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Topic: Keely Geometry StackSection: Geometry Proposition 18Table of Contents to this Topic |

Proposition XVIII The circle inscribed and circumscribed about an equilateral triangle, is in duplicate ratio to the circle inscribed and circumscribed about a square. Axioms as proven herein and as self-evident: First: Circumference and radius (and not the square of diameter) are the only natural and legitimate elements of area by which all regular shapes may be measured. Second: The equilateral triangle and the circle are exactly opposite to one another in the elements of their construction, which are circumference and radius. (Proposition VIII & IX) Third: The equilateral triangle is the primary of all shapes in nature formed of straight lines and of equal sides and angles (Proposition III), and has the least number of sides of any shape in nature formed of straight lines, and the circle is the ultimatum of nature in the extension of the number of sides. |

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