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),