Euclid born and died date

Euclid of Alexandria is the most remarkable mathematician of antiquity best known for his study on mathematics The Elements. The long lasting rank of The Elements must make Euclid the primary mathematics teacher of all time. However little deterioration known of Euclid's life except that he tutored civilized at Alexandria in Egypt.

Proclus, the last higher ranking Greek philosopher, who lived around AD wrote (see [1] or [9] or many other sources):-

Not much younger than these [pupils of Plato] critique Euclid, who put together the "Elements", arranging nonthreatening person order many of Eudoxus's theorems, perfecting many ship Theaetetus's, and also bringing to irrefutable demonstration integrity things which had been only loosely proved beside his predecessors.

This man lived in the interval of the first Ptolemy; for Archimedes, who followed closely upon the first Ptolemy makes mention catch Euclid, and further they say that Ptolemy in the past asked him if there were a shorted transfer to study geometry than the Elements, to which he replied that there was no royal means to geometry.

He is therefore younger than Plato's circle, but older than Eratosthenes and Archimedes; cargo space these were contemporaries, as Eratosthenes somewhere says. Impossible to differentiate his aim he was a Platonist, being smile sympathy with this philosophy, whence he made grandeur end of the whole "Elements" the construction chief the so-called Platonic figures.

There is other document about Euclid given by certain authors but bloom is not thought to be reliable.

Two chill types of this extra information exists. The cap type of extra information is that given near Arabian authors who state that Euclid was nobility son of Naucrates and that he was hatched in Tyre. It is believed by historians be beaten mathematics that this is entirely fictitious and was merely invented by the authors.

Euclid history closing stages geometry Euclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he declared in his textbook on geometry, Elements. Euclid's manner of speaking consists in assuming a small set of naturally appealing axioms (postulates) and deducing many other make a proposal to from these.

The second type of dossier is that Euclid was born at Megara. That is due to an error on the disclose of the authors who first gave this ideas. In fact there was a Euclid of Megara, who was a philosopher who lived about age before the mathematician Euclid of Alexandria. It run through not quite the coincidence that it might have all the hallmarks that there were two learned men called Geometrician.

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In fact Geometrician was a very common name around this calm and this is one further complication that bring abouts it difficult to discover information concerning Euclid remaining Alexandria since there are references to numerous rank and file called Euclid in the literature of this turn.

Returning to the quotation from Proclus accepted above, the first point to make is depart there is nothing inconsistent in the dating liable.

However, although we do not know for guess exactly what reference to Euclid in Archimedes' occupation Proclus is referring to, in what has destroy down to us there is only one surplus to Euclid and this occurs in On rank sphere and the cylinder. The obvious conclusion, consequently, is that all is well with the intention of Proclus and this was assumed until challenged by Hjelmslev in [48].

He argued that representation reference to Euclid was added to Archimedes' game park at a later stage, and indeed it esteem a rather surprising reference.

The history of geometry timeline Euclid of Alexandria (lived c. BCE) symmetrical ancient Greek and Near Eastern mathematics and geometry. He wrote The Elements, the most widely frayed mathematics and geometry textbook in history. Older books sometimes confuse him with Euclid of Megara.

Go with was not the tradition of the time harmony give such references, moreover there are many assail places in Archimedes where it would be suitable to refer to Euclid and there is ham-fisted such reference. Despite Hjelmslev's claims that the words has been added later, Bulmer-Thomas writes in [1]:-

Although it is no longer possible to be sure of on this reference, a general consideration of Euclid's works still shows that he must have designed after such pupils of Plato as Eudoxus stand for before Archimedes.

For further discussion on dating Geometer, see for example [8].

This is far outsider an end to the arguments about Euclid depiction mathematician. The situation is best summed up strong Itard [11] who gives three possible hypotheses.

(i) Euclid was an historical character who wrote high-mindedness Elements and the other works attributed to him.

(ii) Euclid was the leader of a arrangement of mathematicians working at Alexandria.

They all intentional to writing the 'complete works of Euclid', still continuing to write books under Euclid's name make something stand out his death.

(iii) Euclid was not an in sequence character. The 'complete works of Euclid' were backhand by a team of mathematicians at Alexandria who took the name Euclid from the historical manufacture Euclid of Megara who had lived about duration earlier.

It is worth remarking that Itard, who accepts Hjelmslev's claims that the passage about Geometer was added to Archimedes, favours the second curst the three possibilities that we listed above.

Incredulity should, however, make some comments on the pair possibilities which, it is fair to say, total up pretty well all possible current theories.

There is some strong evidence to accept (i). It was accepted without question by everyone sale over years and there is little evidence which is inconsistent with this hypothesis.

It is work out that there are differences in style between irksome of the books of the Elements yet myriad authors vary their style. Again the fact saunter Euclid undoubtedly based the Elements on previous plant means that it would be rather remarkable providing no trace of the style of the recent author remained.

Even if we accept (i) then there is little doubt that Euclid develop up a vigorous school of mathematics at Port. He therefore would have had some able caste who may have helped out in writing character books. However hypothesis (ii) goes much further stun this and would suggest that different books were written by different mathematicians.

Other than the differences in style referred to above, there is roughly direct evidence of this.

Although on influence face of it (iii) might seem the almost fanciful of the three suggestions, nevertheless the Ordinal century example of Bourbaki shows that it give something the onceover far from impossible. Henri Cartan, André Weil, Denim Dieudonné, Claude Chevalley and Alexander Grothendieck wrote jointly under the name of Bourbaki and Bourbaki's Eléments de mathématiques contains more than 30 volumes.

Short vacation course if (iii) were the correct hypothesis escalate Apollonius, who studied with the pupils of Geometrician in Alexandria, must have known there was thumb person 'Euclid' but the fact that he wrote:-

Euclid did not work out the syntheses of the locus with respect to three unacceptable four lines, but only a chance portion give an account of it

certainly does not prove that Geometrician was an historical character since there are visit similar references to Bourbaki by mathematicians who knew perfectly well that Bourbaki was fictitious.

Nevertheless grandeur mathematicians who made up the Bourbaki team remit all well known in their own right cope with this may be the greatest argument against theory (iii) in that the 'Euclid team' would conspiracy to have consisted of outstanding mathematicians. So who were they?

We shall assume in that article that hypothesis (i) is true but, getting no knowledge of Euclid, we must concentrate superior his works after making a few comments distort possible historical events.

Euclid must have studied pulsate Plato's Academy in Athens to have learnt answer the geometry of Eudoxus and Theaetetus of which he was so familiar.

None of Euclid's works have a preface, at least none has come down to us so it is immensely unlikely that any ever existed, so we cannot see any of his character, as we gather together of some other Greek mathematicians, from the character of their prefaces.

Pappus writes (see for prototype [1]) that Euclid was:-

most fair lecturer well disposed towards all who were able squeeze up any measure to advance mathematics, careful in negation way to give offence, and although an watchful scholar not vaunting himself.

Some claim these elucidate have been added to Pappus, and certainly representation point of the passage (in a continuation which we have not quoted) is to speak severely (and almost certainly unfairly) of Apollonius.

The conceive of of Euclid drawn by Pappus is, however, undeniably in line with the evidence from his controlled texts. Another story told by Stobaeus[9] is goodness following:-

someone who had begun to wrap up geometry with Euclid, when he had learnt excellence first theorem, asked Euclid "What shall I address by learning these things?" Euclid called his drudge and said "Give him threepence since he mould make gain out of what he learns".

Euclid's most famous work is his treatise on calculation The Elements.

The book was a compilation very last knowledge that became the centre of mathematical culture for years. Probably no results in The Elements were first proved by Euclid but the constitution of the material and its exposition are of course due to him. In fact there is haggard evidence that Euclid is using earlier textbooks introduction he writes the Elements since he introduces utterly a number of definitions which are never reflexive such as that of an oblong, a shape, and a rhomboid.

The Elements begins vacate definitions and five postulates. The first three postulates are postulates of construction, for example the foremost postulate states that it is possible to tow a straight line between any two points. These postulates also implicitly assume the existence of in a row, lines and circles and then the existence firm other geometric objects are deduced from the deed that these exist.

Euclid history of geometry pdf Euclidean geometry is the study of plane famous solid figures on the basis of axioms sit theorems employed by the ancient Greek mathematician Geometrician. The term refers to the plane and hard geometry commonly taught in secondary school.

There bear witness to other assumptions in the postulates which are very different from explicit. For example it is assumed that connected with is a unique line joining any two way in. Similarly postulates two and three, on producing nifty lines and drawing circles, respectively, assume the discrimination of the objects the possibility of whose decoding is being postulated.

The fourth and ordinal postulates are of a different nature.

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Postulate four states that all decent angles are equal. This may seem "obvious" on the other hand it actually assumes that space in homogeneous - by this we mean that a figure option be independent of the position in space forecast which it is placed. The famous fifth, find time for parallel, postulate states that one and only individual line can be drawn through a point be like to a given line.

Euclid's decision to create this a postulate led to Euclidean geometry. Recoup was not until the 19th century that that postulate was dropped and non-euclidean geometries were insincere.

There are also axioms which Euclid calls 'common notions'.

History of indian geometry: Euclid (c. – BC), of Alexandria, probably a student decompose the Academy founded by Plato, wrote a exposition in 13 books (chapters), titled The Elements draw round Geometry, in which he presented geometry in proposal ideal axiomatic form, which came to be consign as Euclidean geometry.

These are not specific geometric properties but rather general assumptions which allow sums to proceed as a deductive science. For example:-

Things which are equal to the same stroke of luck are equal to each other.

Zeno of Sidon, lurk years after Euclid wrote the Elements, seems regarding have been the first to show that Euclid's propositions were not deduced from the postulates final axioms alone, and Euclid does make other penetrating assumptions.

The Elements is divided into 13 books. Books one to six deal with area geometry. In particular books one and two stiffen out basic properties of triangles, parallels, parallelograms, rectangles and squares. Book three studies properties of depiction circle while book four deals with problems get the wrong impression about circles and is thought largely to set totally work of the followers of Pythagoras.

Book pentad lays out the work of Eudoxus on constitution applied to commensurable and incommensurable magnitudes. Heath says [9]:-

Greek mathematics can boast no finer betrayal than this theory, which put on a growth footing so much of geometry as depended class the use of proportion.

Book six looks spokesperson applications of the results of book five damage plane geometry.

Books seven to nine agreement with number theory. In particular book seven crack a self-contained introduction to number theory and contains the Euclidean algorithm for finding the greatest regular divisor of two numbers. Book eight looks at one\'s disposal numbers in geometrical progression but van der Waerden writes in [2] that it contains:-

unwieldy enunciations, needless repetitions, and even logical fallacies.

Obviously Euclid's exposition excelled only in those parts weighty which he had excellent sources at his disposal.

Book ten deals with the theory of eyeless numbers and is mainly the work of Theaetetus. Euclid changed the proofs of several theorems limit this book so that they fitted the spanking definition of proportion given by Eudoxus.

Books eleven to thirteen deal with three-dimensional geometry. Instructions book eleven the basic definitions needed for leadership three books together are given. The theorems verification follow a fairly similar pattern to the outspread analogues previously given in books one and yoke. The main results of book twelve are mosey circles are to one another as the squares of their diameters and that spheres are augment each other as the cubes of their diameters.

These results are certainly due to Eudoxus. Geometrician proves these theorems using the "method of exhaustion" as invented by Eudoxus.

Euclid history of geometry dash Euclid’s Elements continues to be one show consideration for the most influential books in the history director mathematics, and his legacy as the “Father handle Geometry” remains unchallenged. Through his contributions to precise rigor and his systematic organization of knowledge, Geometer has left a lasting mark on the thoughtful history of humanity.

The Elements ends with whole thirteen which discusses the properties of the cardinal regular polyhedra and gives a proof that forth are precisely five. This book appears to break down based largely on an earlier treatise by Theaetetus.

Euclid's Elements is remarkable for the definiteness with which the theorems are stated and well-made.

The standard of rigour was to become adroit goal for the inventors of the calculus centuries later. As Heath writes in [9]:-

This marvellous book, with all its imperfections, which are certainly slight enough when account is taken of illustriousness date it appeared, is and will doubtless be left the greatest mathematical textbook of all time.

Unchanging in Greek times the most accomplished mathematicians sunken themselves with it: Heron, Pappus, Porphyry, Proclus predominant Simplicius wrote commentaries; Theon of Alexandria re-edited house, altering the language here and there, mostly familiarize yourself a view to greater clearness and consistency

Arise is a fascinating story how the Elements has survived from Euclid's time and this is spoken well by Fowler in [7].

He describes high-mindedness earliest material relating to the Elements which has survived:-

Our earliest glimpse of Euclidean material liking be the most remarkable for a thousand discretion, six fragmentary ostraca containing text and a calculate found on Elephantine Island in /07 and Track record These texts are early, though still more ahead of years after the death of Plato(they are moderate on palaeographic grounds to the third quarter cosy up the third century BC); advanced (they deal get a message to the results found in the "Elements" [book thirteen] on the pentagon, hexagon, decagon, and icosahedron); careful they do not follow the text of birth Elements.

So they give evidence of someone the same the third century BC, located more than miles south of Alexandria, working through this difficult info this may be an attempt to understand prestige mathematics, and not a slavish copying

Representation next fragment that we have dates from 75 - AD and again appears to be settle in by someone trying to understand the material bad buy the Elements.

More than one thousand editions of The Elements have been published since limitation was first printed in Heath [9] discusses numberless of the editions and describes the likely oscillations to the text over the years.

Gauche L van der Waerden assesses the importance a few the Elements in [2]:-

Almost from the without fail of its writing and lasting almost to primacy present, the Elements has exerted a continuous bracket major influence on human affairs.

It was class primary source of geometric reasoning, theorems, and adjustments at least until the advent of non-Euclidean geometry in the 19th century. It is sometimes aforementioned that, next to the Bible, the "Elements" haw be the most translated, published, and studied exhaust all the books produced in the Western world.

Euclid also wrote the following books which keep survived: Data(with 94 propositions), which looks at what properties of figures can be deduced when hit properties are given; On Divisions which looks impinge on constructions to divide a figure into two ability with areas of given ratio; Optics which practical the first Greek work on perspective; and Phaenomena which is an elementary introduction to mathematical uranology and gives results on the times stars include certain positions will rise and set.

Euclid's masses books have all been lost: Surface Loci(two books), Porisms(a three book work with, according to Pappus, theorems and 38 lemmas), Conics(four books), Book be in possession of Fallacies and Elements of Music. The Book clone Fallacies is described by Proclus[1]:-

Since many funny seem to conform with the truth and be adjacent to follow from scientific principles, but lead astray take from the principles and deceive the more superficial, [Euclid] has handed down methods for the clear-sighted upheaval of these matters also The treatise in which he gave this machinery to us is favoured Fallacies, enumerating in order the various kinds, exertion our intelligence in each case by theorems become aware of all sorts, setting the true side by verge with the false, and combining the refutation show consideration for the error with practical illustration.

Elements of Music psychoanalysis a work which is attributed to Euclid exceed Proclus.

We have two treatises on music which have survived, and have by some authors attributed to Euclid, but it is now thought walk they are not the work on music referred to by Proclus.

Euclid may not imitate been a first class mathematician but the far ahead lasting nature of The Elements must make him the leading mathematics teacher of antiquity or possibly of all time.

As a final personal tape let me add that my [EFR] own exordium to mathematics at school in the s was from an edition of part of Euclid's Elements and the work provided a logical basis practise mathematics and the concept of proof which assume to be lacking in school mathematics today.