A Treatise on Descriptive Geometry: For the Use of the Cadets of the United States Military Academy, Volume 1 |
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Common terms and phrases
abscisses asymptotes auxiliary planes axis of rotation base bisect centre chords circumscribed common intersection conceive cone conic section conical surface consequently construction contains corresponding curve of intersection cutting plane cylinder described Descriptive Geometry determined developement diagonal dicular directrix distance draw a tangent ellipse equal evanescent evident face figure generatrix gent given line given point graphic hori horizontal plane horizontal projection horizontal trace hyperbola hyperboloid intersections of surfaces line pierces lines drawn meridian curve meridian plane oblique plane oblique projections obtained operation parabola perpen pierces the horizontal pierces the vertical plane parallel plane passing plane perpendicular plane tangent planes of projections point D point H point of contact point of intersection position PROBLEM projecting line propositions pyramid radius revolve round right angles right line secant sides solution sphere surface of revolution tangent plane THEOREM tion triangle vertex vertical plane vertical projection vertical trace whence zontal
Popular passages
Page 138 - G'H' ; hence GH is equal to G'H, or every diameter bisects its double ordinates. Cor. 2. The squares of the ordinates to any diameter are to each other as the rectangles of their abscissas. PROPOSITION XX. THEOREM. If a cone be cut by a plane...
Page 36 - ... point without the plane of it, be moved around the circumference without ceasing to pass through the point, the surface generated is called a conic surface, and the solid terminated by the surface is called a cone. II. The point is called the vertex, and the circle the base of the cone. The straight line drawn from the vertex to the centre of the circle, is called the axis. If the axis be perpendicular to the plane of the base, the cone is said to be right. III. If the generating line be produced...
Page 18 - Hence, if a right line is perpendicular to a plane, its projections are perpendicular to the traces of the plane, respectively.
Page 146 - AB be made movable about the point B, a string ADC, being tied to the other end of the rule, and to the point C, and if the point A...
Page 129 - A plain curve, such that the distance of every point in it from a fixed point called the focus is equal to the distance of the same point from a fixed line called the directrix and generated from a plane cutting a cone parallel to its side.
Page 140 - The three intersections of the opposite sides of any hexagon inscribed in a conic section are in one right line.
Page 105 - ... known. For, from the vertex B, draw BH perpendicular to AB, and make it equal to the semi-conjugate axis. Join H and the centre C. Then, with C as a centre and CH as a radius, describe a semicircumference, intersecting AB produced in F and F, and these points will be the foci. PROPOSITION II. THEOREM. The squares of the ordinates are to each other, as the rectangles of the segments from the foot of each ordinate respectively, to the vertices of the transverse axis. The equation of the hyperbola...