The intercept on the axis of y is 2a/7r; therefore, if it were possible to accurately construct the curve, the quadrature of the circle would be effected.
His chief works are: Astronomical History of Observations of Heavenly Motions and Appearances (1634); Ecliptica prognostica (1634); Controversy with Longomontanus concerning the Quadrature of the Circle (1646?); An Idea of the Mathematics, 12m0 (1650); A Table of Ten Thousand Square Numbers (fol.; 1672).
5 For minute and lengthy details regarding the quadrature of the circle in the Low Countries, see de Haan, " Bouwstoffen voor de geschiedenis, &c.," in Versl.
Montucla, successful attempt to show that quadrature of the circle by a Euclidean construction was impossible.'
quadrature of the circle.
He attempted the quadrature of the circle by interpolation, and arrived at the remarkable expression known as Wallis's Theorem (see Circle, Squaring Of).
Rectification and quadrature of the circle have thus been, since the time of Archimedes at least, practically identical problems. Again, since the circumferences of circles are proportional to their diameters - a proposition assumed to be true from the dawn almost of practical geometry - the rectification of the circle is seen to be transformable into finding the ratio of the circumference to the diameter.
He is described as the first to treat theology on mathematical principles and he also wrote on the quadrature of the circle.
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