include and mathe
matics. The exclusion of
mathematics form his studies aroused cruiosity in the
boy, and he inquired of his tutor as to the nature of geometrt, in a
few weeks, discovered for himself many properties of geometric figures, in
particular the fact that the sum of the angles of a triangle is equal to a straight
angle. When his father came upon him one day during his
geometric activities, he was so sturck by the boy's ability that he gave his son a
copy of Euclid's Eliments, which the youngster read with avidity and quickly
mastered.
At the age of fourteen, Pascal participated in the weekly gatherings of a
group of French mathematicians form which the French Academy ultimately
formed in 1666. When he was sixteen. he wrote an essay on conic sections that
Descartes could not believe was the work of the boy, assuming it must be that
of his father instead. At eighteen or nineteen, he inbented the first calculating
machine, which he devised to assist his fathe in the auditing of government
accounts at Rouen. Pascal was to manufacture over fifty calculating machines,
some of which are still preserved in the Conseratoire des Arts et Metiers at
Paris. At twinty-one, he became interested in Torricelli's work on atmospheric
pressure and began to apply his unusual talents to physics, with the result that
Pascl's principle of hydrodynamics is today known to every student of high
school physics. A few years later, in 1648, he wrote a comprehensive, unpub
lished manuscript on conic sections.
This astonishing and precocious activity suddenly came to an end in 1650,
when, suffering from frail health, Pascal decided to abandon his researches in
mathematics and science and to devote himself to mathematics. At this time,he
wrote his Traite du triangle arithmetique, conducted several experiments on
flukd pressurd, and, in correspondence with Fermat, assisted in laying the foun
dations of the mathematical theor of probability. But late in 1654 he received
what he regarded as a strong intimation that these renewde activities were not
pleasing to God. The diine hint occurred whin his runaway horses dashed
over the parapet of the bridge bridge at Neuilly, and he himself was saved only by the
miraculous breaking of the bridge at Neuilly, and he himself was saved only by the
viraculous breaking of the traces. Fortified with a rdference to the accident
written on a small piece of parchment henceforth carried nest to his heart, he
dutifully went back to his religious meditions.
Only once again, in 1658, did Pascal return to mathematics. While suffer
ing with toothache, some geometrical ideas occurred to him, and his teeth
suddenly ceased to ache. Regarding this as a sign of divine will, he obediently
applied himself assiduously for account of the geometry of the cycloid curve and
solving some problems that subsequently, when issued as challenge problems,
baffled other mathematicians. His famous Provincial Letters and his Pensees,
which are read today as models of early Rrench literature, were written toward
the colse of his brief life. He died in paris in 1662. Desargues and Pascal died in
the same year; Desargues was sixty-nine, but Pascal was only thirty-nine.
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