[Solved] books of euclids elements

Euclid is one of the most influential and best read mathematician of all time. His prize work,Elements, was the textbook of elementary geometry and logic up to the early twentieth century. Forhis work in the field, he is known as the father of geometry and is considered one of the greatGreek mathematicians.

Very little is known about the life of Euclid. Both the dates and places of his birth and death areunknown. It is believed that he was educated at Plato’s academy in Athens and stayed there until hewas invited by Ptolemy I to teach at his newly founded university in Alexandria. There, Euclidfounded the school of mathematics and remained there for the rest of his life. As a teacher, he wasprobably one of the mentors to Archimedes.

Personally, all accounts of Euclid describe him as a kind, fair, patient man who quickly helped andpraised the works of others. However, this did not stop him from engaging in sarcasm. One storyrelates that one of his students complained that he had no use for any of the mathematics he waslearning. Euclid quickly called to his slave to give the boy a coin because he must make gain out ofwhat he learns. Another story relates that Ptolemy asked the mathematician if there was some easierway to learn geometry than by learning all the theorems. Euclid replied, There is no royal road togeometry and sent the king to study.

Euclid’s fame comes from his writings, especially his masterpiece Elements. This 13 volume work isa compilation of Greek mathematics and geometry. It is unknown how much if any of the workincluded in Elements is Euclid’s original work; many of the theorems found can be traced toprevious thinkers including Euxodus, Thales, Hippocrates and Pythagoras. However, the format ofElements belongs to him alone. Each volume lists a number of definitions and postulates followed bytheorems, which are followed by proofs using those definitions and postulates. Every statement wasproven, no matter how obvious. Euclid chose his postulates carefully, picking only the most basicand self-evident propositions as the basis of his work. Before, rival schools each had a different setof postulates, some of which were very questionable. This format helped standardize Greekmathematics. As for the subject matter, it ran the gamut of ancient thought. The subjects include: thetransitive property, the Pythagorean theorem, algebraic identities, circles, tangents, plane geometry,the theory of proportions, prime numbers, perfect numbers, properties of positive integers, irrationalnumbers, 3-D figures, inscribed and circumscribed figures, LCD, GCM and the construction ofregular solids. Especially noteworthy subjects include the method of exhaustion, which would beused by Archimedes in the invention of integral calculus, and the proof that the set of all primenumbers is infinite.

Elements was translated into both Latin and Arabic and is the earliest similar work to survive,basically because it is far superior to anything previous. The first printed copy came out in 1482 andwas the geometry textbook and logic primer by the 1700s. During this period Euclid was highlyrespected as a mathematician and Elements was considered one of the greatest mathematical worksof all time. The publication was used in schools up to 1903. Euclid also wrote many other worksincluding Data, On Division, Phaenomena, Optics and the lost books Conics and Porisms.

Today, Euclid has lost much of the godlike status he once held. In his time, many of his peersattacked him for being too thorough and including self-evident proofs, such as one side of a trianglecannot be longer than the sum of the other two sides. Today, most mathematicians attack Euclid forthe exact opposite reason that he was not thorough enough. In Elements, there are missing areaswhich were forced to be filled in by following mathematicians. In addition, several errors andquestionable ideas have been found. The most glaring one deals with his fifth postulate, also knownas the parallel postulate. The proposition states that for a straight line and a point not on the line,there is exactly one line that passes through the point parallel to the original line. Euclid was unable toprove this statement and needing it for his proofs, so he assumed it as true. Future mathematicianscould not accept such a statement was unproveable and spent centuries looking for an answer. Onlywith the onset of non- Euclidean geometry, that replaces the statement with postulates that assumedifferent numbers of parallel lines, has the statement been generally accepted as necessary.

However, despite these problems, Euclid holds the distinction of being one of the first persons toattempt to standardize mathematics and set it upon a foundation of proofs. His work acted as aspringboard for future generations.

Mathematics Essays

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