A HISTORY OF SCIENCE 



circumscribed within a cone, which cone is made 

 tangible and measurable by the shadows cast by 

 the non-luminous bodies ; since, continuing, he clearly 

 states in proposition nine, that "when the sun is 

 totally eclipsed, an observer on the earth's surface is 

 at an apex of a cone comprising the moon and the 

 sun." Various propositions deal with other relations 

 of the shadows which need not detain us since they 

 are not fundamentally important, and we may pass 

 to the final conclusions of Aristarchus, as reached in 

 his propositions ten to nineteen. 



Now, since (proposition ten) "the diameter of the 

 sun is more than eighteen times and less than twenty 

 times greater than that of the moon," it follows 

 (proposition eleven) "that the bulk of the sun is to 

 that of the moon in ratio, greater than 5832 to i, and 

 less than 8000 to i." 



"Proposition sixteen. The diameter of the sun is 

 to the diameter of the earth in greater proportion than 

 nineteen to three, and less than forty-three to six. 



" Proposition seventeen. The bulk of the sun is to 

 that of the earth in greater proportion than 6859 to 

 27, and less than 79,507 to 216. 



"Proposition eighteen. The diameter of the earth 

 is to the diameter of the moon in greater proportion 

 than 1 08 to 43 and less than 60 to 19. 



" Proposition nineteen. The bulk of the earth is to 

 that of the moon in greater proportion than 1,259,712 

 to 79,507 and less than 216,000 to 6859." 



Such then are the more important conclusions of 

 this very remarkable paper a paper which seems to 

 have interest to the successors of Aristarchus genera- 



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