CHAP. IX.] METHODS OF ABBREVIATION. 137 



deliberate preference, and keeping in view the mean relative to 

 human nature. 



Properly speaking, this is not a definition, but a description 

 of virtue. It is all, however, that can be correctly inferred from 

 the premises. Aristotle specially connects with it the necessity 

 of prudence, to determine the safe and middle line of action ; and 

 there is no doubt that the ancient theories of virtue generally 

 partook more of an intellectual character than those (the theory 

 of utility excepted) which have most prevailed in modern days. 

 Virtue was regarded as consisting in the right state and habit of 

 the whole mind, rather than in the single supremacy of con- 

 science or the moral faculty. And to some extent those theories 

 were undoubtedly right. For though unqualified obedience to 

 the dictates of conscience is an essential element of virtuous con- 

 duct, yet the conformity of those dictates with those unchanging 

 principles of rectitude (alwvta Sticma) which are founded in, or 

 which rather are themselves the foundation of the constitution of 

 things, is another element. And generally this conformity, in 

 any high degree at least, is inconsistent with a state of ignorance 

 and mental hebetude. Reverting to the particular theory of 

 Aristotle, it will probably appear to most that it is of too ne- 

 gative a character, and that the shunning of extremes does not 

 afford a sufficient scope for the expenditure of the nobler energies 

 of our being. Aristotle seems to have been imperfectly conscious 

 of this defect of his system, when in the opening of his seventh 

 book he spoke of an "heroic virtue"* rising above the measure 

 of human nature. 



7. I have already remarked (VIII. 1) that the theory of sin- 

 gle equations or propositions comprehends questions which can- 

 not be fully answered, except in connexion with the theory of 

 systems of equations. This remark is exemplified when it is 

 proposed to determine from a given single equation the relation, 

 not of some single elementary class, but of some compound class, 

 involving in its expression more than one element, in terms of 

 the remaining elements. The following particular example, and 

 the succeeding general problem, are of this nature. 



* Tt}v vnep 7/ict dptr^v rjpuiiicfiv nva /cat 0tiav.- NIC. ETII. Book vii. 



