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By H. S. M. Coxeter

One of several appealing and nontrivial theorems in geometry present in Geometry Revisited are the theorems of Ceva, Menelaus, Pappus, Desargues, Pascal, and Brianchon. a pleasant evidence is given of Morley's impressive theorem on perspective trisectors. The transformational perspective is emphasised: reflections, rotations, translations, similarities, inversions, and affine and projective variations. many desirable homes of circles, triangles, quadrilaterals, and conics are built.

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Let ABC be an isosceles triangle with equal angles 80' at B and C. Find L EDB. 5. If two lines through one vertex of an equilateral triangle divide the semicircle drawn outward on the opposite side into three equal arcs, these same lines divide the side itself into three equal line segments. CHAPTER 2 Some Properties of Circles Although the Greeks worked fruitfully, not only in geometry but also in the most varied fields of mathematics, nevertheless we today have gone beyond them everywhere and certainly also in geometry.

K 3. 9D, then L CPB = L DPA. 9D 4. Let ABC be an isosceles triangle with equal angles 80' at B and C. Find L EDB. 5. If two lines through one vertex of an equilateral triangle divide the semicircle drawn outward on the opposite side into three equal arcs, these same lines divide the side itself into three equal line segments. CHAPTER 2 Some Properties of Circles Although the Greeks worked fruitfully, not only in geometry but also in the most varied fields of mathematics, nevertheless we today have gone beyond them everywhere and certainly also in geometry.

Monthly, vol. -Sept. 1940, pp. 462-466). He finds that the nth pedal n-gon of any n-gon is similar to the original n-gon. I t is instructive to try this for the fourth pedal quadrilateral of a quadrilateral. At this point let us pause in our investigations. We have done part of what we set out to do: beginning with well-known data, we have developed a few simple but significant facts. There are many problems that lend themselves to solution by the methods described here. Some of them are well-known posers that the reader may have seen before.

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