272. The proof of this necessity of decomposition, besides being fully established by the above example, is found in the elements of all instruction, where, under a form of demonstration, it is necessary to explain propositions which express simply the definitions or axioms that have been before established. For example: we find in the elementary works on geometry this theorem: all the diameters of a circle are equal; and we must, if we would have beginners understand it, give a demonstrative form to that which neither is nor can be any thing more than an explanation, and is almost a repetition of the idea of the circle. When we describe a circle, we fix a point around which we revolve a line called the radius; since then the diameter is nothing more than the sum of two radii continued in the same right line, the mere enunciation of the theorem would seem sufficient to show that it is evidently contained in the idea of the circle, and is as a sort of repetition of the postulate, on which the construction of the curve is founded: still it is not so, and it must be explained as if it were a proof; we must show the diameter to be equal to two radii, these radii to be equal, and at times repeat that this is supposed in its construction: in a word, it is necessary to employ many conceptions to show a truth, which ought to have been known by the simple intuition of one alone, as is the case when the geometrical powers of the intellect have acquired a certain strength and robustness.