75 o THE POPULAR SCIENCE MONTHLY. 



every verse was taken to pieces and looked at grammatically, meteric- 

 ally, and historically. (They had rules for the position of the mouth 

 in pronunciation.) Greek was, after some time, introduced into the 

 Western schools and taught in the same general manner as the Latin. 

 Hebrew was seldom an object of study. The modern languages were 

 not taught. 



Dialectic. This represented philosophy in general. In the lower 

 schools it was a mere collection of phrases. The boy learned the cate- 

 gories, the moods and figures of the syllogism and practiced definitions 

 and disputations. There was a partial translation of Plato's " Timre- 

 us," which prevailed to the thirteenth century. In the higher schools, 

 especially from the tenth to the twelfth century, religion was taught 

 in connection with philosophy, and this latter study was in every way 

 made to defend the faith. 



Rhetoric. This was taught, at first, according to Quintilian and 

 Cicero ; later the text-books of Capella and Bede took their place ; in 

 the tenth century Quintilian became again the leader. The rules of 

 rhetoric were applied to sermon-writing, and the first treatise on this 

 subject was composed about the year 1300. 



Music. This study received special attention. Ambrose of Milan 

 originated the church songs, and Charlemagne summoned teachers of 

 song from Rome, and laid great stress upon musical training. Instruc- 

 tion in this department was based upon the text-books of Boethius, 

 and the notes were marked by the letters of the alphabet until Bene- 

 dict of Pomposa and Guido of Arezzo (1030) introduced the system of 

 lines. The marking of the notes according to their continuance and 

 length was devised in the fourteenth century by Johns of Myris, while 

 before this the higher and lower notes were expressed by ascending 

 and lowering lines. 



Arithmetic. This was next to music in importance as an object 

 of study. To express numbers the hands and feet were used. The 

 left hand upon the breast signified 10,000 and both hands 100,000. 

 In business and housekeeping accounts a reckoning-board was used. 

 This was a table upon which upright parallel lines were cut, that rep- 

 resented values of units, tens, hundreds, etc. These lines were filled 

 with stones to express numbers : thus, for 4,576 we should have on 

 the first line at the right, six stones, then seven, and so on. 



Geometry. This was taught in the higher and lower schools after 

 selections from Euclid. Lines, figures, and solids were defined, and 

 chief examples of them given. There was generally associated with 

 this study a kind of geography, and it is said that the cloister of St. 

 Gallen had a map as early as the seventh century. 



Astronomy. This study, which had been pursued long before 

 among the Greeks, and which was a principal concern with the Ara- 

 bians, received no attention in the Western Church until Charlemagne 

 had some correspondence with Rabanus respecting it. The schools 



