The Geometry of the Roman Torino, that is to say the Varatio of Augusta Taurinorum

This work is proposing the use of the geometry based on rectangular triangles, the varatio, in the study of the planning of Roman Torino, that is, of Augusta Taurinorum. It is known that the planning of Roman towns was based on the centuriation, a grid of parallel and perpendicular streets, where the two main axes were the Decumanus and the Cardo. By means of the varatio, the angle the Decumanus was forming with the east-west direction was given by the ratio of the catheti of a rectangular triangle. In the case of Torino, the town planning seems based on the ratio of catheti 1:2, which is giving an azimuth of the decumanus (Via Garibaldi) of 116,565° from true north. This value is in good agreement with the measurement of the direction of this street.