Universa Philosophia

The four modes of the first figure are the prototype and model of the most perfect reasoning, to which the other modes are recalled, as gold to the Lydian stone. I warn, however, that those modes have their beginning from four consonants, B. C, D. F.; the other modes begin from the same consonants, in order to signify that they are recalled to those perfect modes to which they are similar in that consonant: for example, all those to which B. gives a beginning, to Barbara: to celarem, all beginning with C. and so on.

In some modes m. is found, to signify that modes of this kind are to be converted, with the premises changed: for example, so that in the conversion there is placed as the major proposition what was the minor in the converted syllogism: and the major becomes the minor. S. and P. are also found. S. signifies that the proposition which precedes S. ought to be converted simply: but P. signifies that the preceding proposition ought to be converted per accidens. But what conversion simply and per accidens is, I have already shown in disputation 3.

To Barbara are reduced Baraliptom, Barocho, and Bocardo: only Baraliptom is deduced ostensively, but Bocardo and Barocho through the impossible. Baraliptom differs from Barbara only because the conclusion was indirect: but it is deduced to Barbara, not through conversion per accidens: for this cannot be in a particular proposition: but it is converted in this way, there ought to be in Barbara, every rational thing runs, it is said in Baraliptom, some running thing is rational, which was conversion per accidens: but in order that Baraliptom be reduced to Barbara, that conversion is dissolved, and the converted proposition is taken as if it had not been converted, and it is said, therefore every rational thing runs: for thus one returns to the direct conclusion in Barbara. And so P. in Baraliptom does not signify that the conclusion is to be converted per accidens, but rather that it is already converted per accidens from Barbara in Baraliptom.

To celarem are converted celantes, Cesare, camestres. An example in celantes, by converting simply only the conclusion, for in the others celarem and celantes do not differ: for example, no man runs: every rational thing is a man: therefore no running thing is rational, but if you say, therefore no rational thing runs, it will be in Cesare: but this is done through the simple conversion of the celantic conclusion.

Cesare is converted through only the simple conversion of the major: for example, no man runs: every lion runs: therefore no lion is a man: but if in the major you say no running thing is a man, the syllogism is in celarem.

Camestres is more difficult to convert: because the premises are to be transposed, likewise the minor and the conclusion are to be converted simply: for example, every lion runs, no man runs, therefore no man is a lion: but if you say, no running thing is a man: every lion runs, therefore no lion is a man, you will make celarem: but the camestric minor has been converted simply, and made the major, and similarly the conclusion has also been converted simply.

To Dary are reduced dabitis, darapti, dissamis, and datisi. Dabitis by the simple conversion of the conclusion alone, an example of which is easy. Darapti by the conversion per accidens of the minor alone, for example, every man runs, every man is rational: therefore some rational thing runs. It is in darapti; but if in the minor you say some rational thing is a man, you will make a syllogism in darii with the same major and conclusion. Dissamis is converted with the premises changed, and the major converted simply, and similarly also the conclusion, for example: some man runs, every man is rational: therefore some rational thing runs, is in dissamis; but say, every man is rational, some running thing is a man; therefore some running thing is rational. Datisi is deduced with the minor simply converted, the major and conclusion retained.

To ferio are reduced sapesmo with the major converted per accidens, and the minor converted simply, and with the premises changed. For example, every man runs: no lion is a man, therefore some running thing is not a lion, is in sapesmo: but it ought to be converted. No man is a lion, some running thing is a man: therefore some running thing is not a lion, is in ferio. Frise somorum is converted with the premises changed, and with them simply converted. Festino with the major converted simply. Felaptom with the minor converted per accidens. Ferison, with the minor converted per accidens.