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The modern mathematician will readily sympathise with Plato's delight
in the properties of pure mathematics. He will not be disinclined to say
with him:--Let alone the heavens, and study the beauties of number and
figure in themselves. He too will be apt to depreciate their application
to the arts. He will observe that Plato has a conception of geometry,
in which figures are to be dispensed with; thus in a distant and
shadowy way seeming to anticipate the possibility of working geometrical
problems by a more general mode of analysis. He will remark with
interest on the backward state of solid geometry, which, alas! was not
encouraged by the aid of the State in the age of Plato; and he will
recognize the grasp of Plato's mind in his ability to conceive of
one science of solids in motion including the earth as well as the
heavens,--not forgetting to notice the intimation to which allusion has
been already made, that besides astronomy and harmonics the science
of solids in motion may have other applications. Still more will he be
struck with the comprehensiveness of view which led Plato, at a time
when these sciences hardly existed, to say that they must be studied in
relation to one another, and to the idea of good, or common principle
of truth and being. But he will also see (and perhaps without surprise)
that in that stage of physical and mathematical knowledge, Plato has
fallen into the error of supposing that he can construct the heavens a
priori by mathematical problems, and determine the principles of harmony
irrespective of the adaptation of sounds to the human ear. The illusion
was a natural one in that age and country.


 
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