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Vera circuli et hyperbolae quadratura archive#
Hyperbola and Limacon of Pascal (both in red dots).Įquations of polynomials of degree 2 with 2 variables have cross sections that are hyperbola, ellipse, parabola in various ways.Andersen, K.: Cavalieri’s Method of Indivisibles, Archive for History of Exact Sciences 31, 1985, 291–367Īrnauld, A./Nicole, P.: La Logique ou l’art de penser, Paris, Savreux 1662īarrow, I. The inversion of any hyperbola with respect to a focus is a limacon of Pascal Right: Hyperbola (purple) and a right strophoid (red dots). Left: hyperbola and lemniscate of Bernoulli (both in red dots). If the inversion point is at a vertex, the inversion curve is a right strophoid. The inversion of a rectangular hyperbola with respect to its center is again a lemniscate of Bernoulli. The pedal of a rectangular hyperbola with respect to its center is a lemniscate of Bernoulli The pedal of a hyperbola with respect to a focus is a circle. The catacaustic and diacaustic of a hyperbola with eccentricity 2.5. Light rays coming from one focus of a hyperbola will refract to the other focus. The locus of intersection g and B1, as D moves on the circle, is a hyperbola.Let there be a line passing B1 and parallel to x-axis.Let there be a line g, passing E and parallel to y-axis.
Let the intersection of this circle and positive x-axis be E.
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