A Treatise on Special or Elementary Geometry Volume 3; In Four Parts (Paperback)

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1872 Excerpt: ...with geometrical figure, yet having a latitude in its use which the other does not possess. The locus of a point is the line (geometrical figure) generated by the motion of the point according to some given law. With strict propriety only the latter sections of this chapter belong to the Modern Geometry, technically so called. Bnt, as the entire chapter is composed of matter which has not hitherto found place in our common text-books, and the relative importance of which is becoming more fully appreciated in modern times, the author has ventured to embrace the whole under this title. t The word Locus is the Latin tot place. In the same manner, a surface is conceived as the locus of a line moving in some determinate manner. Ill's.--The locus of a point in a plane, which point is always equidistant from the extremities of a given right line, is a straight line perpendicular to the given line at its middle point. Thus, suppose AB a fixed line, and the locus of a point equidistant from its extremities is required; that point may be anywhere in a perpendicular to AB at its middle point, and cannot be anywhere else in this plane. A 1 8 This perpendicular is the locus (place) of a point subject to the given law. Again, a boy on the green is required to keep at just 0 20 feet from a certain stake; where may he be found? FlG 444 i. -., what is his locus (place)? Evidently, the circumference of a circle whose radius is 20 feet. Thus, the locus of a point in a plane, equidistant from a given point, is the circumference of a circle. This is the place of such a point. What is the locus in space of a point equidistant from a given point? What is the locus of a point in space equidistant from the extremities of a given line? A plane. What is the locus of a line movin...