ALEXANDRIAN OR HELLENISTIC PERIOD 



sun, as we now know, is something like four hundred 

 times that of the moon. Fourth, the circumference 

 of the sun is greater than one side of the thousand- 

 faced figure inscribed in its orbit. The measure- 

 ment, it is expressly stated, is based on the measure- 

 ments of Aristarchus, who makes the diameter of the 

 sun y^ of its orbit. Archimedes adds, however, that 

 he himself has measured the angle and that it appears 

 to him to be less than yi-j, and greater than ^ part of 

 the orbit. That is to say, reduced to modern termi- 

 nology, he places the limit of the sun's apparent size 

 between thirty-three minutes and twenty-seven min- 

 utes of arc. As the real diameter is thirty-two min- 

 utes, this calculation is surprisingly exact, considering 

 the implements then at command. But the honor of 

 first making it must be given to Aristarchus and not to 

 Archimedes. 



We need not follow Archimedes to the limits of his 

 incomprehensible numbers of sand-grains. The calcu- 

 lation is chiefly remarkable because it was made be- 

 fore the introduction of the so-called Arabic numerals 

 had simplified mathematical calculations. It will be 

 recalled that the Greeks used letters for numerals, 

 and, having no cipher, they soon found themselves in 

 difficulties when large numbers were involved. The 

 Roman system of numerals simplified the matter 

 somewhat, but the beautiful simplicity of the decimal 

 system did not come into vogue until the Middle Ages, 

 as we shall see. Notwithstanding the difficulties, 

 however, Archimedes followed out his calculations 

 to the piling up of bewildering numbers, which 

 the modern mathematician finds to be the con- 



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