By Wassenaar J.
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3) Kuipers 1966 p. 370. 4) substitute the partial derivatives by x en y in: hyperbola conic section last updated: 2003−05−21 The hyper part in the hyperbola word is derived from the Greek word 'huper', what means to surpass a certain limit 1). This excess is reached while adapting the areas in the old Greek way, in the case of the hyperbola. The same quality we find in the hyperbole, what has the meaning of a stylistic exaggeration. For example: an ocean of tears. Apollonius gave the hyperbola its name.
He used the cissoid to solve the Delian problem, dealing with the duplication of the cube. He did not use the name cissoid. The name of the curve, meaning 'ivy−shaped', is found for the first time in the writings of the Greek Geminus (about 50 BC). Because of Diocles' previous work on the curve his name has been added: cissoid of Diocles. Roberval and Fermat constructed the tangent of the cissoid (1634): from a given point there are either one ore three tangents. In 1658 Huygens and Wallis showed that the area between the curve and his asymptote is π/4.
In this 6) knowledge, he followed a book of Zenodorus (180 BC) . Some relations of the circle with other curves are the following: • it is the radial of the cycloid • it has three well−known catacaustics, depending on the position of the source: ♦ cardioid (source on circle) ♦ limaçon (source not on circle) ♦ nephroid (source at infinity) • the circle with the pole as center is invariant under inversion and is called the circle of inversion; in all situations when the pole is not situated on the circle, the inverse is a circle too • it is the orthoptic of the deltoid • the circle is a specimen of the sinusoidal spiral • the pedal of the circle is the limaçon (pedal point not on the circumference) or the cardioid (pedal point on the circumference) • the circle is the pedal of the hyperbola • the hyperbolism of the circle is the witch of Agnesi • its barycentric is the cochleoid • the circle is the rose for which c=1 Sometimes the forces of nature cause circular motions.