A HISTORY OF SCIENCE 



of its circumference which divides the illuminated part 

 from the dark part. 



"Fourth. When the moon appears dichotomized its 

 distance from the sun is less than a quarter or the 

 circumference [of its orbit] by a thirtieth part of that 

 quarter." 



That is to say, in modern terminology, the moon 

 at this time lacks three degrees (one thirtieth of ninety 

 degrees) of being at right angles with the line of the 

 sun as viewed from the earth; or, stated otherwise, 

 the angular distance of the moon from the sun as 

 viewed from the earth is at this time eighty -seven 

 degrees this being, as we have already observed, the 

 fundamental measurement upon which so much de- 

 pends. 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. The diameter of the shadow [cast by the 

 earth at the point where the moon's orbit cuts that 

 shadow when the moon is eclipsed] is double the 

 diameter of the moon." 



Here again a knowledge of previously established 

 measurements is taken for granted; but, indeed, this is 

 the case throughout the treatise. 



" Sixth. 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 termi- 

 nology, one degree of arc. This is Aristarchus's meas- 

 urement of the moon to which we have already referred 

 when speaking of the measurements of Archimedes. 



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