Heron's works may be divided into two classes, the geometrical and the mechanical. The geometrical works deal largely with problems on mensuration and the mechanical ones with descriptions of ingenious mechanical devices.

The most important of Heron's geometrical works in his Metrica, written in three books and discovered in Constantinople by R. Schone as recently a

Once again, Heron of Alexandria is best known in the history of mathematics for the formula, bearing his name, for the area of a triangle:

The angles SPM and EPM' are equal. That no other path SP'E can be as short as SPE is apparent on drawing SQS' perpendicular to MM', with SQ = QS', and comparing the path SPE with the path SP'E. Since paths SPE and S'P'E as are equal in length to paths S'PE and S'P'E respectively, and inasmuch as S'PE is a straight line (because angle M'PE is equal to angle MPS), it follows that S'PE is the shortest path.

Heron is remembered in the history of science as the inventor of a primitive type of steam engine, described in his Pneumatics, of a forerunner of the thermometer, and of various toys and mechanical contrivances based on the properties of fluids and on the laws of the simple machines. He suggested in the Mechanics a law (clever but incorrect) of the simple machine whose principle had eluded even Archimedes-the inclined plane. His name is attached also to "Heron's algorithm" for finding square roots, but this method of iteration was in reality due to the Babylonians of 2000 years before his day. Although Heron evidently learned much of Mesopotamian mathematics, he seems not to have appreciated the importance of the positional principle for fractions had become the standard tool of scholars in astronomy and physics, but it is likely that they remained unfamiliar to the common man. Common fractions were used to some extent by the Greeks, at first with numerator placed below the denominator, later with the positions reversed (and without the bar separating the two), but Heron, writing for the practical man, seems to have preferred unit fractions. In dividing 25 by 13 he wrote the answer as 1 + 1/2 +1/3 + 1/13 + 1/78. The old Egyptian addiction to unit fractions continued in Europe for at least a thousand years after the time of Heron. (Boyer, 190-193)

Where a, b, c are the sides and s is half the sum of these sides, that is, the semiperimeter. The Arabs tell us that "Heron's formula" was known earlier to Archimedes, who undoubtedly had a proof of it, but the demonstration of it in Heron's Metrica is the earliest that we have. Although now the formula usually is derived trigonometrically, Heron's proof is conventionally geometric. The Metrica, like the Method of Archimedes, was long lost, until rediscovered at Constantinople in 1896 in a manuscript dating from about 1100. The word "geometry" originally meant "earth measure," but classical geometry, such as that found in Euclid's Elements and Apollonius' Conics, was far removed from the mundane surveying. Heron's work, on the oth

Some common words found in the essay are:
Moreover Heron, Apollonius' Conics, S'PE S'P'E, Dioptrica Mechanica, Heron Alexandria, Constantinople Schone, Greek Oriental, Plato Heron, Heron Geometrica, Method Archimedes, inclined plane, + 2 =, shortest path, steam engine, path spe, easily found, unit fractions, required move, example heron, 280 course, + 2,
Approximate Word count = 1786
Approximate Pages = 7 (250 words per page double spaced)