A Plane's Aspect

Abstract

I AGREE with Mr. Proctor that the disuse of the term “position” in geometry would be a serious misfortune; happily, however, it is not its disuse, but the prevention of its misuse which is contemplated. I cannot agree with him that “position” is a word “which no one can misunderstand,” for his own letter is a striking example of its being misunderstood, either by Mr. Proctor, or by others. “Aspect and slope,” he tells us, “indicate two elements, which, together, fix the position” of a plane. Geometers, however, certainly understand, when a plane is said to be given in position, that something more than its aspect and slope may be regarded as known. Parallel planes have necessarily the same slope and aspect, but surely not the same position. To be told that, because its slope and aspect are invariable, the plane of Saturn's rings has a fixed position in space, notwithstanding that the planet moves bodily in its orbit, would scarcely satisfy a student of astronomy accustomed to geometrical precision.