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[9] Being about to give a strict logical definition of Virtue,

Aristotle ascertains first what is its genus [Greek: ti estin].

[10] That is, not for merely having them, because we did not make

ourselves.

See Bishop Butler's account of our nature as containing

"particular propensions," in sect. iv. of the chapter on Moral

discipline, and in the Preface to the Sermons.

[11] This refers to the division of quantity ([Greek: poson]) in

the Categories. Those Quantities are called by Aristotle

Continuous whose parts have position relatively to one another,

as a line, surface, or solid, those discrete, whose parts have no

such relation, as numbers themselves, or any string of words

grammatically unconnected.

[12] Numbers are in arithmetical proportion (more usually called

progression), when they increase or decrease by a common

difference thus, 2, 6, 10 are so, because 2 + 4 = 6, 6 + 4= 10,

or vice versa, 10 - 4 = 6, 6 - 4 = 2.