To these curves, which were also applied to effect some quadratures, Evangelista Torricelli gave the name of "Robervallian lines."

00In 1649 he accompanied the mission of Henry, count of Nassau, to Denmark, and in 1651 entered the lists of science as an assailant of the unsound system of quadratures adopted by Gregory of St Vincent.

00It has not indeed proved practically available; but his system of calculating cometary perturbations by means of "mechanical quadratures" has formed the startingpoint of all subsequent researches on the subject.

00The remainder of the first volume relates to the Eulerian integrals and to quadratures.

00Of less interest nowadays are Robins's more purely mathematical writings, such as his Discourse concerning the Nature and Certainty of Sir Isaac Newton's Methods of Fluxions and of Prime and Ultimate Ratios (1735), "A Demonstration of the Eleventh Proposition of Sir Isaac Newton's Treatise of Quadratures" (Phil.

00The only geometry known to the Egyptian priests was that of surfaces, together with a sketch of that of solids, a geometry consisting of some simple quadratures and elementary cubatures, which they had obtained empirically.

00He found that, although the two inequalities found by Hipparchus and Ptolemy correctly represented the moon's longitude near conjunction and opposition, and also at the quadratures, it left a large outstanding error at the octants, that is when the moon was 45° or 135° on either side of the sun.

00Poisson's application to them in 1809 of Lagrange's theory of the variation of constants; Philippe de Pontecoulant successfully used in 1829, for the prediction of the impending return of Halley's comet, a system of " mechanical quadratures " published by Lagrange in the Berlin Memoirs for 1778; and in his Theorie analytique du systeme du monde (1846) he modified and refined general theories of the lunar and planetary revolutions.

00He found that, although the two inequalities found by Hipparchus and Ptolemy correctly represented the moon's longitude near conjunction and opposition, and also at the quadratures, it left a large outstanding error at the octants, that is when the moon was 45Ã‚° or 135Ã‚° on either side of the sun.

00

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