412 APPENDIX OF DRAWING THE 



Fig. 374. 



Let as suppose the edge k 1 m', fig. 373, to be to the 

 edge k' i'", as 7 to 4, and to the edge k' k" as 7 to 6. 



Let the line a b, fig, 374, be the length we may 

 determine upon for the greater terminal edge of the 

 prism ; divide this into 7 equal parts, and 4 of those 

 parts will be the length of the edge k 1 i 1 ", fig. 373, 

 and 6 of them will give the height of the prism. 



Let the inclination of P on M, fig. 373, be known 



and called /,, 

 P..T ....... / 



M..T J 3 . 



And let the plane angle i'" k 1 k", be also known and 



called A t9 



ki'k'm', A z . 



And let us suppose A v an acute, and AI an obtuse 

 angle. 



It is evident that if the solid angle at wz', of such a 

 figure, be supposed to touch the horizontal plane 

 m, the lateral edges being kept perpendicular, the 

 solid angle at k 1 must stand above the plane, and the 

 solid angle at i 1 " still more above it. The elevation 

 of the point at k' may be known by drawing the arc 

 afj fig. 374, with a radius a b, and drawing a second 

 radius bf, making the angle a bf= A 2 90. 



The perpendicular a g dropped on the line f b, 

 will be the required height of the point k 1 above the 

 horizontal plane, and the line g b will be the length 

 of the horizontal projection of the greater terminal 

 edge of the prism. 



