Such is the basis of the algebraical or modern analytical geometry.

During the later years of his life he resided in London, devoting himself to the construction of machines capable of performing arithmetical and even algebraical calculations.

This is an algebraical process.

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And therefore T, are measured by the algebraical sum of their individual moments with respect to the axis.

A rational integral algebraical function) of x, or of x and y, of a degree which is known.

It includes the properties of numbers; extraction of roots of arithmetical and algebraical quantities, solutions of simple and quadratic equations, and a fairly complete account of surds.

In his youth he went to the continent and taught mathematics at Paris, where he published or edited, between the years 1612 and 1619, various geometrical and algebraical tracts, which are conspicuous for their ingenuity and elegance.

Arithmetical and Algebraical Treatment of Equations.-The following will illustrate the passage from arithmetical to algebraical reasoning.

The first, which is the best known but is of limited application, consists in replacing each successive portion of the figure by another figure whose ordinate is an algebraical function of x or of x and y, and expressing the area or volume of this latter figure (exactly or approximately) in terms of the given ordinates.

The leading idea of this work was contained in a paper published in the Berlin Memoirs for 1772.5 Its object was the elimination of the, to some minds, unsatisfactory conception of the infinite from the metaphysics of the higher mathematics, and the substitution for the differential and integral calculus of an analogous method depending wholly on the serial development of algebraical functions.