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Menaechmus-Euclides\' theory developed around 300 a.C. and is based on the fact that cones are right, obtained by rotating a right triangle about one of its legs and cut using planes perpendicular to a generatrix. The orthotome is a curve obtained by cutting a cone generated by rotating a right isceles triangle. Later on this same curve will be named parabola by Apollonio. The carachteristic property of the section curve (called \"symptom\" by the Greek geometers) is a proportion between two constant segments: the main axes of the curve and the right side relative to the same axes. The right side relative to the main axes is a segment equal to twice the distance between the vertex on the generatrix perpendicular to the section plane and the intersection point btween this same plane and the cone axes. This way the symptom is linked to the position of the curve on the cone.


To retrieve the curve symptom

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machines and simulations