402 



SCIENCE. 



[N. S. Vol. XIX. No. 480. 



The appearance of courses on the history 

 of mathematics in all our foremost univer- 

 sities is a fortunate and promising sign of 

 the times. I had the honor of being the 

 first to give such a course in America, at 

 Princeton, in 1881. 



2. GEOMETRY AND ITS FOUNDERS. 



But something especially fascinating, 

 pure, divine, seems to pertain to geometry. 



When asked how God occupies himself, 

 Plato answered, 'He geometrizes contin- 

 ually. ' 



It is a difficult, though highly interest- 

 ing, undertaking to investigate the vestiges 

 of primitive geometry. Geometric figures 

 and designs appear in connection with the 

 primitive arts; for example, the making of 

 pottery. Arts long precede anything prop- 

 erly to be called science. The first crea- 

 tions by mankind are instraments for life, 

 though it is surprising how immediately 

 decoration appears; witness the sketches 

 from life of mammoth and mastodon and 

 horses by prehistoric man. But, in a sense, 

 even the practical arts must be preceded by 

 theoretical creative acts of the human mind. 

 Man is from the first a creative thinker. 

 Perhaps even some of our present theo- 

 retical presentation of the universe is due 

 to creative mental acts of our pre-human 

 ancestors. For example, that we inevitably 

 view the world as consisting of distinct in- 

 dividuals, separate, distinct things, is a pre- 

 human contribution to our working theory 

 and representation of the universe. It is 

 conscious science, as a potential presenta- 

 tion and explanation of everything, which 

 comes so late. 



Rude instruments were made for astron- 

 omy. 



The creative imagination which put the 

 bears and bulls and crabs and lions and 

 scorpions into the random-lying stars made 

 figures which occur in the Book of Job, 

 more ancient than Genesis itself. 



The daring astrologer, whose predictions 

 foretold eclipses, saw no reason why his 

 constructions should not equally fit human 

 life. He chose to create a causal relation 

 between the geometric configurations of the 

 planets and the destinies of individuals. 

 This was the way of science, where thought 

 precedes and helps to make fact. No de- 

 scription or observation is possible without 

 a precedent theory, which stays and sticks 

 until some mind creates another to fight it, 

 and perhaps to overshadow it. 



That legend of the origin of geometry 

 which attributes it to the necessity of re- 

 fixing land boundaries in Egypt, where all 

 were annually obliterated by the Nile over- 

 flow, is a too-ingenious hypothesis, made 

 temporarily to serve for history. Some 

 practical devices for measurement arose in 

 Egypt, where periodic fertility fostered a 

 consecutive occupancy, whose records, ac- 

 cording to Flinders Petrie, we have for 

 more than nine thousand years. 



But in the Papyrus of the Rhind, meas- 

 urements of volume come before those for 

 surface. 



Geometry as a self-conscious science 

 waits for Thales and Pythagoras. 



We find in Herodotus that Thales pre- 

 dicted an eclipse memorable as happening 

 during a battle between the Lydians and 

 Medes. The date was given by Baily as 

 B. C. 610. 



So we know about when geometry, we 

 may say when science, began; for though 

 primarily geometer, Thales taught the 

 sphericity of the earth, was acquainted 

 with the attracting power of magnetism, 

 and noticed the excitation of electricty in 

 amber by friction. 



A greater than he, Pythagoras, was born 

 B. C. 590 at Samos, traveled also into 

 Egypt and the east, penetrating even into 

 India. Returning in the time of the last 

 Tarquin, and finding Samos under the do- 

 minion of the tyrant Polycrates, he went 



