Elements of Descriptive Geometry: With Their Application to Spherical Trigonometry, Spherical Projections, and Warped Surfaces

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Barnes, 1868 - Geometry, Descriptive - 174 pages
 

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Page 61 - Any geometrical magnitude or object is said to be revolved about a right line as an axis, when it is so moved that each of its points describes the circumference of a circle whose plane is 'perpendicular to the axis, and whose centre is in the axis.
Page 41 - A right circular cone is often called a cone of revolution, because it can be generated by the revolution of a right-angled triangle about one of its shorter sides.
Page 131 - The angle formed by the intersection of two chords is measured by half the sum of the two intercepted arcs. Let the two chords AB, CD intersect each other at the point E ; then will the angle DEB, or its equal, AEC, be measured by half the two arcs DB and A C.
Page 163 - AB, the horizontal projection of one directrix, the parts from 2 to 3, from 3 to 4, from 4 to 5, &c. be each made equal to the part from 1 to 2 ; and on CD...
Page 14 - A'B' are the projections, is the line of intersection of these two planes, and since the planes are determined in position, their intersection is also determined. If the horizontal projection only be given, the line is somewhere in a plane passing through the horizontal projection and perpendicular to the horizontal plane, but its position in this projecting plane is not determined. So, when the vertical projection only is given, the line may have any position in the plane passing through the projection...
Page 112 - ID" do not touch or cut the circle FEE", the conditions of the problem are impossible, and then no triangle can be constructed with such data, CASE VI. The three angles of a spherical triangle being given, to find the sides-. § 154. PI. 3. Fig. 2. Let ABC be the triangle, and A, B{ and C the given angles. Let G'l be the intersection of two planes at right angles to each other. Draw a plane perpendicular to the vertical plane, and making one of the given angles, as A, for example, with the horizontal...
Page 115 - The solution of problems relating to these magnitudes in space. These drawings are so made as to present to the eye, situated at a particular point, the same appearance as the magnitude or object itself, were it placed in the proper position. The representations thus made are the projections of the magnitude or object.
Page 163 - From 1 to 2 From 2 to 3 From 3 to 4 From 4 to 5 From 5 to 6 From 6 to 7 From 7 to...
Page 118 - Hie pole above the horizon of anyplace is equal to the latitude of that place. For, let (PI. 1. Fig. 1) HESP be the meridian passing through the place P on the surface of the sphere ; HO perpendicular to PP', the horizon, NS the axis, and EQ the equator. The arc NH measures the elevation of the pole above the horizon, and QP is the latitude of the place (168). But the arc PNH...
Page 14 - ... the line itself will be at the same time parallel to the two planes of projection. If a line be perpendicular to one of the planes of projection, its projection upon this plane will only be a point, and its projection upon the other plane will be perpendicular to the ground-line. Thus, for example, if the line in question be perpendicular to the horizontal plane, its horizontal projection will be only a point, and its vertical projection will be perpendicular...

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