beaune's Notae Breves. In his Exercitationes Mathematicae,
( 1657; Netherlands, 1660) van Schooten also took up the most
important individual results achieved by his pupils. The great
two volume revised edition of the Geometria ( 1659, 1661) con-
tained as supplements, Debeaune's studies on the theory of equa-
tions, Hudde's excellent works on extreme value methods and
the determination of the limits of roots, de Witt's striking theory
of conic sections based on instrumental methods of generation,
beside numerous lesser corollaries and improvements in the ex-
planations of the text, in which Huygens also took part.

This work which appeared in an edition having a large number
of copies, was added to again, later on, with great success. It
contained everything that from this time on was regarded as in-
dispensable prerequisite knowledge for such persons as were in-
terested in the newer mathematics and in the physics that was
related to it. It superseded the earlier technical literature and it
created a common foundation for the mathematical sciences of
the Late Baroque period. Now, principle which to Descartes had
been the only thing of importance, no longer received the great-
est emphasis in the methods of thinking. The greatest promi-
nence was given to operative points of view and to skillful
handling of numerous individual examples. This work owed its
great success, above all to this change in interpretation, whereas
an abridged Netherlands treatment by G. Kinckhuysen ( 1660-
63) met with less favor. Upon van Schooten's death, the Nether-
lands school collapsed. His insignificant successors remained
immobilized in formalism. The interest of the next generation
was devoted to the infinitesimal methods of richer prospect. The
difficult basic problems of algebra (fundamental theorem, na-
ture of the roots of an equation) were not to be undertaken
again until the beginning of the 19th century, and then, on the
basis of new points of view.

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