78 GARDEN DESIGN 



gles three points can be found from which an accur- 

 ate line can be sighted. 



2. Find the length of A B, or a convenient 

 portion of it, and stretch the line as in the previous 

 method making C B and C A the same length as 

 the base. Leave the tape fixed at B, release it at 

 A and carry it in the same direction as C B to the 

 same length that it was fromB, giving a point D. 

 A line from D to A is at right angles to A B. This 

 is a practical application of the proposition that the 

 three angles of a triangle are together equal to 

 two right angles. In the diagram the value of 

 the angles has been marked, and it will be seen 

 that the Equilateral triangle ABC has its angles 

 each worth 60. The line CA with BD must 

 cause 1 80, which leaves 120 on the other side of 

 the angle A C B. Then if C D and C A are equal 

 the isosceles triangle formed has the angles at 

 the base equal, and with 120 at the apex, 30 must 

 be their respective values ; 30 added to 60 makes 

 90, which is the right angle required. An isosceles 

 triangle set up on the base gives the same result, 

 but the proof is not so evident. 



3. This method depends on the Euclid proposi- 

 tion that " the square on the sides subtending a 

 right angle is equal to the squares on the sides 

 containing the right angle." The measurements 

 of 3, 4 and 5, and their multiples fulfil these con- 

 ditions. 3x3 = 9. 4 x 4 = 16. 9 + 16 = 25 

 which is 5 x 5. In practice 3, 4 and 5 ft. make 



