DEFINITION OF POSITIONS
14. Take a pencil and a piece of paper. With the pencil, on the paper, mark a dot or point.
Fig. 3
By this dot (A) three ideas are expressed: an idea of Tone, the tone of lead in the pencil; an idea of Measure, the extent of the space covered by the dot; and an idea of Shape, the character given to the dot by its outline or contour. The dot is so small that its tone, its measure, and its shape will not be seriously considered. There is another idea, however, which is expressed by the dot or point,—an idea of Position. That is its proper meaning or signification. There is presumably a reason for giving the dot one position rather than another.
POSITIONS DETERMINED BY
DIRECTIONS AND DISTANCES
15. Put another dot (B) on your paper, not far from dot “A.”
Fig. 4
We have now a relation of two positions,—the relation of position “A” to position “B.” The relation is one of Directions and of Distances. Proceeding from “A” in a certain direction to a certain distance we reach “B.” Proceeding from “B” in a certain direction and to a certain distance we reach “A.” Every position means two things; a direction and a distance taken from some point which may be described as the premise-point.