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The Whole Euclid's Life History

The Whole Euclid's Life History

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- 1. Euclid Life HistoryIntroductionEuclid fl. 300 BC, 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 I (323–283 BC). His Elements isone of the most influential works in the history of mathematics, serving as the main textbook forteaching mathematics(especially geometry) from the time of its publication until the late 19th or early 20thcentury. In the Elements, Euclid deduced the principles of what is now called Euclidean geometry from a smallset of axioms. Euclid also wrote works on perspective, conic sections, spherical geometry, numbertheory and rigor."Euclid" is the anglicized version of the Greek name Εὐ κλείδης, meaning "Good Glory". Here is a short and tablesummary of Euclid – Born: c. 365 BC Birthplace: Alexandria, Egypt Died: c. 275 BC Location of death: Alexandria, Egypt Cause of death: unspecified Occupation: Mathematician, Educator Nationality: Ancient Greece Executive summary: Father of geometryEuclid was a Greek mathematician three centuries before Christ, who taught at the ancient Library of Alexandria and laid out the principles that came to define Euclidean geometry. His masterwork, Stoicheia (Elements), is a 13-volume exploration all corners of mathematics, based onthe works of Aristotle, Eudoxus of Cnidus, Plato, Pythagoras, and others who came before him. Little is known about his life, and what little is recounted is often in error, as the name Euclid was fairly common in his time and place.He is sometimes credited with one original theory, a method of exhaustion through which the area of a circle and volume of a sphere can be calculated, but he left a much greater mark as a teacher. Hepresented the theorems and problems with great clarity, showed the solutions concisely and logically, and his Elements have remained a standard geometry text for more than two thousand years since his death. University: Platos Academy, Athens, Greece Teacher: Library of Alexandria, Alexandria, Egypt Asteroid Namesake 4354 Euclides Lunar Crater Euclid (7.4S, 29.5W, 11km dia, 700m height) Eponyms Euclidean geometry Slaveowners Author of books: Elements (13 volumes) Data (plane geometry) On Divisions (geometry) Optics (applied mathematics) Phenomena (astronomy)
- 2. LifeLittle is known about Euclids life, as there are only a handful of references to him. The date and place of Euclidsbirth and the date and circumstances of his death are unknown, and only roughly estimated in proximity tocontemporary figures mentioned in references. No likeness or description of Euclids physical appearance madeduring his lifetime survived antiquity. Therefore, Euclids depiction in works of art is the product of the artistsimagination.The few historical references to Euclid were written centuries after he lived, by Proclus and Pappus of [5]Alexandria. Proclus introduces Euclid only briefly in his fifth-century Commentary on the Elements, as theauthor of Elements, that he was mentioned by Archimedes, and that when King Ptolemy asked if there was ashorter path to learning geometry than Euclids Elements, "Euclid replied there is no royal road to [6]geometry." Although the purported citation of Euclid by Archimedes has been judged to be an interpolation by [7][8][9]later editors of his works, it is still believed that Euclid wrote his works before those of Archimedes. Inaddition, the "royal road" anecdote is questionable since it is similar to a story told [10]about Menaechmus and Alexander the Great. In the only other key reference to Euclid, Pappus brieflymentioned in the fourth century that Apollonius "spent a very long time with the pupils of Euclid at Alexandria, and [11]it was thus that he acquired such a scientific habit of thought." It is further believed that Euclid may havestudied at Platos Academy in Athens.ElementsAlthough many of the results in Elements originated with earlier mathematicians, one of Euclidsaccomplishments was to present them in a single, logically coherent framework, making it easy to use and easyto reference, including a system of rigorous mathematical proofs that remains the basis of mathematics 23 [13]centuries later.There is no mention of Euclid in the earliest remaining copies of the Elements, and most of the copies say they [14]are "from the edition ofTheon" or the "lectures of Theon", while the text considered to be primary, held by theVatican, mentions no author. The only reference that historians rely on of Euclid having written the Elements wasfrom Proclus, who briefly in his Commentary on the Elements ascribes Euclid as its author.Although best known for its geometric results, the Elements also include number theory. It considers theconnection between perfect numbers and Mersenne primes, the infinitude of prime numbers, Euclids lemma onfactorization (which leads to the fundamental theorem of arithmetic on uniqueness of prime factorizations), andthe Euclidean algorithm for finding the greatest common divisor of two numbers.The geometrical system described in the Elements was long known simply as geometry, and was considered tobe the only geometry possible. Today, however, that system is often referred to as Euclidean geometry todistinguish it from other so-called non-Euclidean geometries that mathematicians discovered in the 19th century.The Book Of ElementsBOOK 1 – stThe 1 book of elements contains all the basic definitions, postulates & axioms of various common topics likecircles, lines & angles, geometry, polygons etc...Some of the Definitions by Euclid were –Definition 1. A point is that which has no part.
- 3. Definition 2. A line is breadth less length.Definition 3. The ends of a line are points.Definition 4. A straight line is a line which lies evenly with the points on itself.Definition 5. A surface is that which has length and breadth only.BOOK 2 – ndThe 2 book of elements mainly contained about the propositions and definitions about quadrilateralslike Square and Rectangle.BOOK 3 – rdThe 3 book of elements all about the characteristics and features of Circles, its radius, diameter,chords etc.BOOK 4 – thThe 4 book of elements tells us about the nature of rectilinear and circular figures that when they areinscribed and sometime when they are circumscribed.BOOK 5 –Ratio is an indication of relative size of two magnitudes. This is what the book 5 of elements is basedon. It covers the abstract theory of ratio and proportion.BOOK 6 – This book is just the expansion of book 5. It contains the theory and geometrics based upon the ratioand proportion.BOOK 7 –The book 7 of elements was one of the finest books based on unit and number, part and multiple,even and odd, and prime and relative prime. The basic construction of book 7 was known asEuclidean Algorithm, a kind of reciprocal subtraction.This book also contained the Euclid’s Division Lemma which is the easiest way to find a H.C.F of agiven couple of number.BOOK 8 – thThe 8 book of elements is the advancement of book 7, telling about the cubic numbers, unitarynumbers etc.
- 4. BOOK 9 –The book 9 is again an continuation of book 8 which fully describes about the multiplication of prime,even, odd no. etc.BOOK 10 –This book tells us about the rationality and irrationality of straight lines and the figures and ratiosformed by them.BOOK 11 –The solid figures, angles and planes and similarity are all just in this book.BOOK 12 –This book was the first book giving about the 3d figures, their designs and properties.BOOK 13 –The last book of elements describes about the mean ratio, straight lines high sided polygons likehexagon, decagon etc.Additional Works which were found -In addition to the Elements, at least five works of Euclid have survived to the present day. They follow the samelogical structure as Elements, with definitions and proved propositions. Data deals with the nature and implications of "given" information in geometrical problems; the subject matter is closely related to the first four books of the Elements. On Divisions of Figures, which survives only partially in Arabic translation, concerns the division of geometrical figures into two or more equal parts or into parts in given ratios. It is similar to a third century AD work by Heron of Alexandria. Catoptrics, which concerns the mathematical theory of mirrors, particularly the images formed in plane and spherical concave mirrors. The attribution is held to be anachronistic however by J J OConnor and E F [15] Robertson who name Theon of Alexandria as a more likely author. Phaenomena, a treatise on spherical astronomy, survives in Greek; it is quite similar to On the Moving Sphere by Autolycus of Pitane, who flourished around 310 BC. Optics is the earliest surviving Greek treatise on perspective. In its definitions Euclid follows the Platonic tradition that vision is caused by discrete rays which emanate from the eye. One important definition is the fourth: "Things seen under a greater angle appear greater, and those under a lesser angle less, while those under equal angles appear equal." In the 36 propositions that follow, Euclid relates the apparent size of an object to its distance from the eye and investigates the apparent shapes of cylinders and cones when viewed from different angles. Proposition 45 is interesting, proving that for any two unequal magnitudes, there is a point from which the two appear equal. Pappus believed these results to be important in
- 5. astronomy and included Euclids Optics, along with his Phaenomena, in the Little Astronomy, a compendium of smaller works to be studied before the Syntaxis (Almagest) of Claudius Ptolemy.Additional Works which were lost - Conics was a work on conic sections that was later extended by Apollonius of Perga into his famous work on the subject. It is likely that the first four books of Apollonius work come directly from Euclid. According to Pappus, "Apollonius, having completed Euclids four books of conics and added four others, handed down eight volumes of conics." The Conics of Apollonius quickly supplanted the former work, and by the time of Pappus, Euclids work was already lost. Porisms might have been an outgrowth of Euclids work with conic sections, but the exact meaning of the title is controversial. Pseudaria, or Book of Fallacies, was an elementary text about errors in reasoning. Surface Loci concerned either loci (sets of points) on surfaces or loci which were themselves surfaces; under the latter interpretation, it has been hypothesized that the work might have dealt with quadric surfaces. Several works on mechanics are attributed to Euclid by Arabic sources. On the Heavy and the Light contains, in nine definitions and five propositions, Aristotelian notions of moving bodies and the concept of specific gravity. On the Balance treats the theory of the lever in a similarly Euclidean manner, containing one definition, two axioms, and four propositions. A third fragment, on the circles described by the ends of a moving lever, contains four propositions. These three works complement each other in such a way that it has been suggested that they are remnants of a single treatise on mechanics written by Euclid.

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