NATURAL SCIENCE IN THE MIDDLE ACES 281 



Though naked unassisted eyes 



Can scarce perceive them. Grains of sand 



Seem stones when through these glasses scanned. 



The poet goes on to say that through these glasses one can read 

 letters from such a distance that one would not believe it unless he had 

 seen it. Then he concludes, 



But to these matters blind affiance 



No man need give; they're proved by science. 



From the testimony of several other contemporaries we know that 

 eye-glasses had been invented before the close of the thirteenth century. 



Another important physical treatise besides Witelo's was a " Book on 

 Weights " by Jordanus Nemorarius earlier in the century. In this work 

 he is said to have made progress in dynamics beyond the ancients. 

 Another invention of great use to science, clocks, was worked out during 

 the middle ages. An innovation of great convenience in scientific 

 reckoning and records was made when Leonardo, a merchant of Pisa, in 

 a work written first in 1202 and then revised in 1228, brought the so- 

 called Arabic numerals to the attention of "Western Europe. Some 

 progress in algebra was also made in the middle ages, and Roger Bacon 

 emphasized the importance of mathematical method in scientific inves- 

 tigation. 



It can not be shown that Roger Bacon actually anticipated any of 

 our modern inventions, but the following passage from one of his works 

 does indicate that an interest existed then in machinery and mechanical 

 devices, and that men were already beginning to struggle with the 

 problems which have recently been solved. 



Machines for navigation can be made without rowers so that the largest 

 ships on rivers or seas will be moved by a single man in charge with greater 

 velocity than if they were full of men. Also cars can be made so that without 

 animals they will move with unbelievable rapidity; such we opine were the 

 scythe-bearing chariots with which the men of old fought. Also flying ma- 

 chines can be constructed so that a man sits in the midst of the machine re- 

 volving some engine by which artificial wings are made to beat the air like a 

 flying bird. Also a machine smaH in size for raising or lowering enormous 

 weights, than which nothing is more useful in emergencies. For by a machine 

 three fingers high and wide and of less size a man could free himself and hia 

 friends from all danger of prison and rise and descend. Also a machine can 

 easily be made by which one man can draw a thousand to himself by violence 

 against their wills, and attract other things in like manner. Also machines can 

 be made for walking in the sea and rivers, even to the bottom without danger. 

 For Alexander the Great employed such, that he might see the secrets of the 

 deep, as Ethicus the astronomer tells. These machines were made in antiquity 

 and they have certainly been made in our times, except possibly a flying ma- 

 chine which I have not seen nor do I know any one who has, but I know an ex- 

 pert who has thought out the way to make one. And such things can be made 

 almost without limit, for instance, bridges across rivers without piers or other 

 supports, and mechanisms, and unheard of engines. 



