46 
changing substance, and were perpetually inviting attention to an arith- 
metic that took hold upon continuous number and rate of change. Yet 
for centuries without result. The method of exhaustions came very near 
to the invention of the calculus, yet Grecian civilization, with its brilliant 
record, flourished and died without any knowledge of it. A Scotch pro- 
fessor in Dalhousie University was accustomed to say that with the cal- 
culus the Greeks would easily have outstripped us in invention. In depth 
and clearness of thought, in majesty, beauty and originality of ideas and 
ideals, in strength and suppleness of limb and delicney of touch, they 
were Clearly our masters. They could geometrize amazingly, but they had 
no science of continuous number; therefore modern civilization is passing 
theirs with giant strides. 
When the Reformation occurred in Germany, its spirit was abroad 
everywhere. Had Luther not come to the leadership at that time, who 
will say that another Champion would not have arisen to espouse the new 
ideas and stake his life upon their success? 
So, in the intellectual progress of the seventeenth century, new no- 
tions had permeated the mathematical world. The idea of the dependent 
and the independent variable had gained such ground that the then new 
science, analytic geometry, was the necessary result. This new subject 
lent itself readily to the graphic representation of mathematical interde- 
pendence and thus furnished in mathematical form a generalized expres- 
sion and representation for a thing changing in obedience to law. The rate 
of change necessarily followed soon after, and isolated cases of its use 
in determining the tangent to a curve show that it was in the air. New- 
ton and Leibnitz immortalized themselves by noting the mathematical 
drift, seizing the new methods and constructing from them the new disci- 
pline. 
Thus man came into possession of an instrument adapted to discover 
and establish the laws and processes of nature because it is constructed on 
nature’s model. Trees do not increase instantly a foot in height and then 
rest for a period before the next jump. Rivers are not at one instant a 
swelling, muddy flood, and at the next a clear, tranquil stream. The 
Knickerbocker Express does not go by jerks and instantaneous leaps from 
point to point as it passes over the space between Indianapolis and New 
York. But everything from external nature to the innermost soul of 
man connect yarious times, seasons and conditions by continuous num- 
