46 THE HISTORY OF SCIENCE 



of trigonometry. The Syntaxis sets forth his method 

 of drawing up a table of chords. For example, the 

 side of a hexagon inscribed in a circle is equal to 

 the radius, and is the chord of 60, or of the sixth 

 part of the circle. The radius is divided into sixty 

 equal parts, and these again divided and subdivided 

 sexagesimally. The smaller divisions and the sub- 

 divisions are known as prime minute parts and sec- 

 ond minute parts (partes minutce primce and partes 

 minutce secundce), whence our terms " minute " and 

 " second." The sexagesimal method of dividing the 

 circle and its parts was, as we have seen in the first 

 chapter, of Babylonian origin. 



Ptolemy was the last of the great Greek astrono- 

 mers. In the fourth century and at the beginning 

 of the fifth, Theon and his illustrious daughter Hy- 

 patia commented on and taught the astronomy of 

 Ptolemy. In the Greek schools of philosophy Plato's 

 doctrine of the supreme reality of the invisible world 

 was harmonized for a time with Christian mysticism, 

 but these schools were suppressed at the beginning 

 of the sixth century. The extinction of scientific and 

 of all other learning seemed imminent. 



What were the causes of this threatened break in 

 the historical continuity of science ? They were too 

 many and too varied to admit of adequate statement 

 here. From the latter part of the fourth century the 

 Roman Empire had been overrun by the Visigoths, 

 the Vandals, the Huns, the Ostrogoths, the Lom- 

 bards, and other barbarians. Even before these incur- 

 sions learning had suffered under the calamity of 

 war. In the time of Julius Caesar the larger of the 

 famous libraries of Alexandria, containing, it is com- 



