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Updated: June 18, 2025
Pope's account of him is well worth reading: of his travels in France; of his encounter with the redoubtable Thomas Hobbes, whose quadrature of the circle he proved false: that hard-headed philosopher's logic or "computation" must have failed him on this occasion, for finding, as he thought, errors in Rooke's criticism, he concluded that his own solution must be true.
In the quadrature of curves, the method of exhaustions was most ancient, whereby similar circumscribed and inscribed polygons, by continually increasing the number of their sides, were made to approach the curve until the space contained between them was exhausted, or reduced to an inappreciable quantity. The sides of the polygons, it was evident, must then be infinitely small.
It is not improbable therefore that the problem of laying down a practical calendar which should correspond at once to the moon and the sun a problem which may be compared in some sense to the quadrature of the circle, and the solution of which was only recognized as impossible and abandoned after the lapse of many centuries had already employed the minds of men in Italy before the epoch at which their contact with the Greeks began; these purely national attempts to solve it, however, have passed into oblivion.
"The properties of the spiral and the quadrature of the parabola were added to ancient geometry by Archimedes, the last being a great step in the progress of the science, since it was the first curvilineal space legitimately squared."
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