Calculating the height of an inaccessible object

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Calculating the height of an inaccessible object


Be it that for the need of the manufacturing of a siege engine, the finding of the height of an enemy city wall is requested. In our army camp, we engrave a rectangular triangle so that its hypotenuse and its one perpendicular side aim the requested point of the enemy wall. From an accessible point of the hypotenuse of the triangle we draw a perpendicular line to its other perpendicular side. Due to the creation of two similar triangles, as many times the base of the large triangle is greater than the base of the small one, so many times is the height of one (i.e. the distance of the enemy wall) greater than the height of the other. Henceforth, with the known distance of the enemy wall, we calculate its height with the help of a stick and the localisation of a point on the ground from where we can aim, through the top of the stick, the top of the wall.

SOURCES: "Proklos Diadochos, A Commentary on the First Book of Euclid's Elements"