Descriptive geometry . adrant to cast a shadow upon both l^and H. 67. To determine the shadow of a point ona given surface pass the umbra of the point, oras is generally termed, pass a ray of lightthrough the point and determine its intersec-tion with the given surface by Art. 24, page16, or by Art. 57, page 42, according as theshadow is required on a coordinate or on anoblique plane. 68. To determine the shadow of a line upona given surface it is necessary to determinethe intersection of its umbra with that the line be a right line, this is generally bestaccomplished by finding the
Descriptive geometry . adrant to cast a shadow upon both l^and H. 67. To determine the shadow of a point ona given surface pass the umbra of the point, oras is generally termed, pass a ray of lightthrough the point and determine its intersec-tion with the given surface by Art. 24, page16, or by Art. 57, page 42, according as theshadow is required on a coordinate or on anoblique plane. 68. To determine the shadow of a line upona given surface it is necessary to determinethe intersection of its umbra with that the line be a right line, this is generally bestaccomplished by finding the shadows of eachend of the line and joining them. If the linebe curved, then the shadows of several pointsof the line must be obtained. In Figs. 108 and 109 cb is an oblique linehaving one extremity, c, in H. By passingthe ray of light through h and locating itshorizontal trace, the shadow of h is found to fall upon H at h^. Since c lies in H, it is itsown shadow upon H\ therefore, the shadow ofline ch upon H is c^h^^.. 48 DESCRIPTIVE GEOMETRY 69. To determine the shadow of a solid upona given surface it is necessary to determine theshadows of its shade lines. When it is diffi-cult to recognize which lines of the object areits shade lines, it is well to cast the shadow ofevery line of the object. The outline of theseshadows will be the required result. Fig. 110 I represents an hexagonal prismlocated in the first quadrant with its axis per-pendicular to H. Its shadow is representedas falling wholly upon FJ as it would appearif 5^ were removed. Fig. Ill represents theprism when the shadow falls wholly upon H^as it would appear if Fwere removed. represents the same prism when both Vand H are in position, a portion of the shadowfalling upon F, and a portion falling upon is now readily observed that the shade linesare he, cd, de, ep, ps, sg, gk, and M, and thatthe shadow of the prism is the polygon in-closed by the shadows of these shade lines. When an object is so loca
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