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HISTORICAL VIEW OP THE

him as the greatest, the most universal, and the most elo-quent of philosophers.” *

Algebraic Geometry. — Des Cartes .

The succession of discoveries to which we have re-ferred, during the latter part of the sixteenth andbeginning of the seventeenth centuries, brought alge-braic analysis to a state of very considerable perfection.The way was thus prepared for the brilliant disco-veries in reference to the application of this analysisto geometry, which constitute the peculiar characteristicof the “ modern geometry,” and confer upon it thoseextended powers and capacities to which the ancientsystem could not attain. Such applications had beenmade in a few instances (as we have noticed) by Vietaand others. But the grand advance, to which we nowrefer, was that effected by Des Cartes , and which formsone of the most important epochs in the history of ma-thematical science.

This philosopher, celebrated in so many departmentsof science, was born at La Haye, in Touraine , in 15<)6,and at an early age displayed great proficiency in variousbranches both of literature and science. After goingthrough the usual course in the Jesuits’ college at LaFleche , he entered upon the military profession, and,soon after, visited various parts of Europe . The versa-tility of his genius showed itself in the variety of dif-ferent studies he pursued, embracing almost everydepartment of science, metaphysical as well as mathe-matical. He died in 1650. It was in Holland, in 1637,that he first published his Geometry , in which the greatinventions above referred to are contained. This workis a tract of no more than 106 quarto pages : but thereis, probably, no production of the same size which everconferred so much and so just celebrity on its author.

In the first book, he treats of such geometrical pro-blems as can he resolved by the help of circles and

* Disc. Preliminaire de l’Encyclop.