Fibonacci’s Pratica geometrie: philological and linguistic remarks on Distinctio VII.

The paper analyses the seventh distinction of Fibonacci's Pratica Geometrie, dedicated to the heights, and examines its manuscripts' tradition. The calculations are performed using specific measuring instruments, as well as by applying classical geometric theorems. Leonard first explains how to use a vertical stuff of known height (asta in Latin) to determine the height of an object situated at a certain distance by employing the theory of proportions. The author then shows a simple method for calculating the heights of masts suitable for shipbuilding. He recommends using a vertical rod (arundo) as tall as the measurer (mensor). The mensor then lies down on the ground with his feet towards the rod and proceeds as in the previous examples. A third method involves the application of the Pythagorean theorem, as described by Euclid in the first book of the Elements. Leonard presents an exemplum fictum, a fake strategy, in which the mensor uses a bow (arcus) and two arrows (sagittae). He ties two strings of known length to the arrows and then shoots them at the height he wishes to measure, one upwards and the other downwards. The choice of using bow and arrows is rather peculiar, but it is also an example of Leonard’s creativity, as he often devises imaginative exercises in his works. Finally, the author introduces and explains how to use two tools for calculating heights using the properties of similar triangles. One of these tools is the so-called wooden triangle, an instrument frequently used by architects; the second is the well-known quadrant, also called oroscopum. As Annalisa Simi explains, the quadrant is made up of two rigid rods of equal length that define a 90-degree circular sector. A string with a small weight (plumbinum) is attached to the vertex, and two holes are drilled along one of the straight sides. By holding the quadrant vertically and aligning the holes with the upper part of the object we want to measure, the elevation angle can be read from the graduated scale based on the position of the plumbinum.