Euclid's elements - traducción al ruso
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Euclid's elements - traducción al ruso

MATHEMATICAL TREATISE BY EUCLID
Euclid's Elements.; Euclid's elements; Elements of Geometry; Euclid elements; Elements (book); Euclid’s Elements; Euclid's Geometry; Euclids Elements; Elements of Euclid; Στοιχεῖα; Stoicheia; The Elements by Euclid
  • Byrne]]'s ''The Elements of Euclid'' and published in colored version in 1847.
  • A page with marginalia from the first printed edition of ''Elements'', printed by [[Erhard Ratdolt]] in 1482
  • Euclidis – Elementorum libri XV Paris, Hieronymum de Marnef & Guillaume Cavelat, 1573 (second edition after the 1557 ed.); in  8:350, (2)pp. THOMAS–STANFORD, Early Editions of Euclid's ''Elements'', n°32. Mentioned in T.L. Heath's translation. Private collection Hector Zenil.
  • Codex Vaticanus 190
  • p=18}}
  • Ishaq ibn Hunayn's]] Arabic Translation of Elementa. [[Iraq]], 1270. [[Chester Beatty Library]]
  • The different versions of the parallel postulate result in different geometries.
  • A fragment of Euclid's ''Elements'' on part of the [[Oxyrhynchus papyri]]

Euclid's elements         

математика

"Начала" Евклида

the four elements         
  • 🜁
  • [[Artus Wolffort]], ''The Four Elements'', before 1641
  • 🜃
  • 🜂
  • Seventeenth century alchemical emblem showing the four Classical elements in the corners of the image, alongside the tria prima on the central triangle
  • The four classical elements of [[Empedocles]] and [[Aristotle]] illustrated with a burning log. The log releases all four elements as it is destroyed.
  • Four classical elements
  • 🜄
GROUP OF FOUR ELEMENTS INTO WHICH ACCORDING TO ANCIENT NOTIONS ANY OBJECT MAY BE ANALYZED
Classical Element; Greek Element; Greek four elements; Four elements; Classical Elements; The Four Elements; Classical elements; Primary elements; Alchemical elements; The four elements; Four Elements; Four element theory; Essential element theories; Four classical elements; Greek elements; Four element; Panchamahabhuta; Pancha mahabhuta; Greek element; The Four Entities; Empedoclean elements; Classic element; Classic elements; Classic Element; Aristotelian element; 4 Elements; The World elements; Traditional element; Traditional elements; Empedoclean element; Water, earth, fire and air; Earth, air, fire, and water; Stoicheion
земля, воздух, огонь, вода
the four elements         
  • 🜁
  • [[Artus Wolffort]], ''The Four Elements'', before 1641
  • 🜃
  • 🜂
  • Seventeenth century alchemical emblem showing the four Classical elements in the corners of the image, alongside the tria prima on the central triangle
  • The four classical elements of [[Empedocles]] and [[Aristotle]] illustrated with a burning log. The log releases all four elements as it is destroyed.
  • Four classical elements
  • 🜄
GROUP OF FOUR ELEMENTS INTO WHICH ACCORDING TO ANCIENT NOTIONS ANY OBJECT MAY BE ANALYZED
Classical Element; Greek Element; Greek four elements; Four elements; Classical Elements; The Four Elements; Classical elements; Primary elements; Alchemical elements; The four elements; Four Elements; Four element theory; Essential element theories; Four classical elements; Greek elements; Four element; Panchamahabhuta; Pancha mahabhuta; Greek element; The Four Entities; Empedoclean elements; Classic element; Classic elements; Classic Element; Aristotelian element; 4 Elements; The World elements; Traditional element; Traditional elements; Empedoclean element; Water, earth, fire and air; Earth, air, fire, and water; Stoicheion
четыре (основные) стихии (земля, вода. воздух, огонь)

Definición

Euclid's Algorithm
<algorithm> (Or "Euclidean Algorithm") An algorithm for finding the greatest common divisor (GCD) of two numbers. It relies on the identity gcd(a, b) = gcd(a-b, b) To find the GCD of two numbers by this algorithm, repeatedly replace the larger by subtracting the smaller from it until the two numbers are equal. E.g. 132, 168 -> 132, 36 -> 96, 36 -> 60, 36 -> 24, 36 -> 24, 12 -> 12, 12 so the GCD of 132 and 168 is 12. This algorithm requires only subtraction and comparison operations but can take a number of steps proportional to the difference between the initial numbers (e.g. gcd(1, 1001) will take 1000 steps). (1997-06-30)

Wikipedia

Euclid's Elements

Euclid's Elements (Ancient Greek: Στοιχεῖα Stoikheîa) is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt c. 300 BC. It is a collection of definitions, postulates, propositions (theorems and constructions), and mathematical proofs of the propositions. The books cover plane and solid Euclidean geometry, elementary number theory, and incommensurable lines. Elements is the oldest extant large-scale deductive treatment of mathematics. It has proven instrumental in the development of logic and modern science, and its logical rigor was not surpassed until the 19th century.

Euclid's Elements has been referred to as the most successful and influential textbook ever written. It was one 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 of editions published since the first printing in 1482, the number reaching well over one thousand. For centuries, when the quadrivium was included in the curriculum of all university students, knowledge of at least part of Euclid's Elements was required of all students. Not until the 20th century, by which time its content was universally taught through other school textbooks, did it cease to be considered something all educated people had read.

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