The Elements of Euclid
It is a tragedy of mathematics that what we know of Euclid's life is so meager. It is because of Euclid's work that mathematics was able progress so rapidly in classical times. Euclid's masterpiece The Elements was so popular that it became the most widely read book until the twentieth century (with the exception of The Bible). However, our tragedy lies in what we actually know about Euclid. The sources of Euclid's life are but a few passages from commentators who claim they knew who Euclid was. To this day, there have been only five commentators of Euclid, which are Proclus, Heron, Porphyry, Pappus, and Simplicius (Proclus being the most prominent).1 Pre-twentieth century The Elements was considered the authoritative standard of basic concepts in geometry , number theory, and logic.It is speculated that Euclid flourished around 300BCE. This has been estimated by one of the passages that Proclus wrote in his Commentary on the First Book of Euclid's Elements. The passage is as follows:"Not much younger than these(sc. Hermotimus of Colophon and Philippus of Medma) is Euclid, who put together the Elements, Collecting many of Eudoxus' theorems, perfecting many of Theaetetus', and also bringing
4- And if there is no d, then the supposition that primes are finite is a contradiction. (s+1)2- If s+1 is prime, we're finished and the theorem is proved (because we would've proved that there's more prime numbers). However interesting enough, in Arabia there was a rumor that The Elements contained a XIV and a XV book. To this day Euclid's significance in mathematics is unmatched. The Euclidean Algorithm works so well that it is still one of the most effective ways to find the greatest common divisors today. 7 Euclid's most famous accomplishments were probably those in number theory (although he is referred to as "The Father of Geometry). "2Here Proclus mentions people of which we are more clear of their life span, such as Plato (d. The formula is as follows:1- Suppose a, b ,and c are the greatest prime numbers we know of and s is the smallest number divisible by a, b, and c (which is a*b*c). Unfortunately, all of Euclid's extant works are all translations and more than probably they have been edited. Second, what is known as the Euclidean Algorithm for finding the greatest common divisors of two integers. After this, Euclid is said to have set up a school of mathematics in Alexandria where Archimedes read The Elements. 3- Next we divide the previous divisor by the remainder which would be 4- Then we continue in the same way until we reach a remainder of 0, which would look like this: = 1 R4 = 2 R05- Thus our last divisor would be the greatest common divisor of both 20 and 72. When Euclid proved that there is infinitude of prime numbers, he more than probably had a lot of critics. 3- If s+1 is not prime, then it is divisible by a prime d.
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