metaphysical speculation formed the starting point while the
justification of these conjectures was tested and resolved most
rigorously by comparison with observed data. In Galileo ( 1564-
1642) the battle of contemporary physics against the basic
tendencies of Aristotelianism came to the fore prominently. We
shall meet with like viewpoints in R. Descartes ( 1596-1650)
the highly gifted creator of the first modern system in the field
of mathematics.

Descartes came of an old Norman family of nobility. His
father, Joachim Descartes (d. 1640) was a councillor in the
Breton parliament at Rennes. The boy, frail and motherless
soon after he was born, was lovingly cared for ( 1604-12) in the
newly established Jesuit college at La Fleche. There he received
a painstaking and comprehensive education in science, the
course in mathematics being prescribed by the textbooks by
Clavius ( Euclid edition of 1574, Geometria Practica 1604, Al-
gebra 1608). As he was the second son of a well-to-do and highly
respected family, it was intended that he should prepare himself
for one of the higher public offices or for a military command. In
1613, he was presented at court, but finding that life in the world
of Society was not suited to his tastes, he soon withdrew from it.
In 1614, he began the study of law in Poitiers--although he had
no deep inclination toward it--and there, in 1616, he was
granted the degrees of Baccalaureus and Licentiate. In 1617, as
a volunteer for active duty, he joined the Protestant army of the
celebrated Maurice of Nassau, greatest general of his time. Des-
cartes's friendship with the mathematician and natural philoso-
pher, I. Beeckman ( 1588-1637) began in the encampment be-
fore Breda. Under the command of Duke Maximilian I of
Bavaria and of Bucquoy, he took part in the expedition against
the Winter King, Frederick V of the Palatinate. In Ulm, he came
in contact with the master arithmetician, Faulhaber, and in the
army winter quarters before Neuberg on the Danube, he discov-

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