Practical engineering drawing and third angle projection, for students in scientific, technical and manual training schools and for ..draughtsmen .. . n the figures used with S.^- ^i-s- ©3. Finally, the line A^ A^ being the hor-izontal trace of the plane determined bythe hnes joining A^ with S^ and S^ mustcontain the horizontal trace, 0, of the linejoining S^ with S^ But this puts A,, andA^ into the same relation with 0 that A^and A sustain to S^; or that of A^ andA^ to »Si. Hence we rightly conclude thaton one plane we can take a point 0 as acentre of projection, and a figure A^ B, G,,and fro
Practical engineering drawing and third angle projection, for students in scientific, technical and manual training schools and for ..draughtsmen .. . n the figures used with S.^- ^i-s- ©3. Finally, the line A^ A^ being the hor-izontal trace of the plane determined bythe hnes joining A^ with S^ and S^ mustcontain the horizontal trace, 0, of the linejoining S^ with S^ But this puts A,, andA^ into the same relation with 0 that A^and A sustain to S^; or that of A^ andA^ to »Si. Hence we rightly conclude thaton one plane we can take a point 0 as acentre of projection, and a figure A^ B, G,,and from them derive a second figure, ^IjJBi C,, which corresponds to the assumedfigure in the same way as if they lay indifferent planes. Figures so related in oneplane are called homological figures and thecentre, 0, a centj-e of homology. 146. Had Ai B^ C, been a circle, and allits points joined with S^, then from what haspreceded we know that A^ 5 C would havebeen an ellipse; as also would have beenthe case were A.^ B^ C„ a circle used in con-nection with (Sj. But our conclusions should enable us to substitute a circle for A^ B^ C„ and using. 48 THEORETICAL AND PRACTICAL GRAPHICS. 0 in the same plane with it get an ellipse in place of the triangle A^Bi Cj. Before illustrating thisit is necessary to show the relation of the axis to the other elements of the problem and to supplya test as to the nature of the conic. 147. First as to the axis, and employing again for a time a space figure (Fig. 93), it is evidentthat raising or lowering the horizontal plane c X Y jDarallel to itself, and with it, necessarily, theaxis, would not alter the kind of curve that it would cut from the cone S. H A B, were the elementsof the latter prolonged. But raising or lowering the centre, S, would decidedly affect the it is, there are two elements of the cone, S A and S B, which would never meet the planec X Y. The shaded plane containing those elements meets the vertical plane in vani
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Keywords: ., bookcentury1800, bookdecade1890, booksubjec, booksubjectlettering
