ABSTRACT
BOOK III deals with the construction of problems solid and supersolid. It contains an analysis of the algebra then current, and it makes some contributions of value to the study of equations; Cantor, in fact, regards
it as a milestone in the development of this important branch of algebra (einen wirklichen Markstein in der geschichtlichen Entwickelung in der Lehre ~)on Gleichungen)*. But Cantor's judgment mu'}t be accepted with considerable reserve. It would not be difficult to name many other works of the period which have a juster claim to that title than La Geometrie. The outstanding achievements of the sixteenth century had been the solution of the cubic and the biquadratic. The seventeenth century. busied itself with the investigation of the properties of equations and their roots, and in this connexion the names of Harriot in England and Girard in Holland are conspicuous. Descartes by introducing a more workmanlike notation than had hitherto been employed, and by his freer use of negative roots, effected some lasting improvements, and he showed, as we have seen, considerable dexterity in his use of the method of indeterminate coefficients. But apart from contributions such as these , marks of originality are few; furthermore, in his belief that by the methods he had employed, equations of any degree might be solved, he erred.
