412 



GARDEN PLANNING 



to five units, and from A as centre another arc of radius 

 equal to four units. Join the point D where the arcs 

 intersect to A, and the line D A will be at right angles 

 to A B. This follows from the well-known property 

 of the right-angled triangle, that the square on the 



Fig. VIII 



hypothenuse is equal to the sum of the squares on the 

 other two sides, thus : 



3X3+4X4 = 5X5^ 



When using this method on a considerable scale, 

 apply it to the longest lines in the figure, and work out 

 the smaller details with reference to the two right-angled 

 lines first laid down. This method was used in setting 

 out the Pyramids. 



An Equilateral Triangle. Taking A B as the dimension 

 of one side, describe arcs of radius A B intersecting at 

 C and join C A, C B. See Figure VII. 



Stars. These should be described within a circle 

 so that all points lie on the circumference. A second 

 smaller circle should be described to fix the points of the 

 entering angles, which must be midway between the 

 circumferential points. This may be done by describing 

 arcs of equal radius from two adjacent points, and con- 

 necting their intersections with the centre of the circle. 

 The point where this line intersects the smaller circle 



