A science, then, may be analysed into three constituents. These are: (1) a determinate class of objects which form the subject-matter of its inquiries. In an orderly exhibition of the contents of the science, these appear, as in Euclid, as the initial data about which the science reasons; (2) a number of principles, postulates, and axioms, from which our demonstrations must start. Some of these will be principles employed in all scientific reasoning. Others will be specific to the subject-matter with which a particular science is concerned; (3) certain characteristics of the objects under study which can be shown by means of our axioms and postulates to follow from our initial definitions, the _accidentia per se_ of the objects defined. It is these last which are expressed by the conclusions of scientific demonstration. We are said to know scientifically that B is true of A when we show that this follows, in virtue of the principles of some science, from the initial definition of A. Thus if we convinced ourselves that the sum of the angles of a plane triangle is equal to two right angles by measurement, we could not be said to have scientific knowledge of the proposition. But if we show that the same proposition follows from the definition of a plane triangle by repeated applications of admitted axioms or postulates of geometry, our knowledge is genuinely scientific. We now know that it is so, and we see _why_ it is so; we see the connection of this truth with the simple initial truths of geometry.