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Record 1,  Textual support,  English

Record number: 1, Textual support number: 1 DEF

Curve formed by intersection of plane with right circular cone.  3, record 1, English, - conic%20section

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When a right circular cone of revolution is cut by planes at different angles, four curves of intersection are obtained that are called conic sections ... When the intersecting plane is perpendicular to the axis ... a circle ... If the plane makes a greater angle with the axis than do the elements ... an ellipse ... If the plane makes the same angle with the axis as the elements ... a parabola ... Finally, if the plane makes a smaller angle with the axis than do the elements or is parallel to the axis ... a hyperbola.  4, record 1, English, - conic%20section

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The parabola and the hyperbola, together with the ellipse and the circle, make up the family of conic sections, so called because each can be obtained by slicing a circular cone with a plane at various angles. Conic sections became objects of intense interest in the seventeenth century, first when the German astronomer Johannes Kepler determined that planets, comets and other bodies orbit the sun in elliptical paths, and later when Newton discovered that those bodies may also follow parabolic and hyperbolic orbits.  5, record 1, English, - conic%20section

Record 1,  Textual support,  French

Record number: 1, Textual support number: 1 DEF

Courbe ou section déterminée par la rencontre d'un cône et d'un plan [...] qui ne passe pas par son sommet. Selon leurs positions respectives, on obtient une section elliptique [...], hyperbolique [...] ou parabolique [...]  3, record 1, French, - section%20conique

Record number: 1, Textual support number: 1 CONT

Les différentes courbes obtenues par l'intersection d'un plan avec la surface latérale d'un cône circulaire droit [...] sont au nombre de quatre : la circonférence, l'ellipse, la parabole et l'hyperbole. On désigne ces courbes sous le titre général de coniques.  4, record 1, French, - section%20conique

Record 1,  Textual support,  Spanish