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below and illustrated inFigure 2.9. The centres of the Sun, Earth and Moon are S, E and M, respectively, and the lines SA, EB and MC are all perpendicular to SEM and intersect the circles representing the Sun, Moon and Earth at A, B and D, respectively. Then ABF is a good approximation to the tangent to the Sun and Earth and, hence, | MC| is close to the radius of the shadow of the Earth at the distance of the Moon, which is 2rM according to Aristarchus' fifth hypothesis.

Using the similarity of the triangles ASF, BEF and CMF we can deduce that

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