Of the basic truths used in the demonstrative sciences some are
peculiar to each science, and some are common, but common only in
the sense of analogous, being of use only in so far as they fall
within the genus constituting the province of the science in question.
Peculiar truths are, e.g. the definitions of line and straight;
common truths are such as 'take equals from equals and equals remain'.
Only so much of these common truths is required as falls within the
genus in question: for a truth of this kind will have the same force
even if not used generally but applied by the geometer only to
magnitudes, or by the arithmetician only to numbers. Also peculiar
to a science are the subjects the existence as well as the meaning
of which it assumes, and the essential attributes of which it
investigates, e.g. in arithmetic units, in geometry points and
lines. Both the existence and the meaning of the subjects are
assumed by these sciences; but of their essential attributes only
the meaning is assumed. For example arithmetic assumes the meaning
of odd and even, square and cube, geometry that of incommensurable, or
of deflection or verging of lines, whereas the existence of these
attributes is demonstrated by means of the axioms and from previous
conclusions as premisses.
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