y have declared nothing whatsoever, inasmuch as affirming,
in my opinion, nothing that is peculiar concerning _sensible_
natures.[438] They looked, as we have previously remarked, to the
relations of phenomena, and having discovered certain "numerical
similitudes," they imagined they had attained an universal principle, or
law. "If all the essential properties and attributes of things were
fully represented by the relations of numbers, the philosophy which
supplied such an explanation of the universe might well be excused from
explaining, also, that existence of objects, which is distinct from the
existence of all their qualities and properties. The Pythagorean
doctrine of numbers might have been combined with the doctrine of atoms,
and the combination might have led to results worthy of notice. But, so
far as we are aware, no such combination was attempted, and perhaps we
of the present day are only just beginning to perceive, through the
disclosures of chemistry and crystallography, the importance of such an
inquiry."[439]

[Footnote 4398: Id., ib., bk. i. ch. ix.]

[Footnote 439: Whewell's "History of Inductive Sciences," vol. i. p.
78.]

These preliminary considerations will have cleared and prepared the way
for a fuller presentation of the philosophic system of Pythagoras. The
most comprehensive and satisfactory exposition of his "method" is that
given by Wm Archer Butler in his "_Lectures on Ancient Philosophy_," and
we feel we can not do better than condense his pages.[440]

[Footnote 440: Lecture VI. vol. i.]

Pythagoras had long devoted his intellectual adoration to the lofty idea
of _order_, which seemed to reveal itself to his mind, as the presiding
genius of the serene and silent world. He had, from his youth, dwelt
with delight upon the eternal relations of space, and determinate form,
and number, in which the very idea of _proportion_ seems to find its
first and immediate development, and without the latter of which
(number), all proportion is absolutely inconceivable. To this ardent
genius, whose inventive energies were daily adding new and surprising
contributions to the sum of discoverable relations, it at length began
to appear as if the whole secret of the universe was hidden in these
mysterious correspondences.

In making this extensive generalization, Pythagoras may, on his known
principles, be supposed to have reasoned as follows: The mind of man
perceives the relations of an eternal _order_