First, a few definitions. Surveying is the science based on mathematics which involves measuring any part of the earth's surface and any artificial features on it, and plotting the result on a map or plan drawn to a suitable scale. Often, though by no means always, it also involves levelling or some similar process to record relative heights. Setting out is effectively the converse process, namely locating intended boundaries, structures or engineering works on the ground, in the correct position in all three dimensions. The surveyor will often have to carry out both procedures, especially when linear features such as aqueducts or railways are to be built: first to record the existing shape of the terrain and then, in the light of this information, to decide the best route and to mark it on the ground.

Almost without exception, surveying with instruments that rose above the level of low technology began with the Greeks and Romans, and a proper understanding of their achievements entails straddling two very different disciplines. The present-day surveyor who is curious about the origins of his profession may not be deeply informed on ancient history or engineering, while the classical historian may not have a detailed command of the principles of surveying. The resulting challenge, constantly encountered by historians of technology, is to try to put across the background, the material and the arguments at such a level that no reader feels neglected or patronised. I have done my best to strike a happy mean.