An Elementary Course in Synthetic Projective GeometryLehmer, Derrick Norman
Science
An Elementary Course in Synthetic Projective Geometry
Lehmer, Derrick Norman
Geometry, Projective
*173.* It must be understood that the "Essay" was only a résumé of a more
extended treatise on conics which, owing partly to Pascal’s extreme youth,
partly to the difficulty of publishing scientific works in those days, and
also to his later morbid interest in religious matters, was never
published. Leibniz(12) examined a copy of the complete work, and has
reported that the great theorem on the mystic hexagram was made the basis
of the whole theory, and that Pascal had deduced some four hundred
corollaries from it. This would indicate that here was a man able to take
the unconnected materials of projective geometry and shape them into some
such symmetrical edifice as we have to-day. Unfortunately for science,
Pascal’s early death prevented the further development of the subject at
his hands.
*174.* In the "Essay" Pascal gives full credit to Desargues, saying of
one of the other propositions, "We prove this property also, the original
discoverer of which is M. Desargues, of Lyons, one of the greatest minds
of this age ... and I wish to acknowledge that I owe to him the little
which I have discovered." This acknowledgment led Descartes to believe
that Pascal’s theorem should also be credited to Desargues. But in the
scientific club which the young Pascal attended in company with his
father, who was also a scientist of some reputation, the theorem went by
the name of ’la Pascalia,’ and Descartes’s remarks do not seem to have
been taken seriously, which indeed is not to be wondered at, seeing that
he was in the habit of giving scant credit to the work of other scientific
investigators than himself.
Public-domain text, read in full here on John Shaqi.
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