The Contents of the Fifth and Sixth Books of Euclid

angles reciprocally proportional arc CD B₂C₂ BEFG BEHC bisected BLNO centre circle congruent corresponding sides cross-ratio diagonal draw duplicate ratio EFGH ENUNCIATION EQPS equimultiples Euclid EXAMPLE express the facts expressed by Fig Fifth Book four harmonic points four magnitudes four straight lines given straight line greater Hence the scale hypotenuse kind mean proportional middle point parallel to BC parallelogram point of division PQRST Prop PROPOSITION rA rB rA sB rA sC radical axis ratio compounded ratio of equality rect rectangle contained rectilineal figure relative multiple scale required to prove respectively equal right angle second column side BC side corresponding similar figures similar triangles similarly described Sixth Book square supplementary angles Take any integer THEORY OF RELATIVE three magnitudes triangle ABC triangle are respectively triangle DEF triangles are similar vertex whole numbers