We owe the first evidences of the more profound insights into
the domain of infinitesimals to the almost simultaneous studies
by Fermat, Roberval and Torricelli. Fermat, especially, pushed
forward to comprehensive general methods, but these were not
accepted at their true value by his contemporaries.

P. de Fermat ( 1601-1665), a native of southern France, came
of a respected middle class family. In his small home town,
Beaumont de Lomagne, he acquired wide literary and linguistic
knowledge. He studied law at Toulouse and served in the court
of justice, first as a lawyer, then, from 1631, as a member and
from 1634 as a councillor. We have learned of Fermat's mathe-
matical achievements through his partially preserved corre-
spondence, and of some of his methods through rather small
treatises, very few of which were printed during the lifetime of
the author. Most of his treatises were not printed until 1679
when they appeared in inadequate form. However, their contents
had become known earlier, for the greatest part, through copies
which were in circulation. An extremely busy man, Fermat was
given to making notes of ideas that came to his mind on slips of
paper which were later heedlessly laid aside, or to making nota-
tions in the form of marginal notes in books which he was using.
The celebrated marginal notes in his manuscript copy of the
Bachet edition of Diophantus ( 1621) were added to the second
edition of 1670.

Fermat desired to combine mathematical methods taken from
the ancients with those of contemporary mathematicians and to
realize the greatest possible rigor and generality. Before 1629, he
had found

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