When truly adjusted the theodolite measures the horizontal angle between any two objects, however much they may differ in altitude, as the pole star and any terrestrial object.
They are based upon theodolite traverses 15 m.
Akin to the geometrical works is that On the Dioptra, a remarkable book on land-surveying, so called from the instrument described in it, which was used for the same purposes as the modern theodolite.
It combines the planisphere and armillae of Hipparchus and others, and the theodolite of Theon, and was usually of brass, varying in diameter from a couple of inches to a foot or more.
If, however, a theodolite, fitted with a telescope which can rotate about a horizontal axis and having an altitude circle, is employed, so that when observing a transit the altitude of the sun or star can be read off, then the time need only be known to within a minute or so.