Abstract
GREEK geometry passed through several stages from its inception to its highest development in the hands of Archimedes and Apollonius of Perga. The geometry which Thales brought from Egypt early in the sixth century B.C. was little more than a few more or less accurate rules for the mensuration of simple figures; it was the Greeks who first conceived the idea of making geometry a science in and for itself. With Pythagoras and the Pythagoreans, who represent the next stage after Thales, geometry became a subject of liberal education. Apart from special discoveries such as those of the theorem of the square on the hypotenuse, the equality of the three angles ctf any triangle to two right angles, the construction of the nve cosmic figures (the five regular solids), and the incommensurability of the diagonal of a square with its side, the Pythagoreans invented two methods which remained fundamental in Greek geometry, that of proportions (though in a numerical sense only) and that known as application of areas, which is the geometrical equivalent of the solution of a quadratic equation.
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HEATH, T. Greek Geometry, with Special Reference to Infinitesimals. Nature 111, 152–153 (1923). https://doi.org/10.1038/111152a0
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DOI: https://doi.org/10.1038/111152a0