A UNIQUE COLLECTION OF ARITHMETICS 227 
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 num- 
bers 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 mathe- 
matician 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 sci- 
entific 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 de- 
fending Syracuse with his catapults and burning glasses, appears in the 
“Rara Arithmetica ” as the author of a work on numeration. Archi- 
medes 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 Nico- 
machus 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 
