Rational Geometery

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. 1904 Excerpt: ...either is in the plane through their point of intersection (cross) perpendicular to the other. Ex. 479. If three planes have two of their intersection-straights parallel, the third is parallel to both. Ex. 480. All straights on two intersecting straights, but not on their cross, are coplanar. Ex. 481. If the vertices of a triangle give equal sects when joined to a point without their plane, the foot of the perpendicular from this point to the plane is the triangle's circumcenter. Ex. 482. All points which joined to three given points give three equal sects are where? Ex. 483. All coplanar points which joined to a given point give equal sects are where? Ex. 484. If a plane contains one straight perpendicular to a second plane, every straight in the first plane perpendicular to the intersection-straight (the meet) of the planes is also perpendicular to the second. Ex. 485. Any plane is equally inclined to two parallel planes. Ex. 486. If JLs from a point to two intersecting planes be = it determines with their meet a plane equally inclined to them. Ex. 487. Construct a plane containing a given straight and perpendicular to a given plane. Ex. 488. Two perpendiculars from a point to two intersecting planes determine a plane perpendicular to the meet of the two planes. Ex. 489. If each of three planes be perpendicular to the other two, their three meets are also perpendicular to the planes and to one another. Ex. 490. If any number of planes perpendicular to a given plane have a common point, they have a common meet (intersection-straight). Ex. 491. If the meets of several planes are parallel, the perpendiculars to them from any given point are coplanar. Ex. 492. Perpendiculars from two vertices of a parallelogram to a plane through the other two are equal. Ex. ...