Nec minor est virtus, quam quaerere, parta tueri.
Ovid, Ars Amandi, lib. II, 13.

In contrast to the preceding periods of development which
were characterized by the coexistence of great numbers of indi-
vidually gifted personalities within the same type of environ-
ment, the mathematics of the High Baroque period was marked
by the emergence of several leading spirits of genius, who, in the
space of a few decades, brought about a complete change in the
interpretation of science. It now became a matter, not merely of
improving practical methods of application, but rather of estab-
lishing a comprehensive systematic structure of scientific
thought, to be constructed with mathematics as its model. To
make this possible it was necessary, first of all, to transform the
mosaic of conceptions arrayed starkly side by side into a self-
contained system determined by consistent tendencies.

Even for Copernicus ( 1473-1543) the point in question was
the construction of a new system of astronomy and, indeed, of
revitalizing and transforming ancient notions. Kepler ( 1571-
1630) abandoned tradition as a basis and followed intuition at
the crucial point. Plausible conjectures made on the grounds of

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