Pantometria — A Geometrical Treatize of Measuring

Of the Scale.

For the scale, you shall draw from either side of your quadrant a straight hanging line (as is declared) touching the middle line in one point. So have you the sides of your scale each to be divided into 12, 60, 100, or 1000 points, all marked from the center A; the more, the more convenient. Do not forget to have two equally fine plates of brass pierced in the middle (for your sights) and placed on the side A D, as you see E F, with a line and plummet hanging from the center A. I call the scale in this quadrant the two sides within, divided into certain portions or parts. These 12 parts next to your sights I name "points of right shadow"; the other side of the scale, "portions or points of contrary shadow." It would be better, indeed more for the purpose, if each side had 60, 100, or 1000 divisions.

The 8th Chapter.

A woodcut illustration depicting a landscape with a tall building on the left and a hill with a ruin on the right. The sun is shining, and rays are directed toward the building. In the foreground, figures are using quadrants on stands to measure the shadows cast by the structures. The diagram includes labels A, B, C, and numerical markings on the quadrants.

Convey the left side of your geometrical quadrant toward the sun, the thread and plummet having their free course, moving it up or down until both your sights have received the sunbeams. Then, if your thread is found on the twelfth part, the shadows of all things (being perpendicularly elevated) are equal to their bodies. If the plummet with the thread is perceived cutting the parts next to the sights, which I call "right shadows," then every direct thing is more than its shadow. By that proportion which 12 exceeds the parts where the thread was found: if it falls on the first part of right shadow, take the shadow 12 times to make the height; if it chances on the second portion, six times; on the third, four times; on the fourth, three times; on the fifth, twice and two-sixths of the shadow; on the sixth point, twice; on the seventh, once and five-sevenths of the shadow; on the eighth portion, once and a half; on the ninth, once and the third part; on the tenth, once and the fifth part; on the eleventh point, you shall take the shadow once and the eleventh part of that shadow. Or, in few words, multiply the length of the shadow by 12, and divide the product by the parts in which you found the thread; your quotient shows the height. But if it is in the parts of "contrary shadow," multiply the length of the shadow by the parts declared by the plummet, and divide the increase by 12; thus comes the altitude also. An example of this is plain to be perceived in the preceding figure.