Vitruvio (10, 9, 1-4) e l’approssimazione archimedea per il Valore Di Π nella CirCuli dimensio. Commentando il de Architectura nella traduzione di Fabio Calvo per Raffaello

Abstract

This paper deals with the value of π that Vitruvius uses in the
description of the odometer (10, 9, 1-4). As known, the value 3 +
1/8, which clearly emerges from the calculations, has been
questioned several times, as if Vitruvius, due to a lack of knowledge
of mathematics, was not aware of the well-known formula 3 +
10/71 < π < 3 + 10/70. In reality Vitruvius resorts to the most
easily memorized value and in use in practice, also handed down by
a branch of the Κύκλου μέτρησις, known through the Latin
translation of the works of Archimedes by Iacopo da San Cassiano.
The De architectura, therefore, represents the oldest attestation
of the formula 3 + 1/8 < π < 3 + 1/7.