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 the first who devoted themselves to mathematics, and, by exclusive attention to that study, they were led, at first, to consider their principles as the principles of entities; but as numbers must be before mathematics, they were brought to perceive many resemblances to beings and conditions in numbers, rather than in fire or earth, water or air. Thus, they assumed that a particular combination of numbers is justice, that another is Vital Principle and mind, another proportion or fitness; and further, perceiving the proportions and impressions of harmonic sounds to be numbers, and other things appearing to bear a to numbers, and numbers to be the first of created entities, they assumed that the elements of numbers must be the elements of entities; and that the heavens and every kind of harmony must be numbers. But some, while they held that numbers are elements, believed odd and even to be the origin of numbers, and, therefore, elements in a stricter sense; and, as the unit is derived from odd and even, they regarded it as the origin of all numbers. Enough, however, has been said for rendering apprehensible to the general reader, the import of the terms and the tenour of the argument; and it would be idle, even were the doctrine fully known, to attempt any such as would be required for a full elucidation of this the most abstruse, perhaps, of all the topics of antiquity.

Note 9, p. 22. There are writers who have combined, &c.] Simplicius and Philoponus attribute this opinion to