around the world brought mathematical finds to the Plimpton and Smith collections in the shape of Arabic and Persian, Hindu and Chinese and Japanese manuscripts and rolls.
Mention should also be made of the medallions of mathematicians, on exhibition in Teachers College, extending back nearly to the time of Pythagoras. The Smith collection of portraits of the devotees of numbers is without parallel and the autograph letters and documents are priceless. Here is an original note-book from the hand of Newton, and the more prosaic receipt for his semi-annual annuity of fifty pounds granted by parliament. The diploma of the great physiologist E. H. Weber, signed by Carl Friedrich Gauss, probably the greatest mathematician of all time, will interest especially those who are familiar with the labors of these men.
The invention of printing gave a tremendous stimulus to all scientific work by making possible the wide diffusion of knowledge, as well as by facilitating the intercourse of scholars. A potent indication of the really scientific spirit of the learned men of that day is the fact that the newly discovered art was used to give the older classics a wider circulation. Thus it need not surprise us to find in this bibliography of the fifteenth and sixteenth centuries the names of the more ancient writers.
Archimedes (287–212 B.C.), whom we ordinarily recall as a geometer tracing figures in the sand and incidentally being killed while engaged in this harmless occupation, or as a master of applied mechanics defending Syracuse with his catapults and burning glasses, appears in the "Rara Arithmetica" as the author of a work on numeration. Archimedes explains how it is possible to obtain numbers sufficient to express the grains of sand in a sand-heap as large as the world and even as large as the universe, a problem which is also found in India.
The arithmetic of Boethius (c. 480–524) involving that of Nicomachus of Gerasa (fl. c. A.D. 100) was the most widely used text-book in the monastic schools of the middle ages. Doubtless never again will any text-book be kept in use for approximately a thousand years, and yet an examination of the content of this text reveals not science, but hair-splitting philosophical discussions and extreme poverty of ideas. Boethius might have been expected to be a more practical philosopher, for he wrote his "Consolations of Philosophy" while he was in prison.
The exchange of professors by the leading universities was more common in the early days of these institutions than it is even now. Thus the Englishman, John of Halifax, or Holywood, who was known in the middle ages by the Latin form of his name Sacrobosco, studied and probably lectured at Oxford before settling in Paris about 1250. Sacrobosco's "Algorism," while by no means the first European work on the Hindu art of reckoning, was one of the most widely used and
