Abstract
§ 1. The famous theorem of the pedal line of a triangle in ordinary geometry can be stated as follows:—“Given a triangle ABC and a point P such that the feet of the perpendiculars X, Y, Z, dropped from P on the sides of the triangle, are collinear, then the locus of P is the circumcircle.” In noneuclidean geometry this locus is not a circle or even a curve of the second degree, but a cubic; and in both cases the envelope of the line XYZ is a curve of the third class. The explanation of the inconsistency in ordinary geometry is that the complete locus consists of the circumcircle together with the straight line at infinity.
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