Essentials of Descriptive Geometry |
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allel Analysis auxiliary planes axis circle cube curve of intersection cylinder develop the surface directrix draw a tangent Draw the projections ellipse Find the angle Find the intersection find the line Find the projection Find the traces generatrix given line given oblique given point given straight line ground line helicoid helix horizontal plane horizontal trace hyperbola hyperbolic paraboloid hyperboloid intersecting lines line MN line of intersection line pierces oblique to H OP Art parabola parallel to H pass a plane perpendicular to H pierce H plane containing plane parallel plane perpendicular Plane section plane tangent planes of projection planes will cut point in space position prism problem projecting lines pyramid radius rectilinear element required line right circular cone secant strike an arc surface of revolution system of auxiliary tangent plane third angle tion true length vertex vertical plane vertical projection vertical trace warped surface zontal
Popular passages
Page 50 - An ellipse is a curve which is the locus of a point that moves in a plane so that the sum of its distances from two fixed points in the plane is constant.
Page 52 - F'. These points will be the foci, for DF + DF' = 2CV = VV. IV. The hyperbola, which may be generated by moving a point in the same plane, so that the difference of its distances from two fixed points shall be equal to a given line.
Page 69 - Any position of the generatrix is called an element of the surface. This surface has a second rectilinear generation in which any two rectilinear elements of the first generation may be taken as directrices and a plane which is parallel to the first directrices as a plane directer.
Page 31 - ... understood to be the angle which the line makes with its projection on that plane. If a perpendicular be dropped to the plane from any point in the given line, the angle between this perpendicular and the given line is the complement of the angle which the line makes with the plane. Therefore, find the angle between the given line and a perpendicular to the plane from any point of the line and construct its complement. This complement is the required angle. Let the construction be made in accordance...
Page 14 - When an object is revolved about a straight line as an axis, the relative position of its points is not changed. The object can thus be brought into a simpler position with reference to the planes of projection. The...
Page 15 - ... be revolved about a right line as an axis, when it is so moved that each of its points describes the circumference of a circle whose plane is perpendicular to the axis, and whose center is in the axis. if the point M, Fig. 6, be revolved about an axis DD', in the horizontal plane, it will describe the circumference of a circle whose center is at o and whose radius is Mo ; and since the point must remain in the plane perpendicular to DD', when it reaches the horizontal plane it will be at p or...
Page 48 - Tangent to a curve. 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. 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 as it moves about the point A remains in the plane of the curve.
Page 74 - ... contact. If any plane be passed through the point of contact, it will cut a straight line from the tangent plane and a line from the surface, and these lines will be tangent to each other. Since two intersecting lines will determine a plane, it follows that a plane tangent to a surface at a given point is determined by two straight lines tangent at this point to two lines of the surface. In any ruled surface, the rectilinear element through the point of contact lies in the tangent plane; for...
Page 53 - An ordinary helix is the path, of a point moving on the surface of a cylinder of revolution so as to intersect its elements at a constant acute angle. The axis of the cylinder is the axis of the helix.
Page 31 - Given the projections of two lines of a plane and the projections of a line in space, find the angle which the line makes with the given plane. Analysis. The angle which a line makes with a given plane is understood to be the angle which the line makes with its projection on that plane. If a perpendicular be dropped to the plane from...