SEQUEL TO THE EPOCH OF HIPPARCHUS. 213 



gress in trigonometry ; for instance, a table of the 

 tangents of angles. 



Instruments were soon invented for measuring 

 angles, by means of circles, which had a border, 

 or limb, divided into equal parts. The whole cir- 

 cumference was divided into 360 degrees : perhaps 

 because the circles, first so divided, were those 

 which represented the sun's annual path; one such 

 degree would be the sun's daily advance, more 

 nearly than any other convenient aliquot part which 

 could be taken. The position of the sun was de- 

 termined by means of the shadow of one part of 

 the instrument upon the other. The most ancient 

 instrument of this kind appears to be the Hemi- 

 sphere of Berosus. A hollow hemisphere was placed 

 with its rim horizontal, and a style was erected 

 in such a manner that the extremity of the style 

 was exactly at the center of the sphere. The 

 shadow of this extremity, on the concave surface, 

 had the same position with regard to the lowest 

 point of the sphere which the sun had with regard 

 to the highest point of the heavens. But this 

 instrument was in fact used rather for dividing 

 the day into portions of time than for determining 

 position. 



Eratosthenes 7 observed the amount of the obli- 

 quity of the sun's path to the equator; we are 

 not informed what instruments he used for this 

 purpose : but he is said to have obtained, from the 

 7 Delambre, A. A. i. 86. 



