Fesapo. Ferio. No A is B. \ / No B is A. All B is C. | = | Some C is B. .'. Some C is not A./ \ .'. Some C is not A. Fresison. Ferio. No A is B. \ / No B is A. Some B is C. | = | Some C is B. .'. Some C is not A./ \ .'. Some C is not A. § 684. The reason why Baroko and Bokardo cannot be reduced ostensively by the aid of mere conversion becomes plain on an inspection of them. In both it is necessary, if we are to obtain the first figure, that the position of the middle term should be changed in one premiss. But the premisses of both consist of A and 0 propositions, of which A admits only of conversion by limitation, the effect of which would be to produce two particular premisses, while 0 does not admit of conversion at all, It is clear then that the 0 proposition must cease to be 0 before we can get any further. Here permutation comes to our aid; while conversion by negation enables us to convert the A proposition, without loss of quantity, and to elicit the precise conclusion we require out of the reduct of Boltardo. (Baroko) Fanoao. Ferio. All A is B. \ / No not-B is A. Some C is not-B. | = | Some C is not-B. .'. Some C is not-A./ \ .'. Some C is not-A. (Bokardo) Donamon. Darii. Some B is not-A. \ / All B is C. All B is C. | = | Some not-A is B .'. Some C is not-A./ \ .'. Some not-A is C. .'. Some C is not-A. § 685. In the new symbols, Fanoao and Donamon, [pi] has been adopted as a symbol for permutation; n signifies conversion by negation. In Donamon the first n stands for a process which resolves itself into permutation followed by simple conversion, the second for one which resolves itself into simple conversion followed by permutation, according to the extended meaning which we have given to the term 'conversion by negation.' If it be thought desirable to distinguish these two processes, the ugly symbol Do[pi]samos[pi] may be adopted in place of Donamon. § 686. The foregoing method, which may be called Reduction by Negation, is no less applicable to the other moods of the second figure than to Baroko. The symbols which result from providing for its application would make the second of the mnemonic lines run thus-- Benare[pi], Cane[pi]e, Denilo[pi], Fano[pi]o secundae. § 687. The only other combination of mood and figure in which it will be found available is Camenes, whose name it changes to Canene. § 688. (Cesare) Benarea. Barbara. No A is B. \ / All B is not-A. All C is B. | = | All C is B. .'. No C is A. / \ .'. All C is not-A. .'. No C is A. (Camestres) Cane[pi]e. Celarent. All A is B. \ / No not-B is A. No C is B. | = | All C is not-B. .'. No C is A. / \ .'. No C is A.