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 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 hori horizontal circle horizontal plane horizontal projection horizontal trace hyperbolas 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 PROBLEM projecting plane pyramid radius required plane revolved position right line sphere surface of revolution tangent plane tical 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 161 - 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 48 - I'H'), and tangent to the surface of the cone. If we draw through E the tangent EP, it will be the horizontal trace of the second plane which is parallel to the given line (IH, I'H'), and tangent to the surface of the cone. The vertical trace of this plane is easily constructed. § 96. This problem becomes impossible when the line (AE, A'E'), which is drawn through the vertex of the cone and parallel to the given line, passes within the surface : in this case, it would pierce the base of the cone...
Page 126 - ... 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 into an ellipse. For the projecting...
Page 95 - 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 129 - 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 130 - THEOREM The angle formed within a circle by the intersection of two chords is measured by half the sum of the two intercepted arcs.
Page 115 - ... is north or south according as the place is north or south of the equator. § 169. Small circles parallel to the equator are called parallels of latitude. § 170. The ecliptic is a great circle making an angle of 23° 30' nearly, with the equacor ; the points in which it intersects the equator are called the equinoctial points.
Page 14 - ... the projections of cd, PI. I., Fig. 2. 9. Remark. A general principle, which it is important to be perfectly familiar with, is embodied in several of the preceding examples; viz. When any line is parallel to either plane of projection, its projection on that plane is equal and parallel to itself, and its projection on the other plane is parallel to the ground line. 10. The preceding remark serves to show how to find the true length of a line, when its projections are given. When the line, as...
Page 132 - ... 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 into an ellipse. For the projecting...