172 



THE POPULAE EDUCATOE. 



the horizontal portion from the bottom vanishes at the PS. The 

 points TO and n, from which to draw the retiring edge of the 

 pavement, are found thus : Draw a perpendicular line from & 

 downwards, continue the top of the lowest step at each end, 



Fig. 72. 



lines to meet one drawn from r to s in w, w, w, etc. From each 

 of these points w, draw lines to PS. Where they appear beyond 

 the line TO n, will be represented the retiring edges of the slabs. 

 A diagonal line from n to t will enable us to find the parallel edges 



directed from the PS, until the lines meet the perpendiculars in 

 p and o ; make p r and o s each equal to the depth of the step, 

 6 inches ; rule back again from p and s to PS. These last lines, 

 appearing beyond the edge of the lowest step, will be the per- 

 spective of the sides of the horizontal pavement. To draw the 

 widths of the slabs which compose the pavement, first divide i k 

 into the same number of parts as there are slabs to be repre- 

 sented in v, v, v, etc. From these points draw perpendicular 



Fig. 73. 



of the slabs, because their angles meet the retiring lines which 

 represent the retiring edges, and the diagonal which cuts them. 

 PROBLEM XLIV. (Fig. 74). A flight of ascending steps. Angle 

 of ascent, 25. Seven steps to the first landing, each 8 feet long ; 

 tread, or horizontal surface of each step, I foot 2 inches ; length of 

 first landing, exclusive of the top step, 8 feet. Afterwards, four 

 other steps, the same proportions as the lower. Balustrade, 2 feet 

 wide, and 3 feet high. Angle of the ends of the steps with the 



