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Pascal's Essais pour les Coniques
Published online by Cambridge University Press: 20 January 2009
Extract
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In 1640, when only 18 years of age, Pascal published a tract of a few pages with the above title. It contains only a few enunciations, and concludes with the statement that the author has several other theorems and problems, but that his inexperience, and the distrust he has of his own powers, do not allow him to publish them till they have been examined by competent judges. He afterwards wrote a complete work (opus completum) on the Conics, which was submitted to Leibnitz by M. Périer, Pascal's brother-in-law. Leibnitz recommended that it should be published; but this was not done, and we know its contents only from the analysis which Leibnitz sent back to M. Périer.
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- Copyright © Edinburgh Mathematical Society 1883
References
* By a hexagon is to be understood the figure formed by joining consecutively any six points on the circumference of the circle. Sixty different figures are possible according to the order in which the points are joined.
* Both Pascal and Desargues appear to have made mnch use of the propositions known as Menelaus' and Ceva's Theorems (Fig. 17),
D, E, and F are collinear; and conversely;
AD, BE, and CF are concurrent; and conversely;
and tbees I shall assume as known.
* Pentagon here has the same extended meaning as hexagon.
* Six points A, A′, B, B′, C, C′ are in involution, if 
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