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But Clement always regards the articles of the Christian creed as the axioms of a new philosophy.

The "axioms" of geometry are the fixed conditions which occur in the hypotheses of the geometrical propositions.

The special nature of the "axioms" which constitute geometry is considered in the article Geometry (Axioms).

For the subjects under this heading see the articles CONIC SECTIONS; CIRCLE; CURVE; GEOMETRICAL CONTINUITY; GEOMETRY, Axioms of; GEOMETRY, Euclidean; GEOMETRY, Projective; GEOMETRY, Analytical; GEOMETRY, Line; KNOTS, MATHEMATICAL THEORY OF; MENSURATION; MODELS; PROJECTION; Surface; Trigonometry.

The important thing to notice is that where, in any of these five cases, one statement is followed by another, the second is not to be regarded as obtained from the first by logical reasoning involving such general axioms as that " if equals are taken from equals the remainders are equal "; the fact being that the two statements are merely different ways of expressing the same relation.