Surveying no doubt began at the humblest of levels, and for millennia evolved only slowly. Its functions would encompass the recording of the boundaries of plots of land, estimating their area and, if new-won land was being distributed, dividing it fairly; where irrigation or drainage was involved, ensuring that the gradient of water channels was adequate; in architecture, particularly of prestige buildings, establishing a reasonably horizontal level for foundations and sometimes, especially for religious monuments, the appropriate orientation. All these activities, as at every stage in the history of surveying, were based on geometry. At first this was doubtless entirely empirical and of the simplest kind; and at first the surveyors employed the simplest of tools. The real breakthrough to more complex requirements, to a deeper understanding of geometrical theory, and to procedures and instruments of considerably greater sophistication and precision, was due to the Greeks and Romans in the third and second centuries BC, and it is this revolution which forms the main subject of this book. But to understand its nature we need first to look at what it grew out of. A satisfactory investigation, unfortunately, is impossible simply because, before the treatises on the dioptra of Hellenistic Greece and the Corpus Agrimensorum of imperial Rome, our information is deplorably scanty.

For some topics, like measuring cords and plumb-line levels which hardly changed over centuries, the story is here continued to the end of the Roman period.