He suggested that boats would run over the water without oars and without sails. He was anticipating our motor boat. He taught that light moves with a definite rate of velocity, though that fact was not demonstrated for several centuries after his time. He worked out most of the theory of lenses as we have it at the present time. He was sure that experiment and {114} observation constituted the only way by which knowledge of nature could be obtained. In this he was but following his great teacher Albertus Magnus, who insisted that in natural philosophy experiment alone brought sure knowledge; _"Experimentum solum certificat in talibus."_ are his own words. Roger Bacon's devotion to mathematics shows how thoroughly scientific was the trend of his mind. Without mathematics he was sure that one could not reach scientific knowledge, or that what one did get was without certainty. Some of his expressions in this matter are strikingly modern. It is no wonder that his writings and teachings were so great a surprise to his generation that the Pope ordered him to write out his knowledge in books. Without this order we would not have had Roger Bacon's great works, for his vow of poverty voluntarily taken forbade him to be possessed of sufficient money to enable him to purchase writing materials, which were then very expensive. Indeed the mathematics of the mediaeval universities is the best proof of the seriousness of their devotion to science and, may it also be said, of their success. Cantor, in his "History of Mathematics," and he is the great authority in the matter, devotes nearly 100 pages of his second volume to the mathematicians of the thirteenth century alone, two of whom, Leonard of Pisa and Jordanus Nemorarius, did so much in arithmetic, in the theory of numbers, and in geometry, {115} as to work a revolution in mathematics. They had great disciples like John of Holywood (probably a town near Dublin), Johannes Campanus and others. No wonder that at the end of the century Roger Bacon said, "For without mathematics nothing worth knowing in philosophy can be obtained," and again, "for he who knows not mathematics cannot know any other science; what is more, he cannot discover his own ignorance or find its proper remedy." The fourteenth and fifteenth centuries saw even more important work done. Cantor has half a dozen men in the fifteenth century to whom he devotes more than twenty-five pages each. How the place of this in mediaeval teaching can have escaped the notice of those who insist so much on the neglect of science during the Middle Ages, is hard to understand. This alone would convict them of ignorance of what they are talking about.