Elements of Descriptive Geometry: With Their Application to Spherical Trigonometry, Spherical Projections, and Warped Surfaces
Wiley & Long, 1835 - Geometry, Descriptive - 174 pages
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angle auxiliary planes axis base becomes called centre coincides colure common conceive cone consecutive consequently construction contained curve cutting plane cylinder determined dicular directrix distance draw drawn parallel drawn perpendicular drawn tangent element ellipse equal equator face falls fixed formed generatrix given line given point ground line hence hori horizontal plane horizontal projection horizontal trace inclination inter intersects the surface jection joining length manner measures meets meridian plane move oblique plane parallel perpen perpendicular pierces the horizontal plane be drawn plane intersects plane of projection plane parallel plane passing plane tangent plane-directer point of contact polar distance pole position primitive circle primitive plane PROBLEM pyramid radius remains respectively revolved right line side space sphere spherical suppose taken tangent plane tion touches transverse axis triangle vertex vertical plane vertical projection vertical trace
Page 39 - A cylinder is conceived to be generated by the revolution of a rectangle about one of its sides as an axis.
Page 160 - 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 46 - 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 124 - ... 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 94 - 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 125 - 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 126 - 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 114 - ... 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 130 - ... 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...