comprehended by us, for they are infinite; our understanding gives
the general concept of A MAN, in which all individuals agree.
The number of individuals is infinite; the generic or specific
nature of all being is a unit, or to be apprehended as one only
thing; from this one conception we give the genuine measures of all
existence, and therefore we affirm that a certain class of beings
are rational and discoursive. But when we come to give the nature
of a horse, it is that animal which neighs; and this being common
to all horses, it is manifest that the understanding, which hath
such like conceptions, is in its nature unity. It follows that the
number called the infinite binary must be science; in every
demonstration or belief belonging to science, and in every
syllogism, we draw that conclusion which is in dispute from those
propositions which are by all granted, by which means another
proposition is obtained from the premises. The comprehension of
these we call knowledge; for which reason science is the binary
number. But opinion is the ternary; for that rationally follows
from comprehension. The objects of opinion are many things, and
the ternary number denotes a multitude, as "Thrice happy Grecians";
for which reason Pythagoras admits the ternary. This sect of
philosophers is called the Italic, by reason Pythagoras started his
school in Italy; his hatred of the tyranny of Polycrates enforced
him to abandon his native country Samos.

Heraclitus and Hippasus of Metapontum suppose that fire gives the
origination to all beings, that they all flow from fire, and in
fire they all conclude; for of fire when first quenched the world
was constituted. The first part of the world, being most condensed
and contracted within itself, made the earth; but part of that
earth being loosened and made thin by fire, water was produced;