This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1909 Excerpt: ... straight line. Likewise, if the plane of the curve is perpendicular to the vertical plane, the vertical projection will be a straight line. If the plane of the curve is perpendicular to the ground line, both projections will be straight lines perpendicular to the ground line and the curve will be undetermined. If the ...
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1909 Excerpt: ... straight line. Likewise, if the plane of the curve is perpendicular to the vertical plane, the vertical projection will be a straight line. If the plane of the curve is perpendicular to the ground line, both projections will be straight lines perpendicular to the ground line and the curve will be undetermined. If the plane of the curve is parallel to the horizontal plane, the horizontal projection will be equal to the curve. Likewise, if the plane of the curve is parallel to the vertical plane, the vertical projection will be equal to the curve. The projections of a curve of double curvature are always curved lines. TANGENTS AND NORMALS TO LINES 68. If in a secant line AB, Fig. 4C, the point A be kept fixed and the point B moved along the curve until it coincides with A, the secant AB becomes a tangent to the curve at the point A. Two curves are said to be tangent to each other at a point when they have a common tangent at that point. Tangent to a curve If a straight line is tangent to a plane curve, the tangent will lie in the plane of the curve. This is evident since the secant is in the plane of the curve, and as it moves about the point A it remains in this plane. Two straight lines tang-ent to each other will coincide. In this case the secant of Fig. 46 coincides with the given line. 69. If two lines are tangent to each other in space, their projections on the same plane will be tangent. Let Fig. 46 represent a curve in space with its secant AB. Let these lines be projected upon any plane. Then the projections of the points A and B will approach each other as the points A and B in space approach each other. When the secant AB becomes a tangent in space, the points A and B coincide and their projections will also coincide in the only point common to th...
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