"[T]hough Heron's ability is sufficiently indicated by... [his] proofs, as a general rule he confines himself merely to giving directions and formulae. ...[H]e availed himself of the highest mathematics of his time. Thus in the ', two chapters treat of the mode of drawing a plan of an irregular field and of restoring, from a plan, the boundaries of a field in which only a few landmarks remain. ... The method is closely similar to the use of latitude and longitude introduced by Hipparchus. So...Heron gives, for finding the area of a regular polygon from the square of its side, formulae which imply a knowledge of trigonometry. Suppose F_n to be the area of a regular polygon of which {a_n} is a side, and let c_n be the coefficient by which {a_n}^2 is to be multiplied in order to produce the equation F_n = c_n {a_n}^2 then it is easy to see that c_n = \frac{n}{4} \cot \frac{180^\circ}{n}. ...[H]is approximations are generally near enough. We need not be surprised... Hipparchus made a table of chords... [i.e.] the coefficients k_n were known, with the aid of which a_n = k_n r, where r is the radius. Then c_n = \frac{n}{4} \sqrt{\frac{4}{{k_n}^2}-1}, and Heron was competent to extract such square roots. But Heron does not use the sexagesimal fractions, and... sexagesimal fractions were always, as... afterwards called, astronomical fractions... [S]ave by Heron, trigonometry was generally conceived to be a chapter of astronomy and was not used for the calculation of terrestrial triangles."