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.