Heron of Alexandria
Another worker in applied mathematics belonging to the period under consideration was Heron of Alexandria. His much disputed date, with possibilities ranging from 150 BC to 250 AD, has recently been plausibly placed in the second half of the first century AD. His works on mathematical and physical subjects are so numerous and varied that it is customary to describe him as an encyclopedic writer in these fields. There are reasons to suppose he was an Egyptian with Greek training. At any rate his writings, which so often aim at practical utility rather than theoretical completeness, show a curious blend of the Greek and the Oriental. He did much to furnish a scientific foundation for engineering and land surveying. Fourteen or so treatises by Heron, some evidently considerably edited, have come down to us, and there are references to additional last works. 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
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. 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. ) Figure 1: The law of the inclined plane according to Heron and Pappus. One problem calls for the diameter, perimeter, and area of a circle, given the sum of these magnitudes. He takes the power required as the sum of the power required to move the two weights along a horizontal surface. 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. The law of reflection for light had been known to Euclid and Aristotle (probably also to Plato); but it was Heron who showed by a simple geometrical argument, in a work on Catoprics (or reflection), that the equality of the angles of incidence and reflection is a consequence of the Aristotelian principle that nature does nothing the hard way. " This is scarcely the way to teach mathematics, but Heron's books were intended as manuals for the practitioner. ) Thus, although the principle of the lever was well understood in Hellenistic times, that of the inclined plane was not. Book 1 deals with the area mensuration of squares, rectangles, triangles, triangles, trapezoids, various other specialized quadrilaterals, the regular polygons from the equilateral triangle to the regular dodecagon, circles and their segments, ellipses, parabolic segments, and the surfaces of cylinders, cones, spheres, and spherical zones. 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. Moreover, Heron did not solve the problem in general terms but, taking a cue again from pre-Hellenistic methods, chose the specific case in which the sum 212; his solution is like the ancient recipes in which steps only without reasons, are given. Although now the formula usually is derived trigonometrically, Heron's proof is conventionally geometric.
Common topics in this essay:
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,
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Acceptance Essays
