Demonstrative, i. e. reasoning which is of necessary force, and
such as cannot be rejected by the mind that understands and
follows its process. In mathematics not only is the reasoning of
this kind, but the matter on which it is employed is necessary
also. In logic the matter may be necessary, contingent, or even
false, but the reasoning will be necessary or apodeictic,
if the principles of the science have been obeyed.