Practical engineering drawing and third angle projection, for students in scientific, technical and manual training schools and for ..draughtsmen .. . s at infinity where thelower i^lane may be considered as cutting the elements SA and SB. Were S and the shaded f)laneraised to the level of H, so that vanishing line (a) should become tangent to the base, there wouldbe one element, S H, of the cone, parallel to the lower plane, and the section of the cone by the latterwould be the parabola; while the figure as it stands would indicate the hyperbola. The formerwould have but one jjoint at infinit
Practical engineering drawing and third angle projection, for students in scientific, technical and manual training schools and for ..draughtsmen .. . s at infinity where thelower i^lane may be considered as cutting the elements SA and SB. Were S and the shaded f)laneraised to the level of H, so that vanishing line (a) should become tangent to the base, there wouldbe one element, S H, of the cone, parallel to the lower plane, and the section of the cone by the latterwould be the parabola; while the figure as it stands would indicate the hyperbola. The formerwould have but one jjoint at infinity; the latter, two. 148. Raise the centre S so that the vanishing line does not cut the base and, evidently, no Hnefrom S to the base would be parallel to the lower plane; but the latter would cut all the elementson one side of the vertex, giving the ellipse. 149. Bearing in mind that the projection of the circle A H B t is on the lower plane produced,if we wish to bring both these figures and the centre S into one plane, without destroying the relationbetween them, we may imagine the end plane Q L X removed and rotation of the remaining system. occurring about cr ^ in a manner exactly similar to that which would occur were i oj c a system offour pivoted links and the point o pressed toward c. The motion of S would be parallel and equal CONIC SECTIONS AS HOMOLOGOUS FIGURES. 4& to that of 0, and, like the latter, would evidently maintain its distance from the vanishing line anddescribe a circular arc about it. The vanishing line would remain parallel to the axis. 150. From the foregoing we see that to oljtain the hyperbola by projection of a circle from apoint in the plane of the latter we would require simply a secant vanishing line, MX (Fig. 94),,and an axis of homology parallel to it. Take any point P on the vanishing line and join it withany point K of the circle. P K meets the axis at y; therefore the line ky that corresponds to P Kmust also meet the axis at i/. 0 P is anal
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Keywords: ., bookcentury1800, bookdecade1890, booksubjec, booksubjectlettering
