m 



ON THE EARLY 



Chapter third. On measuring the breadth of rivers and the depth of 

 wells, ist. Stand on the bank of the river, and through the two sights 

 look at the opposite bank ; then turn round and look at any thing on the 

 land side, keeping the astrolabe even. The distance from the observer 

 to the object is the same as the breadth of the river, sd. Place something 



Chaucer's astrolabe had only one square, Dhil-i-As'bd, being divided into twelve 

 The Umbra-recta is called Dhil-Mustawi, and the versa, Dhil-Mdcics, 



parts., 



The rule in the text is very inaccu- 

 rately delivered; for the only case in 

 which it will apply is when at the first 

 station the index coincides with the dia- 

 gonal of the square, and being afterwards 

 moved one division on the horizontal 

 side, the observer advances towards the 

 object, till the top is again seen through 

 the sights. For let A C be the height 

 required, B the first station, D the se- 

 cond;, As the angles at A and B are 

 equal, A C = B C. But at the second 

 position A C -. D Ca7 : 6. There- 

 fore^ C==7 B D. 



But suppose at the first station JB, the 

 index falls on the fourth division, Dhil- 

 Kadam, on the, vertical side ; and that, by 

 retiring from the object to D^ it is brought 

 on the third ; then it is evident that 

 B CiAC:: 7:4, and 

 DC t A C i: 7 : 3; 



Therefore DC = ^~ 

 = 4 B D- Conseqxient" 



ly 7 :3°.*.&B D t AC 



