614 ROYAL SOCIETY OF CANADA 



ifl 45° and the triangle is right angled. For the preceding reasons it 

 ia evident that Enciso knew that the true length of a degree was 17 ^jj 

 leagues, although the rate of Ki % leagues was etill held by many when 

 he wrote. It will, I trust, be noted that all these sailors and cosmo- 

 grtiphers knew that the world was a sphere and in speculating upon the 

 length of degrees of latitude and longitude they meant, as we do, de- 

 grees upon great circles unless they mention some specific latitude they 

 are measuring upon. 



I come now to inquire why the round number of 6000 leagues, or 

 24,000 Koman miles, should have been accepted as the measure of the 

 circumference of the earth, and 1 find the answer in a letter of Amerigo 

 Vespucci to Medici as follows : " The reason why I count 16 ^1^ 

 " leagues to a degree is that according to Ptolemy and Alfragan the 

 " world is 24,000 miles in circumference which is equal to 6000 

 *' leagues which divided by 360 is equal to 16 'I., leagues, a result which 

 •' I have many times tested by the point of pilots and have found it 

 " sound and true." The reason is, therefore, to be traced back to 

 Ptolemy ; though by way of Alfragan, and it must be observed there- 

 fore, til at it is a Greek, not an Arabian measurement. 



It has been stated already that, when the Arabs overran the Eastern 

 Koman Empire, they found in use a stade (Egyptian, royal, or Phile- 

 terian) of which 7 ^j, went to a Roman mile. They did not know that 

 this measure did not arise until after Ptolemy's time and they divided 

 the 500 stades of Ptolem/s degree by 7 %, and thus made it 66 % 

 Eonian miles, which, in leagues of four to a mile, was equal to 16 '^Ig 

 leagues ; and this leads to a consideration of the effect the Arabian 

 learning had on the cosmological ideas of the period now in review. 



During the long ages of confusion in the West, while wave after 

 wave of barbarians submerged the Roman civilization and the lamp of 

 learning burned only in the seclusion of the cloister, the Arabians culti- 

 vated the arts and sciences at the chief centres of their power — Bagdad, 

 Cairo and Cordova. The works of Aristotle, Archimedes, and Ptolemy, 

 among other authors, were translated into Arabic for the great school 

 of geography and astronomy founded at Bagdad, and about A.D. 833, 

 the Caliph Almamoun ordered several measurements to be made of an 

 arc of the meridian, the only attempt at a really scientific solution of 

 the problem from the time of the Greeks until the beginning of the 

 eighteenth century. Greek science first reached Western Europe 

 through Arabic translations. The works of Massaudy and other 

 'Arabian geographers, passed into Spain through the Moors, and the 

 Celestial Movcmenls of Alfragan were translated into Latin and became 

 well kno^vn to the learned. The measurements under Almamoun had 



