The Contents of the Fifth and Sixth Books of Euclid (with a Note on Irrational Numbers) |
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ABCD angles reciprocally proportional aR>bR arc CD Archimedes Axiom Axiom of Archimedes B=rA bisected BLNO CÂD Cantor-Dedekind Axiom centre common measure Commutative Law compounded construction corresponding sides cross-ratio diagonal divided duplicate ratio EFGH ENUNCIATION Euclid's EXAMPLE Fifth Book four harmonic points four straight lines greater greatest number hypotenuse integer irrational number kind least number lower class mean proportional middle point multiples of G P₁ P₂ parallel to BC parallelogram points of division positive integer possible PQRST PROPOSITION rA rB radical axis ratio of equality rational fraction rational numbers rect rectangle contained required to prove respectively equal right angle segments similar figures similar triangles similarly described squares described system of rational three magnitudes triangle ABC triangle are respectively triangles are similar upper class vertex