d’Euclide; glwiki Elementos de Euclides; hewiki יסודות (ספר); hiwiki एलिमेन्ट्स (यूक्लिड); hrwiki Elementi (Euklid); huwiki Elemek; hywiki Սկզբունքներ. i dr.n. Sačuvana dela su: “Elementi” (geometrija kao nauka o prostoru) u 13 knjiga.• Euklid je poznati grčki matematičar iz Atine. “Optika” (s teorijom perspektive). Euklid je pokušao da izlaganje bude strogo deduktivno i upravo zbog te doslednosti Elementi su vekovima smatrani najsavršenijim matematičkim delom. Mnoge.

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The Elements Ancient Greek: It is a collection of definitions, postulates, propositions theorems and constructionsand mathematical proofs of the propositions. The books cover plane elemehti solid Euclidean geometryelementary number theoryand incommensurable lines. Elements is the oldest extant large-scale deductive treatment of mathematics.

Euklid/sö – Wikiwand

It has proven instrumental in the development of logic and modern scienceand its logical rigor euilid not surpassed until the 19th century. Elmenti Elements has been referred to as the most successful [1] [2] and influential [3] textbook ever written. It was slementi of the very earliest mathematical works to be printed after the invention of the printing press and has been estimated to be second only to the Bible in the number fuklid editions published since the first printing elenenti[3] with the number reaching well over one thousand.

Not until the 20th century, by which time its content was universally taught through other school textbooks, did it cease to be elemwnti something all educated people had read. Scholars believe that the Elements is largely a compilation of propositions based on books by earlier Greek mathematicians.

Proclus — ADa Greek mathematician who lived around seven centuries after Euclid, wrote in his commentary on the Elements: This manuscript, the Heiberg manuscript, is from a Byzantine workshop around and is the basis of modern editions. Although known to, for instance, Cicerono record exists of the text having been translated into Latin prior to Boethius in the fifth or sixth century.

The first printed edition appeared in based on Campanus of Novara ‘s edition[13] and since then it has been translated into many languages and published in about a thousand different editions. Theon’s Greek edition was recovered in InJohn Dee provided a widely respected “Mathematical Preface”, along with copious notes and supplementary material, to the first English edition by Henry Billingsley.

Copies of the Greek text still exist, some of which can be found in the Vatican Library and the Bodleian Library in Oxford.

The manuscripts available are of variable quality, and invariably incomplete. By careful analysis of the translations and originals, hypotheses have been made about the contents of the original text copies of which are no longer available. Ancient texts which refer to the Elements itself, and to other mathematical theories that were current at the time it was written, suklid also important in this process.

Such analyses are conducted by J. Heiberg and Sir Thomas Little Heath in their editions of the text. Also of importance are the scholiaor annotations to the text. These additions, which often distinguished themselves from the main text depending on the manuscriptgradually accumulated over elejenti as opinions varied upon what was worthy of explanation or further study.

The Elements is still considered a masterpiece in the application of logic to mathematics. In historical context, it has proven enormously influential in many areas of science.

Mathematicians and philosophers, such as Thomas HobbesBaruch Spinoza eleemnti, Alfred North Whiteheadand Bertrand Russellhave attempted to create their own foundational “Elements” for their respective disciplines, by adopting the ekulid deductive structures that Euclid’s work introduced. The austere beauty of Euclidean geometry has been seen by many in western culture as a glimpse of an otherworldly system of perfection and certainty.

Abraham Lincoln kept a copy of Euclid in his saddlebag, and studied it late at night by lamplight; he related that he said to himself, “You never can make a lawyer if you do not understand what demonstrate means; and I left my situation in Springfield, went home to my father’s house, and stayed there till I could give any proposition in the six books of Euclid at sight”. Vincent Millay wrote in her sonnet ” Euclid alone has looked on Beauty bare “, “O blinding hour, O holy, terrible day, When first the shaft into his vision shone Of light anatomized!


Einstein recalled a copy of the Elements and a magnetic compass as two gifts that had a great influence on him as a boy, referring to the Euclid as the “holy little geometry book”. The success of the Elements is due primarily to its logical presentation of most of the mathematical knowledge available to Euclid.

Much of the material is not original to him, although many of the proofs are his.

Euklidovi elementi

However, Euclid’s systematic development of his subject, from a small set of axioms to deep results, and the consistency of his approach euklld the Elementsencouraged its eukllid as a textbook for about 2, years. The Elements still influences modern geometry books. Further, its logical axiomatic approach elemenhi rigorous proofs remain the cornerstone of mathematics. Euclid’s axiomatic approach and constructive methods were widely influential.

Many of Euclid’s propositions were constructive, demonstrating the existence of some figure by detailing the steps he used to construct the object using a compass and straightedge. His constructive approach appears even in his geometry’s postulates, as the ruklid and third postulates stating the existence of a elementk and circle are constructive. Instead elemehti stating that lines and circles exist per his prior definitions, he states that it is possible to ‘construct’ a line and circle.

It also appears that, for him to use a figure in one of his proofs, he needs to construct it in an earlier proposition. For example, he proves the Pythagorean theorem by first inscribing a square on the sides of a right triangle, but only after constructing a square on a given line one proposition earlier.

As was common in ancient mathematical texts, when a proposition needed proof in several different cases, Euclid often proved only one of them often the most difficultleaving the others to the reader. Later editors such as Theon often interpolated their own proofs of these cases. Euclid’s presentation was limited by the mathematical ideas and notations in common currency in his era, and this causes the treatment to seem awkward to the modern reader in some places.

For example, there was no notion of an angle greater than two right angles, [20] the number 1 was sometimes treated separately from other positive integers, and as multiplication was treated geometrically he did not use the product of more than 3 different numbers.

The geometrical treatment of number theory elejenti have been because the alternative would have been the extremely awkward Alexandrian system of numerals. The elementj of each result is given in a stylized form, which, although not invented by Euclid, is recognized as typically classical. It has six different parts: First is the ‘enunciation’, which states the result in general terms i.

Then comes the ‘setting-out’, which gives the figure and denotes particular geometrical ruklid by letters. Next comes the ‘definition’ or euklic, which restates the enunciation in terms of elementj particular figure. Then the ‘construction’ or ‘machinery’ follows. Here, the original figure is extended to forward the proof. Then, the ‘proof’ itself follows. Finally, the ‘conclusion’ connects the proof to the enunciation by stating the specific conclusions drawn in the proof, in the general terms of the enunciation.

No indication is given of the method of reasoning that led to the result, although the Data does provide instruction about how to euilid the types of problems encountered in the first four books of the Elements. However, Euclid’s original proof of this proposition, is general, valid, and does not depend on the figure used as an example to illustrate one given configuration. Euclid’s list of axioms in the Elements was not exhaustive, but represented the principles that were the most eleemnti.

His proofs often invoke axiomatic notions which were not originally presented in his list of axioms. Ekklid editors have interpolated Euclid’s implicit axiomatic assumptions in the list of formal axioms.


For example, in the first construction of Book 1, Euclid used a premise that was neither postulated nor proved: If superposition is to be considered a valid method of geometric proof, all of geometry would be full of such proofs.

For example, propositions I. Mathematician and historian W. Rouse Ball put the criticisms in perspective, remarking that “the fact that for two thousand years [the Elements ] was the usual text-book on the subject raises a strong presumption that it is not unsuitable for that purpose.

It was not uncommon in ancient time to attribute to celebrated authors works that were not written by them. The book continues Euclid’s comparison of regular solids inscribed in spheres, with the chief result being that the ratio of the surfaces of the dodecahedron and icosahedron inscribed in the same sphere is the same as the ratio of their euilid, the ratio being.

This book covers topics such as counting the number of edges and solid angles in the regular solids, and finding the measure of dihedral angles of faces that meet at an edge.

Geometry emerged as an indispensable part of the standard education of the English gentleman in the eighteenth century; by the Eementi period it was also becoming an important part of the education of artisans, children at Board Schools, colonial subjects and, to a rather lesser degree, women.

The standard textbook for this purpose was none other than Euclid’s The Elements. From Wikipedia, the free encyclopedia. Published by Routledge Taylor and Francis Group. As teachers at the school he called a band of leading scholars, among whom was the author of the most fabulously successful mathematics textbook ever written — the Elements Stoichia of Euclid.

The Elements of Euclid not only was the earliest major Greek mathematical work to come down to us, but also the most influential textbook of all times.

Perhaps no book other than the Bible can boast so many editions, and certainly no mathematical work has had an influence comparable with that of Euclid’s Elements. Bedientpage There, the Elements became the foundation of mathematical education. More than editions of the Elements are known. In all probability, it is, next to the Biblethe most widely elmenti book in the civilization of the Western world. A History of Western Philosophy.

Reynolds and Nigel G. Wilson, Scribes and Scholars 2nd.

However, more recent biographical work has turned up no clear documentation that Adelard ever went to Muslim-ruled Spain, although he spent time in Norman-ruled Sicily and Crusader-ruled Antioch, both of which had Arabic-speaking populations.

Charles Burnett, Adelard of Bath: Campanus of Novara and Euclid’s Elements.

Euclid’s Elements – Wikipedia

Archived from the original on Archived from the original on 10 June Retrieved 29 April In ancient times it was not euklkd to attribute to a celebrated author works that were not by him; thus, some leementi of Euclid’s Elements include a fourteenth and even a fifteenth book, both shown by later scholars to be apocryphal.

It is thought that this book may have been composed by Hypsicles on eleementi basis of a treatise now lost by Apollonius comparing the dodecahedron and icosahedron. This book also deals with the regular solids, counting the number of edges and solid angles in the solids, and finding the measures of the dihedral angles of faces meeting at an edge.

SarmaHelaine Selined. Archived from the original on 22 June Archived from the original on 9 October Retrieved 4 October The Elements of Euclid. Problem of Apollonius Squaring the circle Doubling the cube Angle trisection. Cyrene Library of Alexandria Platonic Academy.

Timeline of ancient Greek mathematicians.