Welsh Journals

Mathematics. 497 equality, which last does not require any resemblance in shape. You can, of course, imagine a square, circle, tri¬ angle, or any other plane figure exactly as large ; i.e., containing the same number of square miles, as our tight little Island, whose outline is far from resembling any one of those forms. If, however, the outlines of two plane surfaces fit (or coincide—exactly the same meaning) then they cannot help being also equal. Why do I lay a stress on plane surfaces ? Just because two similar patches would not contain the same number of square miles, if one was flat and the other mountainous: the latter would have the best of it. Axiom 9. Observe that the whole must be equal to all its parts taken together; from which, in fact, this ninth is derived, tacitly. 10th. If two straight lines try to en¬ close at one side, they only get farther from each other on the opposite side. N.B.—It is also an axiom that two plane surfaces cannot enclose a solid. The solid Alps are contained between the fiat surface of the map of Switzer¬ land (see axiom eight), and the uneven surface of their own sides. An air bubble is contained between the fiat circle on the water and the hollow hemisphere floating above it. Your pin-cushion is contained—but I am getting out of my latitude, and shall set you a laughing at me instead of "the Hoax—Canto III."—So tata, Miss Polly. Phlogiston. (Continued from No. X., p. 4&3-) The Algebraic "signs" +, —, being nothing more than words of command for the execution of certain opera¬ tions as soon as practicable, the expression a + b is not a result, like the " answer " of an addition sum, but is used S4