ABSTRACT
The techniques of surveying are required for all the types of construction discussed in the preceding five chapters: for levelling canals, qanats and tunnels; for the lines and levels of dams and bridges; for the alignment and levelling of roads; for the foundations of buildings and setting out the lines of their walls and columns. Another application of surveying, particularly in Roman times, was the division of land into square plots, for example in the allocation of holdings in newly-founded settlements to army veterans. In all these applications, accurate measurements within the limits of the available instruments, together with a knowledge of plane geometry, sufficed to provide satisfactory solutions for the problems. Indeed, the degree of accuracy, from earliest times, was quite astonishing. The Great Pyramid in Egypt, built in the third millenium bc, has a base plan 756 feet square, which comes within 7 inches of forming a perfect square, and the sides are oriented to within less than one tenth of a degree. 1 Survey by triangulation, to determine heights and distances by the use of right-angled triangles, requires a knowledge of plane trigonometry. Geodetic surveying, for example to determine the co-ordinates of places with reference to the equator and a prime meridian, is the most demanding of all from a mathematical point of view, since it involves the use of astronomy and spherical trigonometry. In any type of surveying, however, the final results depend upon the accuracy of the observations.
