Problem VI
To Draw Any Triangle, Given in Position and Magnitude, in a Horizontal Plane
Let A B C (Fig. 18.) be the triangle.
As it is given in position and magnitude, one of its sides, at least, must be given in position and magnitude, and the directions of the two other sides.
Let A B be the side given in position and magnitude.
Then A B is a horizontal line, in a given position, and of a given length.
Draw the line A B. (Problem V.)
Let a b be the line so drawn.
Find V and V′, the vanishing-points respectively of the lines A C and B C. (Problem III.)
Then a b c is the triangle required.
If A C is the line originally given, a c is the line which must be first drawn, and the line V′ b must be drawn from V′ to c and produced to cut a b in b. Similarly, if B C is given, V c must be drawn to c and produced, and a b from its vanishing-point to b, and produced to cut a c in a.
Notes
From a draw a V, and from b, draw b V′, cutting each other in c.