Euclid Wesam Nijim Euclid's life Euclid was born in 330 B.C in Alexandria, Egypt. Some Arabian authors thought that Euclid was raised by a family with a lot of wealth to Naucrates. It is also said by people that Euclid was born in Tyre rather than Alexandria and lived the remainder of his life in Damascus. Specific documents that say that Euclid had studied in Plato's ancient school in Athen which was renowned for all the opulent mathematicians. Later he decided to go to Alexandria in Egypt which is where he later discovered a new division of mathematics which is now known as geometry. There is also someone of the name Euclid of Meguro who is often confused for Euclid of Alexandria. This made it hard for people to find credible information on Euclid of Alexandria. Alexandria was once in history the biggest city in the Western World and was also known as the center of the Papyrus industry. Euclid had took an interest in the subject of mathematics and to this day is known for his path breaking discoveries and theorems. Euclid was in Alexandria when he developed and shared his knowledge and discoveries in mathematics with the rest of the people in this world. People say Euclid had made a private school in the Alexandria library to help teach students make their own discoveries and books in the future. Euclid's appearance is not known with detail and the works of artists who picture Euclid are merely depicting how he looks like with their imagination of how he could have looked like. Not a lot of informations has been written or stored about him in terms of detail or depth. Statements made about Euclid are not to be assumed true since a lot of history about such scholars were either myths or legends in the Ancient Greece time. Historians continue to delve into his life history and reconstruct it to better understand his work in contexts that we cannot determine to this day. Euclid is still known to this day as a hero of thought. Euclid's mathematical works Euclid had accumulated all the knowledge from mathematicians from the past and had further developed them in Greek mathematics at that time and used it to make his cook called "The Elements." This book is considered to be the most influential on-religious book which is not equaled in the history of science. Euclid had also written twelve other books which cover a vast amount of mathematical knowledge including spanning arithmetic, geometry and the number theory. He separated these books by organizing them by subject which cover every section of mathematics made by the Greeks. The first four books were placed in the Plane Geometry category. He then placed his fifth and tenth book in the category Magnitudes and Ratios. His seventh, eighth, and ninth book were placed under the subject Whole numbers. Finally, the last section was called Solid Geometry where he placed his eleventh, twelvth, and thirteenth book. Euclid first established axioms in his book,"The Elements," as the starting point in which developed four hundred and sixty five propositions. He advanced from his first developed principles to the unknown in a series of steps which is a process called the "Synthetic Approach." Euclid focused on geometry and that helped explain why all his work was centered around geometry when he looked at mathematics as a whole. There were ten axions that Euclid uses as the basis of approach. Axioms are statements that possibly could be accepted and proven as true. Another name he gave to these axioms was "postulates" and separated them into two groups with five per group. The first group was set to all mathematics while the second group was set to geometry. While some of these postulates may seem trivial to us, Euclid worked under the principle that he cannot accept an axiom with proving it. His first group of postulates was referred to as the common notions. The first postulate stated that "things which are equal to the same thing are also equal to each other." The second postulate states that "if equals are added to equals, the results are equal." The third postulate is "if equals are subtracted from equals, the remainders are equal." The fourth postulate is "things that coincide with each other are equal to each other." Finally, the fifth postulate states that "the whole is greater than the art." The other five as stated before are relevant to specifically geometry. The first postulate states that "a straight line can be drawn between any two points." The second postulate states that "any finite straight line can be extended indefinetely in a straight line." The third postulate states that "for any line segment, it is possible to draw a circle using the segment as the radius and one end point as the center." The fourth postulate states that "all right angles are congruent." Finally the last postulate states that "if a straight line falling across two other straight lines results in the sum of the angles on the same side less than two right angles, then the two straight lines, if extended indefinitely, meet on the same side as the side where the angle sums are less than two right angles. Anyone who could read and comprehend words according to Euclid. In order to ensure the aforementioned and to avoid semantic errors, he also included definitions of twenty three words like "point" or "line." Using this he was able to develop his whole theory of plane geometry which has helped form the structure of mathematics, science and even philosophies for centuries. He is known for the proof of knowing there will never be a "largest prime number." He proved this by stating that taking the largest prime number and adding one to the product of all prime numbers prior to it and the largest prime will give you an even greater prime number. Euclid's work went far beyond the average work of mathematics. His work not only an explanation of geometry or of mathematics, but also the proofs and logic he uses for each and every theorem helped form thoughts of western philosophers to this day. Many philosopher mathematicians including Descartes and Newton used Euclid's structure and format of his proofs to start focusing on more complex ideas rather than the simple principles they used to work on. In addition, Abraham Lincoln was aware of Euclid's work and the US Declaration of Independence used Euclid's axiomatic system that he developed. 2 Not only is Euclid known for his book "The Elements," but also his works about astronomy, mirrors, optics, perspective and music theory even though some of his work was lost. All of his accomplishments made him one of the greatest mathematicians of all time. Newton used a lot of his work as a foundation for his success as well. Some of Euclid's work remained in mystery until writers have talked about them. The book, "Data," talked about plane geometry and has problems that are demonstrated in which certain data is given about a certain concept and then you can retrieve even more data from it. Another one of Euclid's works is called On Division which happens to be about plane geometry as well. Another of his works called Phaenomena is what is called today applied mathematics. It is about the geometry of spheres which is very important in the study of astronomy. As surprising as it may seem, people used to believe that the sun and other massive bodies seen from a distance are actually the size they percieve them as. Once Euclid released his work called Optics, it corrected that belief and and it talked about the relationship between what is perceived and what it actually is. An example in the work is the following, "the eye always sees less than half of a sphere and as the observer moves closer to the sphere, the part of it that is seen is decreased, although it appears larger." Furthermore, another one of his lost works is called Porisms. A porism is somewhere in the vicinity of being a theorem and a problem. It is rather focused on bringing out another characteristic of something else that is all ready known. Example given in his work of porisms are finding center of a circle or finding the greatest common divisor of two numbers. It is said that this wok is even more complex than his renowned work called "The Elements." Unfortunately this work does not exist or else it would have given Euclid a higher status in the history of mathematics. Euclid's work on Conics was later extended by Apollonius of Perga. It is stated that a lot of Apollonius 'information in his first four books came right from Euclid. According to Pappus, "Apollonius, having completed Euclid's four books of conics and added four others, handed down eight volumes of conics." Unfortunately for Euclid, Apollonius' work rapidly grew past Euclid's work and by the time Pappus was around Euclid's work was all ready gone. 3 Collaboration with other scholars The mathematician's collaboration with other scholar's is described here. 4 Historical events that marked Euclid's life. One of the events that took place in Alexandria, Egypt during Euclid's time there was the ruling of the Ptolemaic dynasty with the rise of Ptolemeny I Soter's rise in power after the death of Alexander the Great in 323 BC which also unfortunately resulted in the death of Cleopatra VIIas well as the Roman Conquest.