First notions of logic (preparatory to the study of geometry)

by Augustus De Morgan

Every X is B;

then we are certain that

All the As make up part (and part only) of the Bs.

But if we are at liberty further to say that

All the As make up part (and part only) of the Xs

All the Xs make up part (and part only) of the Bs

then we conclude that

All the As make up part of part (only) of the Bs

and the words in Italics mark that quality of the conclusion from which the argument is called à fortiori.

Most syllogisms which give an affirmative conclusion are generally meant to imply à fortiori arguments, except only in mathematics. It is seldom, except in the exact sciences, that we meet with a proposition, ‘Every A is B,’ which we cannot immediately couple with ‘Some Bs are not As.’