Elements of Descriptive Geometry: With Their Application to Spherical Trigonometry, Spherical Projections, and Warped Surfaces |
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auxiliary planes centre coincides cone whose vertex cutting plane cylinder describes the arc determined dicular directrix draw a plane drawn parallel drawn perpendicular drawn tangent ecliptic ellipse generatrix given line given point ground line hence horizontal circle horizontal plane horizontal projection horizontal trace hyperbola hyperbolic paraboloid hyperboloid intersects the surface jection Let the plane line drawn line pierces meridian plane oblique plane pendicular perpen pierces the horizontal pierces the plane pierces the vertical plane be drawn plane be revolved plane intersects plane of projection plane parallel plane passing plane perpendicular plane tangent plane which projects plane-directer point a,a point C,C point F point of contact polar distance pole primitive plane projecting plane pyramid radius required plane revolved position right line sphere surface of revolution tangent plane tion transverse axis tropic of Cancer vertical plane vertical projection vertical trace warped surface zontal plane zontal projection
Popular passages
Page 41 - A cylinder is conceived to be generated by the revolution of a rectangle about one of its sides as an axis.
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 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 48 - Represent a plane which contains the point and is tangent to the cone. 4. Represent a plane which is tangent to a given oblique cone at a point on the surface. 5. Represent a plane which is tangent to a given cone and parallel to a given straight line. (A line through the vertex of the cone and parallel to the given line will lie in the required tangent plane.) CONVOLUTES 113.
Page 2 - Office of the District Court of the United States, fur the Southern District of New York.
Page 128 - axis of the primitive circle, and at an infinite distance from this circle, the projections of the sphere are orthographic, Art. (2). If E, Fig. 85, be any point, e will be its orthographic projection on the plane of a circle whose axis is CM. But that is, the orthographic projection of any point of the surface of a sphere is at a distance from the centre of the primitive circle equal to the sine of its polar distance. 197. The circumference of a circle, oblique to the primitive plane, is projected...
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 97 - CD equal to the subtangent cD (Fig. 1), and joining the points c and D (Fig. 2). It is now required to develop the cone, and trace on the development the curve of intersection with the horizontal plane of projection. Let the cone be developed on the tangent plane passing through the point (c,c'), and let the vertex of the cone be placed at C (Fig. 3). With C as a centre, and a radius equal to the radius of the sphere, describe the arc of the circle Imna, &c., and draw a radius CE to represent the...
Page 70 - E'A'B'6' is its vertical projection, and (DE, DE') is the intersecting plane. Let the surface of the cylinder and the cutting plane be intersected by a system of auxiliary planes parallel to the axis of the cylinder and perpendicular to the vertical plane : FC, ab,fg, and kh are the horizontal traces of such planes. These planes intersect the plane (DE, DE') in lines which are perpendicular to the vertical plane at the points D', d', &c. ; the points in which these lines intersect the elements cut...
Page 16 - ... concealed by the planes of projection. Lines that are given, or required, are made full if they can be seen, but are dotted if concealed by other objects or by the planes of projection. Auxiliary lines, or lines used to aid in the construction of a problem, are always dotted.