Euclid
Mathematician
Euclid, also known as Euclid of Alexandria, was a Greek mathematician, often referred to as the "Father of Geometry". He was active in Alexandria during the reign of Ptolemy
Although little is known about Euclid's early and personal life, he was known as the forerunner of geometrical knowledge and went on to contribute greatly in the field of mathematics. Also known as the 'father of Geometry', Euclid was known to have taught the subject of mathematics in Ancient Egypt during the reign of Ptolemy I. He was well-known, having written the most permanent mathematical works of all time, known as the 'Elements' that comprised of the 13 gigantic volumes filled with geometrical theories and knowledge. This would then go on to arouse the Western World and a series of Mathematicians around the globe for over 2000 years breaking all boundaries and defining new ones in the field of Math. Euclid used the 'synthetic approach' towards producing his theorems, definitions and axioms in math. Apart from being a tutor at the Alexandria library, Euclid coined and structured the different elements of mathematics, such as Porisms, geometric systems, infinite values, factorizations, and the congruence of shapes that went on to contour Euclidian Geometry. His works were heavily influenced by Pythagoras, Aristotle, Eudoxus, and Thales to name a few.
Childhood And Early Life
Euclid of ‘Alexandria’ was born around 330 B.C, presumably at Alexandria. Certain Arabian authors assume that Euclid was born to a wealthy family to ‘Naucrates’. It is said that Euclid was possibly born in Tyre and lived the rest of his life in Damascus. There have been certain documents that suggest that Euclid studied in Plato’s ancient school in Athens, where only the opulent studied. He later shifted to Alexandria in Egypt, where he discovered a well-known division of mathematics, known as ‘geometry’.
The life of Euclid of Meguro has often been confused with the life of Euclid of Alexandria, making it difficult to believe any trustworthy information based on the life of the mathematician. He inculcated an interest in the field of mathematics and took the subject to a whole new level with path breaking discoveries and theorems. Alexandria was once, the largest city in the Western World and was also central to the great, flourishing, Papyrus industry. It was in this city where Euclid developed, imparted, and shared his knowledge on mathematics and geometry with the rest of the world.
Career
Euclid was known as the ‘father of geometry’ for a reason. He discovered the subject and gave it its value, making it one of the most complex forms of mathematics at the time. After moving to Alexandria, Euclid spent most of his time at the Alexandria library, like many other eminent scholars who spent their time there wisely. The museum was built by Ptolemy, which was central to literature, arts and sciences. It was here that Euclid began developing geometrical ideas, arithmetic’s, theories and irrational numbers into a section called “geometry”. He began developing his theorems and collated it into a colossal treatise called ‘The Elements’. During the course of his vaguely known career, he developed 13 editions to the ‘Elements’ that covered a wide spectrum of subjects ranging from axioms and statements to solid geometry and algorithm concepts. Along with stating these various theories, he began backing these ideas with methods and logical proof that would approve of the statements produced by Euclid.
His treatise consisted of over 467 propositions to plain and solid geometry, proposes and adages that suggested and agreed to his theories relating to his geometrical ideas. There was a certain case with the Pythagoras equation for the triangle that Euclid used as an example while writing the ‘Elements’. He stated that ‘the equation was always true when it was the matter of every right-angle triangle’. The ‘Elements’ sold more copies than the Bible and was used and printed countless times by mathematicians and publishers, who have used the information, even up to the 20th century. There was no end to Euclid’s geometry, and he continued to develop theorems on various aspects of math such as ‘prime numbers’ and other, basic ‘arithmetic’. With a series of logical steps developed by Euclid, he believed in making the unknown known to the world. The system that Euclid went on to describe in the ‘Elements’ was commonly known as the only form of geometry the world had witnessed and seen up until the 19th century. However, mathematicians of the modern era developed new theorems and ideas pertaining to geometry and divided the subject to ‘Euclidean Geometry’ and ‘Non-Euclidean Geometry’.
He called this the ‘synthetic approach’ that was not based on the logic of trial and error, but on presenting facts from theory. At a time when knowledge was limited, Euclid even began to take on knowledge based quests on subjects relating to a different field such as ‘arithmetic and numbers’. He deciphered that it would be humanly impossible to find out the ‘largest prime number’. He backed this with an example stating that if 1 was added to the largest known prime number, the product will lead to another prime number. This classic example was the proof of Euclid’s clarity of thought and precision at his time and age.
Axioms
Euclid stated that axioms were statements that were just believed to be true, but he realized that by blindly following statements, there would be no point in devising mathematical theories and formulae. He realized that even axioms had to be backed with solid proofs. Therefore, he started to develop logical evidences that would testify his axioms and theorems in geometry. In order to further understand these axioms, he divided them into groups of two called ‘postulates’. One group would be called the ‘common notions’ which were agreed statements of science. His second set of postulates was synonymous with geometry. The first set of notions mentioned statements such as the “whole is greater than the part” and “things which are equal to the same thing are also equal to one another”. These are only two of the five statements written by Euclid. The remaining five statements in the second set of postulates are a little more specific to the subject of Geometry and state theories such as “All right angle are equal” and “straight lines can be drawn between any two points”.
Euclid’s career flourished as a Mathematician and the ‘Elements’ was eventually translated from Greek to Arabic and then into English by John Dee in the early periods of 1570. There were more than 1000 editions of the ‘Elements’ printed ever since its inception, which eventually secured a place in early 20th century classrooms as well. There have been a myriad of Mathematicians who tried to refute and break Euclid’s theories in geometry and mathematics, but these attempts were always futile. An Italian Mathematician called Girolamo Saccheri tried to outdo the works of Euclid, but gave up when he couldn’t pinpoint a single flaw in his theories. It would take another century for a new group of Mathematicians to present new theories in the subject of geometry.
Additional Works
Along with changing the face of mathematics permanently, Euclid also had a wide range of other works that are still used and referred, to date. These works were pure positions backed with solid proof and followed along the lines and the structure of the ‘Elements’. He went on to study and discover ‘Catoptrics’ which essentially stated the mathematical functions of mirrors. Optics, ratios, data, and conics are some of his other reputed works which are now lost with the mists of time. Euclid successfully completed eight editions or books on the theorems related to conics, which failed to exist through time. He also formed hypotheses and propositions based on Mechanics and Loci. Most of these works were said to have been complementary to each other, and it was suggested that these theories developed actually stemmed from his famous works; the ‘Elements’. He also came up with a set of Euclidian ‘Constructions’ that were basic tools needed to produce geometric constructions.
Personal Life
It is believed that Euclid set up a private school at the Alexandria library to teach Mathematical enthusiasts like himself. There are other theories that suggest that Euclid went on to help these students write their own theories and books later in life. Not much is even known about Euclid’s appearance, and the sculptures or paintings seen today are mere products of the imagination of artists of how Euclid could have been.
Death And Legacy
The year and reason behind Euclid’s death is unknown to mankind. However, there have been vague appropriations that suggest that he might have perished around 260 B.C. The legacy he left behind after his death was far more profound than the impression he created when he was alive. His books and treatises were sold and used by personalities all over the world up until the 19th century. His legacy carried on for that 200 centuries after his death and inspired personalities such as Abraham Lincoln along the way. It is said that Lincoln would religiously carry the ‘Elements’ with him wherever he would go, and would often quote the genius of Euclid’s works in his speeches. Even after Euclid’s death, Mathematicians continued to write theorems and his works under his name. In all true sense, at a time when knowledge was inaccessible to a majority of the world’s population, Euclid logically and scientifically developed Mathematical formats of antiquity that are known to the world as “Euclidian Geometry” today.
