The dioptra became the standard surveying instrument of the Greeks and, although no actual example has yet been found (or at least identified), we can discover a surprising amount about its design and employment by tapping sources hitherto almost untouched. Apart from Hero's well-known manual, three treatises or fragments of treatises on the dioptra survive under the names of Julius Africanus, the Anonymus Byzantinus and al-Karaji, along with many passing mentions in other literature. To ease the diffculties of understanding these sources, it may help at this early stage to paint a brief preliminary picture of this very flexible device. Contrary to widespread belief, Hero's complex dioptra was not the only version. It was, rather, a oneoff and probably fruitless attempt at improving on the earlier and much simpler dioptra, which already existed in a number of varieties that differed only in detail.

This simple type was a disc, engraved with two diameters at right angles and carrying an alidade or comparable sighting bar pivoted at its centre (Figs. 3.1–2). It could be mounted in two different ways. If it was suspended on edge by a ring from a suitable stand it acted as its own plumb, and hung vertically. A horizontal sighting line for levelling was obtained by aligning the alidade with the horizontal diameter.