freeman,
he uses pythagorus' theorem, but leaves out the square root (i.e. a calculation), and leaves the numbers as a squared.
Then instead of angles, uses the ratios of opposites (or adjacents) divided by the hypotenuse to define how far apart they are.
He's using trig, just using different terminology, and justifying it by simplicity.
Most engineers and mathematicians would work his way anyway, solving a formula at the end, rather than approximating (through a calculation) each step.
Anyway, the mason's used a compass to work out 30, 45, 60, and 90 degrees (they were so proud to teach us that in Grade 4), and as to
Quote:
If the lines are close to being parallel, the angle is close to zero, while if the lines are
perpendicular, the angle turns out to be, after a highly nontrivial calculation going
back to Archimedes, a number with the approximate value 1. 570 796 326 . . . .

1.57076326x2 = 3.141592652...errm pi, back to the circular reference he started against.