Libro Primo.
9

RULE FOR MEASURING

SQUARE SPIRES

A decorative woodcut printer's ornament featuring symmetrical floral and scrollwork patterns.

BEFORE I applied myself to the enterprise, wanting to assure myself of how much the Spire weighed, I had one palmo of the same stone squared with the greatest diligence, cut from another piece of similar stone in the fashion of a die; and once it was polished, I found that it weighed eighty-six pounds. Then, to investigate how many cubic palmi entered into the body of the Spire, I took the height from the square above, where its point begins, down to the base with a plumb line, and I found the height to be one hundred seven and a half palmi. Having done this, I took the thickness of the foot, which is twelve palmi and five minuti a unit of measurement equivalent to a twelfth of a palmo; I did the same at the square above, under the point, where it is eight palmi and five minuti thick. Above this square, the point rises straight up like another small spire under other angles and another vertex for six palmi. Having noted these measurements, I formed a square similar to the base of the Spire, like the one marked in the margin a. b. c. d. of twelve palmi and five minuti per side, which is the twelfth part of a foot, and inside the first square I formed the second smaller one e. f. g. h. similar to the square above of the Spire, of eight palmi and one-twelfth per side. Now, wanting to measure this body, I found first the area, or let us say the surface, of the smaller square e. f. g. h., which forms a square pillar in the middle of said Spire from top to bottom, which according to the rule, multiplying one face by the other, is sixty-five palmi and forty-nine one-hundred-forty-fourths, which multiplied by the height of the whole Spire, which is one hundred seven and a half palmi, makes seven thousand twenty-four cubic palmi and twenty-three two-hundred-eighty-eighths, which is almost the twelfth part of a palmo; but to show it exactly, we will leave the fraction in its first state. Then, wanting to measure the sloping thicknesses on the four parts, or faces, of the Spire—which thicknesses are those marked e. i. k. f. & f. l. h. m. & h. n. g. o. & g. q. p. e., the sloping remainders of which begin on the square of the base and finish on the smaller square of the point—that is, the surface of that marked e. i. k. f. begins on the face a. b. of the square of the base at points i. & k. and finishes at the angles of the smaller square of the point at points e. & f.; and the f. l. h. m. begins on the face b. d. of said square of the base at points l. & m. and finishes at the angles of said smaller square at points f. & h.; and the h. n. g. o. on the face c. d. at points n. & o. and terminates at the angles g. & h.; and the fourth...

A geometrical diagram showing a large square (a, b, c, d) containing a smaller square (e, f, g, h). Lines connect the corners and midpoints of the outer square to the inner square, creating trapezoidal sections labeled with measurements. Text within the diagram includes "Area P. 65 49/144" and various point labels (a, b, c, d, e, f, g, h, i, k, l, m, n, o, p, q). Measurements like "P. 12 5/12" and "P. 8 1/12" are noted along the sides.