Part 1, sect. 48.

=1639.= Strictly speaking, the theory of numbers has nothing to do with negative, or fractional, or irrational quantities, _as such._ No theorem which cannot be expressed without reference to these notions is purely arithmetical: and no proof of an arithmetical theorem, can be considered finally satisfactory if it intrinsically depends upon extraneous analytical theories.

--MATHEWS, G. B.

_Theory of Numbers (Cambridge, 1892),