Geometry is of much assistance in architecture, and in particular it teaches us the use of the rule and compasses, by which especially we acquire readiness in making plans for buildings in their grounds, and rightly apply the square, the level, and the plummet. By means of optics the light in buildings can be drawn from fixed quarters of the sky. Difficult questions involving symmetry are solved by means of geometrical theories and methods.

Heat is a universal solvent, melting out of things their power of resistance, and sucking away and removing their natural strength with its fiery exhalations so that they grow soft, and hence weak, under its glow.

The Phrygians select a natural hillock, run a trench through the middle of it, dig passages, and extend the interior space as widely as the site admits. Over it they build a pyramidal roof of logs fastened together, and this they cover with reeds and brushwood, heaping up very high mounds of earth above their dwellings. Thus their fashion in houses makes their winters very warm and their summers very cool.

Some springs are acid, as at Lyncestus and in Italy in the Velian country, at Teano in Campania, and in many other places. These when used in drinks have the power of breaking up stones in the bladder, which form in the human body.

All these soft kinds [of stone] have the advantage that they can be easily worked as soon as they have been taken from the quarries. Under cover, they play their part well; but in open and exposed situations the frost and rime make them crumble, and they go to pieces. On the seacoast, too, the salt eats away and dissolves them, nor can they stand great heat either.

As for philosophy, it makes an architect high-minded and not self-assuming, but rather renders him courteous, just, and honest without avariciousness. This is very important, for no work can be rightly done without honesty and incorruptibility.

All machinery is derived from nature, and is founded on the teaching and instruction of the revolution of the firmament.