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ABCD angle ABC angle BAC antecedent Archimedes Aristotle base bisected centre circle ABC circumference construction continued proportion corresponding sides cube number definition diameter drawn enunciation equal angles equiangular equilateral equimultiples Euclid Euclid's proof Eutocius ex aequali four magnitudes geometrical progression given circle given straight line greater ratio greatest common measure Heiberg hypothesis Iamblichus inscribed joined less mean proportional numbers measures the number multiple multitude Nicomachus odd number parallel parallelogram pentagon perpendicular polygon Porism prime number Proclus Prop proper fraction proposition Proposition 22 proved rect rectangle rectangle contained rectilineal figure reductio ad absurdum remaining angle right angles segment semicircle similar and similarly similar plane numbers Simson solid numbers square number subtracted taken Theon of Smyrna theorem touches the circle triangle ABC unit