Synthetic Projective Geometry (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. 1906 edition. Excerpt: ... cut of its eject from a projection-vertex not on it. Homography is the most general transformation which transforms straights into straights. 186. Two planes, taken as both point fields and straight fields, are called 'reciprocal' when they are so correlated that to each point on the one (without exception) one and only one straight on the other corresponds and vice versa; and so that to a point and straight of the one plane which belong to one another correspond in the other plane a point and straight belonging to one another. To costraight points in the first plane correspond copunctal straights in the second. 187. Two sheaves, taken as both plane sheaves and straight sheaves, are called homographic if to each straight of the one corresponds a straight of the other, and to each plane a plane, and vice versa; and so that if a straight and plane belong to each other in the one, so do their correlatives in the other. 188. Two sheaves, taken as both plane sheaves and straight sheaves, are reciprocal if to each straight of the one corresponds a plane of the other, and to each plane a straight, and vice versa; and so that if a straight and plane belong to each other in the one, so do their correlatives in the other. 189. A plane and sheaf are homographic when to every point of the plane corresponds a straight of the sheaf, and to every straight of the plane a plane of the sheaf; and so that if the point and straight in the plane belong to each other, so do the straight and plane of the sheaf. 190. A plane and sheaf are reciprocal when to each point of the plane corresponds a plane of the sheaf, and to every straight of the plane corresponds a straight of the sheaf; and so that if the point and straight belong to each other in the plane, the plane...