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Euclid Wesam Nijim

Euclid’s life

Euclid was born in 330 B.C in , 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 ’s ancient school in Athen which was renowned for all the opulent . Later he decided to go to Alexandria in Egypt which is where he later discovered a new division of which is now known as .

There is also someone of the name Euclid of Meguro who is often confused for Euclid . 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 . 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 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 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 . Euclid had also written twelve other books which cover a vast amount of mathematical knowledge including spanning , geometry and the 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 Geometry category. He then placed his fifth and tenth book in the category Magnitudes and .

His seventh, eighth, and ninth book were placed under the subject Whole . Finally, the last section was called Solid Geometry where he placed his eleventh, twelvth, and thirteenth book. Euclid first established in his book,”The Elements,” as the starting 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 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 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 , it is possible to draw a using the segment as the radius and one end point as the center.” The fourth postulate states that ”all right 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 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 .” 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 he uses for each and every 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, was aware of Euclid’s work and the US Declaration of Independence used Euclid’s that he developed.

2 Not only is Euclid known for his book ”The Elements,” but also his works about astronomy, mirrors, , and 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, ”,” 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 . A 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 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 . Euclid’s work on Conics was later extended by . 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 ’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 in 323 BC which also unfortunately resulted in the death of Cleopatra VIIas well as the Roman Conquest. Immediately after ALexander’s death, a crisis had started among many of his top officials. Perdiccas used to be in charge of the empire as regent for the half-brother of Arrhidaeus. This man is later known as Philip III of Macedon and then even later as regent for Philip III and Alexander’s son, Alexander IV of Macedon.

Soon afterward, had been appointed by Perdiccas to be the ruler of Egypt. Ptolemy then ruled since 323 bc. This ruling is under the names of the kings Philip III and Alexander IV. As Alexander the Great started losing rule over his empire, Ptolemy then took over as the new ruler. He proved himself a great king as he defended Egypt against an attack by Perdiccas in 321 BC. This made him more popular and helped secure his position as the ruler. This also helped him secure a powerful role in surrounding areas as well in time period 322-301 BC. Ptolemy was now called King of Egypt.

As the saviour of Egypt, he made the Ptolemaic dynasty that would lead Egypt for centuries. The was founded by . He declared himself the Pharoah of Egypt. He then used this to make an even more powerful dynasty that took over areas ranging from southern Syria to Cyrene and south to Nubia.

Alexandria later became the capital city as well as the central of all kinds of goods and Greek culture. They would make themselves known by naming themselves successors to the previous Pharoahs. Many fought foreign rebels in wars that later led to the fall of the kingdom and annexation by Rome. Ptolemies previously had embraced Egyptian traditions by taking their sibling’s hand in marriage. They would even dress up in Egyptian style clothing and participated in many of the religious activies they partake in.

Hellinistic culture truly was prominent in the Roman and Byzantine periods. This led to the the Muslim conquest later on. Many of these things had indirectly affected Euclid as he continued to progress in his mathematical works. Later, Ptolemy II Philadelphus was a great and cultured king who sought peace. He was not known to be a strong, fierceful warrior, however his father left the country as a strong and wealthy man.

Three years later he started his reign which was later called the First Syrian War. This left Ptolemy to control the eastern Mediterranean and ruled the Aegean islands and the districts of other territories. Some of these gained territories were later lost consequently due to the Second Syrian War.

5 Significant historical events around the world during Euclid’s life

Many events took place around the world in the time of Euclid that either had a strong impact on him or had little to no affect due to distance or irrelevance to his mathematical work and progress. Euclid had all his attention focused on his mathematical work so some of the following events may not have affected the quality of his work but it may have affected how well his working conditions remained. A tragedy later ensues as Alexander the Great is reported to have left the kingdom for the best of the country of Egypt.

Knowing that Euclid had done a majority of his work in Alexandria, Egypt is a strong connection. Alexander’s four generals had then took over and shaped the empire and ushered into the . Another event that took place that was not so relevant to Euclid himself but rather his work was the Greek astronomer Aristarchus of was born. This is a very important individual who influenced Euclid’s work greatly because Euclid had a work called ”Optics” where he explains how spheres or objects of huge bodies are much bigger than they may appear to the human eye. Aristarchus was one of the first to say that Earth orbited the sun instead of the sun orbiting the Earth.

This encouraged Euclid to study this further and helped rectify the belief that objects are far more massive than they appear due to distance. This carved the path to future discoveries about the solar system and how we perceive things. Finally, one major event that took place in the lifetime of Euclid was Strato of Lampsacus becoming the third head of ’s school called ”the Lyceum.” He was the mathematician that figured out that objects begin to gain speed as they fall. He made this judgement by noticing how water flows down from a roof as a strong stream and then starts slowing down into droplets as they get quicker.

One final thing that happened that proved this was how he noticed that stones dropped from higher altitudes tend to have greater craters in the sand. Euclid was impressed by such work and it motivated him to continue his work. These mathematicians were a model for what Euclid wanted to achieve and discover to make his work known.

6 Significant mathematical progress during Euclid’s lifetime

All relevant mathematical progress.

7 Connections between history and the development of mathematics

In the time span of Euclid’s life going from 323 BC to 283 BC there was an unbelievable amount of mathematical progress. His work alone I would say is enough for the years he has been living for. Needless to say the countless other mathematicians making discoveries and theorems that helped advance mathematics to an extent that no one knew could be reached at that time.

Unfortunately, a lot of the progress and advancements made in this time period was either lost or not made known with the world. For example, the history of physics written by Theophrastus was lost and not to be heard of. These discoveries may have changed human life for the better and could have saved centuries of work done by other mathematicians and scientists.

Following this the death of Alexander the Great, a mathematician who was raised by his parents that wanted him to successful in life and had him tutored as a child. He made a massive amount of discoveries. Another well known mathematician named Aristotle also died the following year. Many of the discoveries made by these two were known while some were lost which is expected. Euclid was still alive at the time of their deaths and wanted to be the difference, the one who wanted to have his work spread among the people of the world and to take credit for it.

Looking back at some of his work may seem like common sense but in reality what we see as common sense back then was a breakthrough to the world. For example, people did not know that the sun was much greater than the size that the human eye perceives it to be. Of course behind all his work was some to help gain the trust of others in his work.

8 Remarks

I was impressed how a lot of things that we do everyday trace back all the way to Euclud’s time in the time period 323 BC to 283 BC. Knowing that he was a mathematician before researching him made me thing I would only find his mathematical works and

References

1. http://www.thefamouspeople.com/profiles/euclid-436.php

2. https://explorable.com/euclid

3. http://www.notablebiographies.com/Du-Fi/Euclid.html

4. http://www.fincher.org/History/WorldBC.shtml

5. http://www.math.wichita.edu/ richardson/timeline.html

6. http://www.math.tamu.edu/ dallen/history/greekorg/greekorg.html

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