PPT Slide
Algorithm for designing a gothic spire
If you want to draw a base plan for a pinnacle, according to the masons’ technique [derived] out of correct geometry, then begin by making a square as shown hereafter with the letters a b c d, so that it is the same distance from a to b as from b to d, d to c, and c to a, as in the figure drawn hereafter.
Then make the square equal in size to the preceding; divide [the distance] from a to b into two equal parts, and mark an e [at the midpoint]. Do the same from b to d and mark an h; from d to c and mark an f; from c to a and mark a g. Then draw lines from e to h, h to f, f to g, and g to e, as in the example of the figure drawn hereafter.
Then make the above-derived square equal in size to the preceding; divide [the side] from e to h into two equal parts, and mark a k [at the midpoint]. Do the same from h to f and mark an m; from f to g and mark an l; from g to e and mark an i. Then draw lines from e to h, h to f, f to g, and g to e, as in the example of the figure drawn hereafter.
Then make the two squares a b c d and i k l m equal in size to the preceding, and rotate the square e h g f, as in the example of the figure drawn hereafter.
Then when you eliminate the remaining lines that are not needed for the setting out, there remains such a form as shown below.