing the corresponding ones of classical celestial mechanics. The results are compared and contrasted with
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1992
Abstract When The Greek geometers had exhausted, as they thought, the more obvious and interesting properties of figures made up of straight lines and circles, they turned to the study of other curves; and, with their almost infallible instinct for hitting upon things worth thinking about, they chiefly devoted themselves to conic ...
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Abstract When The Greek geometers had exhausted, as they thought, the more obvious and interesting properties of figures made up of straight lines and circles, they turned to the study of other curves; and, with their almost infallible instinct for hitting upon things worth thinking about, they chiefly devoted themselves to conic ...
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Conic that best fits an off-axis conic section
Annual Meeting Optical Society of America, 1986To help in the fabrication of off-axis conic sections, we present a method of approximating this off-axis section by an on-axis conic centered on the portion desired. This method is based on the continuum least-squares method to obtain the vertex’s curvature and conic constant of the fitted conic on-axis, given the curvature at the vertex and the conic
O, Cardona-Nunez +4 more
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Annual Meeting Optical Society of America, 1989
In most treatments of the reflecting properties of the conic sections, the properties are stated without proof. In this paper the conic sections are derived from first principles as surfaces which produce specific effects on light rays. For example, the ellipse is taken to be a surface which reflects all rays emanating from one fixed point in a plane ...
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In most treatments of the reflecting properties of the conic sections, the properties are stated without proof. In this paper the conic sections are derived from first principles as surfaces which produce specific effects on light rays. For example, the ellipse is taken to be a surface which reflects all rays emanating from one fixed point in a plane ...
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Canadian Journal of Philosophy, 2014
This paper tries to make sense of Kant’s scattered remarks about conic sections to see what light they shed on his philosophy of mathematics. It proceeds by confronting his remarks with the source that seems to have informed his thinking about conic sections: the Conica of Apollonius. The paper raises questions about Kant’s attitude towards mathematics
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This paper tries to make sense of Kant’s scattered remarks about conic sections to see what light they shed on his philosophy of mathematics. It proceeds by confronting his remarks with the source that seems to have informed his thinking about conic sections: the Conica of Apollonius. The paper raises questions about Kant’s attitude towards mathematics
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Electronic Structure Methods for the Description of Nonadiabatic Effects and Conical Intersections
Chemical Reviews, 2021Spiridoula Matsika
exaly