Hence, as the line of sight to the upper part is the longer, it makes that part look as if it were leaning back. But when the members are inclined to… - Vitruvius

Remembering... that Eratosthenes of Cyrene, employing mathematical theories and geometrical methods, discovered from the course of the sun, the shadows cast by an equinoctial gnomon, and the inclination of the heaven that the circumference of the earth is two hundred and fifty-two thousand stadia, that is, thirty-one million five hundred thousand paces.

There will still be the question why Tuscany, although it abounds in hot springs, does not furnish a powder out of which, on the same principle, a wall can be made which will set fast under water. ...The properties of the soil are as different and unlike as are the various countries. ...Hence it is not in all the places where boiling springs of hot water abound that there is the same combination of favourable circumstances... For things are produced in accordance with the will of nature; not to suit man's pleasure, but as it were by a chance distribution.

In accordance with the foregoing investigations on mathematical principles, let bronze vessels be made, proportionate to the size of the theatre, and let them be so fashioned that, when touched, they may produce with one another the notes of the fourth, the fifth, and so on up the double octave.