Elements of geometry and trigonometry . 192 GEOMETRY Sciiolium. Vertical angles, suchas ACO and BCN are equal ; foreither of them is still the angleformed by the two planes ACB,OCN. It is farther evident, that, in theintersection of two arcs ACB, OCN,the two adjacent angles ACO, OCB,taken together, are equal to tworight PROPOSITION VII. THEOREM. If from the vertices of the three angles of a spherical triangle, aspoles, three a?cs be described forming a second triangle, thevertices of the angles of this second triangle, will be respectivelypoles of the sides of the first. From the vert
Elements of geometry and trigonometry . 192 GEOMETRY Sciiolium. Vertical angles, suchas ACO and BCN are equal ; foreither of them is still the angleformed by the two planes ACB,OCN. It is farther evident, that, in theintersection of two arcs ACB, OCN,the two adjacent angles ACO, OCB,taken together, are equal to tworight PROPOSITION VII. THEOREM. If from the vertices of the three angles of a spherical triangle, aspoles, three a?cs be described forming a second triangle, thevertices of the angles of this second triangle, will be respectivelypoles of the sides of the first. From the vertices A, B. C,as poles, let the arcs EF, FD,ED, be described, forming onthe surface of the sphere, thetriangle DFE ; then will thepoints D, E, and F, be respec-tively poles of the sides BC,ACAB. For, the point A being thepole of the arc EF, the dis-tance AE is a quadrant ; thepoint C being the pole of the arc DE, the distance CE is likewise a quadrant : hence the point E is removed the length of aquadrant from each of the points A and C ; hence, it is thepole of the arc AC (Prop. V. Cor. 3.). It might be shown, bythe same method, that D is the pole of the arc BC, and F thatof the arc AB.
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Keywords: ., bo, bookcentury1800, booksubjectgeometry, booksubjecttrigonometry
