Pantometria — A Geometrical Treatize of Measuring

A geometric diagram positioned to the right of the first paragraph. It illustrates a method for measuring altitude using perpendicular lines labeled with points A, B, C, and D, representing lines of sight and instruments.

With the end C applied to your eye, go backward or forward as you see cause, until you can see the top and base of your altitude by the extremes A and B. By doing so, the distance between your foot and the base is equal to the height, without adding the altitude of your eye, which is required in all the other cases shown before. Only here you shall take heed to couple A and B with C and D so that in beholding the altitude, your line A B may hang perpendicularly or be equidistant to the height. In the same way, you may measure the distance of any two objects in sight, and that exactly, if you use discretion in placing A B so that it is parallel to the line being measured.

The 14th Chapter.

Decorative woodcut initial 'I' with floral motifs.

If any staff is erected, the measurer, upon his back, beholding the top of the object, the distance of the eye from the foot of the object shows the height. Or, receive my meaning more broadly: prepare a straight staff divided into 12 or more equal parts. That done, set it upright at a certain distance (as you wish) from the height you will measure. Now go directly from that staff some distance at your pleasure, placing your eye on the ground level with the base of the object to be measured, moving backward or drawing near to that staff until you can rightly and plainly see the very summit or topmost part of the object to be measured by the top of your staff. Which performed, make a mark where your eye was. Now measure the distance or space from the staff to your eye with the staff itself, and note what proportion the staff has to the distance; the same shall your height have to the length from your eye to the base of that altitude. Example: The staff G D (in this figure) and the distance C E are equal; therefore, affirm the height A B to be equal, as long as the distance between your eye and the base of that required height is A E. If otherwise, according to the proportion aforementioned, you may by the rule (called the "golden precept") bring the just height thus: measure the ground between your eye and the staff, suppose it is 12 feet, then the distance from your eye to the base is 200 feet, and your staff is 5 feet. Say, if 12 yields 5, what shall come of 200? So you have 83 1/3 feet, your exact height.

The 15th Chapter

Decorative woodcut initial 'D' containing a seated human figure.

Example: I would measure the distance between B and G. Suppose the visual line F G cuts your staff (which I would wish divided into 12 parts) upon the 4th part from the top. Then work by the rule of proportion: say 20 parts (the distance between the eye and the staff) gives 200 feet (the distance of the tower); what yields 4 parts? Thus shall you find the fourth number proportional to be 40 feet, which is the exact length of B G. And thus may you measure, only by a staff divided into 12 equal parts (without any other instrument), any altitude, however it be situated.