These
connexions have a perceptible existence though they are manifestations
of forms. For the mathematical sciences concern forms: they do not
demonstrate properties of a substratum, since, even though the
geometrical subjects are predicable as properties of a perceptible
substratum, it is not as thus predicable that the mathematician
demonstrates properties of them. As optics is related to geometry,
so another science is related to optics, namely the theory of the
rainbow. Here knowledge of the fact is within the province of the
natural philosopher, knowledge of the reasoned fact within that of the
optician, either qua optician or qua mathematical optician. Many
sciences not standing in this mutual relation enter into it at points;
e.g. medicine and geometry: it is the physician's business to know
that circular wounds heal more slowly, the geometer's to know the
reason why.
14
Of all the figures the most scientific is the first. Thus, it is the
vehicle of the demonstrations of all the mathematical sciences, such
as arithmetic, geometry, and optics, and practically all of all
sciences that investigate causes: for the syllogism of the reasoned
fact is either exclusively or generally speaking and in most cases
in this figure-a second proof that this figure is the most scientific;
for grasp of a reasoned conclusion is the primary condition of
knowledge.
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