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Thus in Fig. 1 AOA´ and BOB´ are axes. The former would be known as "the axis of A," the latter as "the axis of B." Similarly in Fig. 3 COC´ is "the axis of C."

(2) The point in which two or more axes meet, is called the "Origin" and is commonly denoted by the letter O.

(3) When convenient, I shall use the terms, "Two space," "Three space," "Four space," etc., instead of writing "Two-dimensional space," "Three-dimensional space," "Four-dimensional space," etc. in full each time.

THE ANALOGY OF A TWO-DIMENSIONAL WORLD.

The consideration of the analogy of a two dimensional world is necessary because, as Mr. C.H. Hinton says in his book, "The Fourth Dimension," p. 6.

"The change in our conceptions, which we make in passing from the shapes and motions in two dimensions to those in three, affords a pattern by which we can pass on still further to the conception of an existence in four-dimensional space."

Let us start then by imagining a very large, flat and perfectly smooth surface; such for instance as the top of a highly polished table or the surface of a sheet of still liquid.