EUCLID (Course) (Section No.) Complete Euclid During the Hellenistic period in the reign of Ptolemy I (323 BC – 283 BC), Euclid, the Father of Geometry, son of Naucrates and grandson of Zenarchus, came to being around 300 B.C…
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Despite inadequate accounts of his life, it is believed that Euclid may have gone to Plato’s Academy in Athens for his studies and though Plato’s pupils were a few ages his senior, Archimedes and Eratosthenes were younger than he, according to the latest Greek philosopher Proclus Lycaeus. Modern and early artists alike depict Euclid’s portrait based on analytical imagination since no visual object of his physical appearance had been preserved whereas historians are similarly approximating that he died about 265 B.C due to unidentified circumstances. As a chief contribution to the field of Mathematics, Euclid authored the ‘Elements’ which made possible the deduction of Euclidian geometry from a small set of axioms. The 400 propositions making its text are comprised in thirteen volumes which principally dealt with plane and solid geometries, the number theory, and classifying irrational numbers based on Theaetetus’ theory. While this is founded on a number of postulates which further led to important theorems beginning with the postulate stating that a line may be drawn if there are two given points, the scope of ‘Elements’ extend its application to certain areas in advanced mathematics, trigonometry, and algebra. As such, it essentially put to discourse the basic properties of triangles, parallels, parallelograms, rectangles and squares in the first and second volumes. It lay foundations to handling problems with circles and properties thereof in general and aided mathematicians with Pythagorean concerns as well. Furthermore, Proclus added that in this text, several theorems of Eudoxus were designated in order including those of Theaetetus, placing on solid ground statements that bore unstable approach to proofs before his time which might have potentially resulted from his philosophical stand as a Platonist that also enabled him to generate Platonic figures as one significant outcome of ‘Elements’. To date this work is by far Euclid’s most remarkable accomplishment and remained undisputed until the 19th century when the formation of non-Euclidean geometricians discovered flaws with the fifth postulate after a thousand-year careful study by Greek, Roman, and even Arab scholars. Catoptrics and optics are two other equivalent works by which Euclid is recognized to have arrived at the mathematical theory on mirrors and the argument that discrete rays channeled out of the eye are responsible for constructing vision, respectively. Through relevant propositions in this aspect, Euclid managed to support his claims with reference to the conic and cylindrical shapes at different angular perspectives. By the time of Pappus, Euclid’s work must have begun disappearing yet Pappus had findings that made him attribute conic sections to the endeavor of Euclid. He claimed that conics had been a major initiative of Euclid and that his four books on this course were completed by Apollonius of Perga who happened to release a total of eight volumes on conics, combining the pioneering efforts of Euclid and his. History barely mentioned any direct influences of Euclid. The educational setting, however, may prove adequate to draw a researcher to closely infer that the school of thought attended to by Euclid impacted him in a manner which enhanced his inclinations to the philosophy of Plato besides math, thereby inspiring him to materialize the
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