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 Peacock's investigations on the foundation of algebra were considerably advanced by De Morgan and Hankel.

James Ivory was a Scotch mathematician who for twelve years, beginning in 1804, held the mathematical chair in the Royal Military College at Marlow (now at Sandhurst). He was essentially a self-trained mathematician, and almost the only one in Great Britain previous to the organisation of the Analytical Society who was well versed in continental mathematics. Of importance is his memoir (Phil. Trans., 1809) in which the problem of the attraction of a homogeneous ellipsoid upon an external point is reduced to the simpler problem of the attraction of a related ellipsoid upon a corresponding point interior to it. This is known as "Ivory's theorem." He criticised with undue severity Laplace's solution of the method of least squares, and gave three proofs of the principle without recourse to probability; but they are far from being satisfactory.

By the researches of Descartes and the invention of the calculus, the analytical treatment of geometry was brought into great prominence for over a century. Notwithstanding the efforts to revive synthetic methods made by Desargues, Pascal, De Lahire, Newton, and Maclaurin, the analytical method retained almost undisputed supremacy. It was reserved for the genius of Monge to bring synthetic geometry in the foreground, and to open up new avenues of progress. His Géométrie descriptive marks the beginning of a wonderful development of modern geometry.

Of the two leading problems of descriptive geometry, the one—to represent by drawings geometrical magnitudes—was brought to a high degree of perfection before the time of