Pantometria — A Geometrical Treatize of Measuring (1591) - Page 22

A large landscape woodcut illustration showing practical surveying. On the left stands a large stone building with a vaulted archway and a clock face on its facade. A surveying line is drawn across the middle ground, marked with the letters 'A', 'IIS', and 'L'. A figure stands at point 'A', apparently observing an inaccessible height. The background consists of rolling hills, clusters of trees, and a distant village under a sky with a sunburst appearing behind clouds. In the foreground, a path features a man walking with two dogs, followed by two figures on horseback.

The 13th Chapter.

To get inaccessible heights by calculation (with the help of two places), supposing either side of the scale is divided into 100 parts.

If your thread in the first station falls upon 50 points of the contrary, use those to divide 100, so you have 2. In the other place (going directly backward or forward without deviating), admit it notes 25 of the contrary. Now, 100 divided by 25 results in 4; subtract 2 from 4, and 2 is left as your dividend. Measure the space between both stations and divide that by 2 (your divisor), so you have the height from the eye up. Note: if the difference of the quotient is 1, the space between the stations will be equal to the desired height, adding your stature. If it is 2, the space is double the altitude; if 3, threefold, etc.

Or work thus: reduce the parts of the contrary shadow into portions of the right, and then do as you would with points of the right. That reduction is made thus: multiply 100 by itself, so you have 10,000, which is divided by every part of the contrary shadow; so they shall be as points of the right shadow. If you have made two stations, subtract the lesser quotient from the greater, and weigh the remainder as you have been instructed. The geometer has no end in finding true measures; I could say many, indeed an infinite number of other ways heights are found, by any two equal things orthogonally joined with a staff, cord, square, triangle, glass, etc., as briefly follows.