ABSTRACT

The circle ‘made or defined by the sun’ as it illuminates the moon is called by Aristarchus of Samos 'the great circle which divides the dark and the light portions of the moon',1 and this circle, as he says, 'is in the direction of our eye when the moon appears to us halved'. This means that the plane of the great circle mentioned passes through our eye, or, our eye and the said great circle are in one plane-as the problem states. In his Proposition 5 Aristarchus is more ex a ct; for in the enunciation he explains that 'the great circle parallel to the dividing circle and our eye are in one plane*. This is because, as he goes on to say, the dividing circle is in the direction

of our eye and the great circle parallel to the dividing circle is indistinguishable from it. For, in fact, since the sun is larger than the moon, its rays converge in a cone the apex of which is on the side of the moon away from the sun, and the sun lights up rather

more than half of the moon, so that ‘the circle dividing the dark and the light portions' is rather nearer to the apex of the cone, and therefore rather less than a great circle in the moon. But so far as

our perception goes the dividing circle and the great circle in the moon parallel to it are so nearly equal as to be indistinguishable.