With these tools he was able to show that rotating the unlimited area of a rectangular hyperbola between the y -axis and a fixed point on the curve, resulted in a finite volume when rotated round the y -axis.
This problem in turn led Khayyam to solve the cubic equation x 3 + 200x = 20x 2 + 2000 and he found a positive root of this cubic by considering the intersection of a rectangular hyperbola and a circle.
Its contents are as follows: Euclid's theory of parallel lines; Propositions of incidence; The symbolic representation and Pappus' theorem; Theorems proved from the propositions of incidence; The fundamental hypothesis; The symbols of the real points of a line; Involution and harmonic ranges; Related ranges and pencils; Conics; Assignment of two absolute points, properties of circles; The parabola; The rectangular hyperbola; Theorems on conics; Length and distance; Equation of conic and line.
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Images of rectangular hyperbola
(mathematics)
直角双曲线
矩形双曲线
Synonyms and analogies of "rectangular hyperbola" in English