This analogy I propose to examine in some detail in the paragraphs which follow.
But before doing so I wish to point out, and I do not think it will be necessary to do more, that a "line" which has length, but neither breadth nor thickness, can be correctly described as "One-dimensional space" i.e.:—space having only one dimension.
A mathematical "point," which has only position and neither length nor breadth nor thickness, can similarly be called space of no dimensions or "Zero-dimensional space." Also I wish to take the opportunity of defining one or two words which I may have occasion to use and have the merit of brevity.
(1) Lines which are drawn through a point for the sake of determining direction are called in Geometrical parlance, "Axes."
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.