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The arc subtended in the sky by the moon is a fifteenth part of a sign" of the zodiac; that is to say, since there are twenty-four, signs in the zodiac, one-fifteenth of one twenty-fourth, or in modern terminology, one degree of arc. This is Aristarchus's measurement of the moon to which we have already referred when speaking of the measurements of Archimedes.
We may fairly suppose that some previous paper of Aristarchus's has detailed the measurement which here is taken for granted, yet which of course could depend solely on observation. "Fifth. Here again a knowledge of previously established measurements is taken for granted; but, indeed, this is the case throughout the treatise. "Sixth.
If the hypotheses had been exact, the results would have been correct too; but Aristarchus in fact assumed a certain angle to be 87° which is really 89° 50', and the angle subtended at the centre of the earth by the diameter of either the sun or the moon to be 2°, whereas we know from Archimedes that Aristarchus himself discovered that the latter angle is only 1/2°. The effect of Aristarchus's geometry is to find arithmetical limits to the values of what are really trigonometrical ratios of certain small angles, namely
To be on terms of intimacy with an author or an actor has been an object of delight to many a young man; actually to hob and nob with Bobadil or Henry the Fifth or Alexander the Great, to accept a pinch out of Aristarchus's own box, to put Juliet into her coach, or hand Monimia to her chair, are privileges which would delight most young men of a poetic turn; and no wonder George Warrington loved the theatre.
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