Mathematical recreations and essays . ,XV] THE PARALLEL POSTULATE 309 frorr its history. Pascal was a delicate and precocious boy,and in order to ensure his not being over-worked his fatherdirec:ed that his education should at first be only linguisticand literary, and should not include any mathematics. Natur-ally this excited the boys curiosity, and one day, being abouttwelve years old, he asked in what geometry consisted. Histutor replied that it was the science of constructing exactfigures and determining the relations between their , stimulated no doubt by the injunction agains
Mathematical recreations and essays . ,XV] THE PARALLEL POSTULATE 309 frorr its history. Pascal was a delicate and precocious boy,and in order to ensure his not being over-worked his fatherdirec:ed that his education should at first be only linguisticand literary, and should not include any mathematics. Natur-ally this excited the boys curiosity, and one day, being abouttwelve years old, he asked in what geometry consisted. Histutor replied that it was the science of constructing exactfigures and determining the relations between their , stimulated no doubt by the injunction against readingit, gave up his playtime to the new amusement, and in a fewweeks had discovered for himself several properties of recti-linear figures, and in particular the proposition in question. His proof is said* to have consisted in taking a triangularpiece of paper and turning over the angular points to meet atthe foot of the perpendicular drawn from the biggest angle tothe opposite side. The conclusion is obvious from a figure, for. if the paper be creased so that A is turned over to D, as alsoB and (7, we get B^FBB, A=FDE, and G = EDC; henceA+B-\-G = EDF4- FDB + EDG = tt. But we can only provethese relations on the assumption that when the paper is foldedover BF and ^i^ will lie along BF, and thus that BF=FA= FD,and similarly that GE = EA = ED; this assumption involvesproperties of parallel lines. A similar proof can be obtainedby turning over the angular points to meet at the centre ofthe inscribed circle, and according to some accounts this wasthe method used by Pascal. I may add in passing that hisfather, struck by this evidence of Pascals geometrical ability, * I believe that tbis rests merely on tradition. 310 THE PARALLEL POSTULATE [CH. XV gave him a copy of Euclids Elements, and allowed him to takeup the subject for which evidently he had a natural aptitude. Pythagorean and Euclidean Proof. Leaving the abovedemonstrations which rest on observation and experiment, Iproc
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