10

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17 lemmas, and 27 corollaries. There are also 2
scholia. At the same time, I ought to remark that,
while the possible conclusions are innumerable, yet
after all premisses have been iterated so as to exhaust
all the different ways of using them together with all
simpler ways, there will be no more theorems of any
particular interest, and the branch of mathematics in
question may be said to be substantially exhausted. The
theory of conics is an instance. The great geometer
Chasles after he attained to a great age continued
to grind out, by the bushel-basket full, such theorems
as that in a plane, the number of conics that touch five
given conics is 3264. I think that when a mathematical
theory has nothing new to discover but
such propositions as that it may be said to be