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* Euclid's Elements, All thirteen books, in several languages as Spanish, Catalan, English, German, Portuguese, Arabic, Italian, Russian and Chinese.
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Euclid's and Elements
Matteo Ricci ( left ) and Xu Guangqi ( right ) in the Chinese edition of Euclid's Elements published in 1607.
Euclid's The Elements includes the following " Common Notion 1 ":
Proclus introduces Euclid only briefly in his fifth-century Commentary on the Elements, as the author of Elements, that he was mentioned by Archimedes, and that when King Ptolemy asked if there was a shorter path to learning geometry than Euclid's Elements, " Euclid replied there is no royal road to geometry.
One of the oldest surviving fragments of Euclid's Elements, found at Oxyrhynchus and dated to circa AD 100 ( Papyrus Oxyrhynchus 29 | P. Oxy.
Although many of the results in Elements originated with earlier mathematicians, one of Euclid's accomplishments was to present them in a single, logically coherent framework, making it easy to use and easy to reference, including a system of rigorous mathematical proofs that remains the basis of mathematics 23 centuries later.
* Proclus, A commentary on the First Book of Euclid's Elements, translated by Glenn Raymond Morrow, Princeton University Press, 1992.
* Euclid's Elements, All thirteen books, with interactive diagrams using Java.
* Euclid's Elements, with the original Greek and an English translation on facing pages ( includes PDF version for printing ).
* Euclid's Elements, books I-VI, in English pdf, in a Project Gutenberg Victorian textbook edition with diagrams.
Includes editions and translations of Euclid's Elements, Data, and Optica, Proclus's Commentary on Euclid, and other historical sources.
In the 19th century, it was also realized that Euclid's ten axioms and common notions do not suffice to prove all of theorems stated in the Elements.
* Heath's authoritative translation of Euclid's Elements plus his extensive historical research and detailed commentary throughout the text.
* Euclid's Elements, the mathematical treatise on geometry and number theory
The earliest surviving description of the Euclidean algorithm is in Euclid's Elements ( c. 300 BC ), making it one of the oldest numerical algorithms still in common use.
Book VII, propositions 30 and 32 of Euclid's Elements is essentially the statement and proof of the fundamental theorem.
The proof uses Euclid's lemma ( Elements VII, 30 ): if a prime p divides the product of two natural numbers a and b, then p divides a or p divides b ( or perhaps both ).
Illustration at the beginning of a medieval translation of Euclid's Element ( mathematics ) | Elements, ( c. 1310 )
A proof from Euclid | Euclid's Euclid's Elements | Elements, widely considered the most influential textbook of all time.
( Book X of Euclid's Elements is described by Pappus as being largely based on Theaetetus's work.
Euclid's and All
In a work titled Euclides ab Omni Naevo Vindicatus ( Euclid Freed from All Flaws ), published in 1733, Saccheri quickly discarded elliptic geometry as a possibility ( some others of Euclid's axioms must be modified for elliptic geometry to work ) and set to work proving a great number of results in hyperbolic geometry.
* Euclid's Elements – All thirteen books in one volume, Based on Heath's translation, Green Lion Press ISBN 1-888009-18-7.
Euclid's and thirteen
* Clay Mathematics Institute Historical Archive – The thirteen books of Euclid's Elements copied by Stephen the Clerk for Arethas of Patras, in Constantinople in 888 AD
* Kitāb Taḥrīr uṣūl li-Ūqlīdis Arabic translation of the thirteen books of Euclid's Elements by Nasīr al-Dīn al-Ṭūsī.
* Euclid The thirteen books of Euclid's Elements ( Cambridge: Cambridge University Press, 1908 )
*" About the translator: Thomas L. Heath " in Euclid's Elements: all thirteen books complete in one volume ( 2002 ) Green Lion Press.
* Heath: The thirteen books of Euclid's elements Preface
It considers the pedagogic merit of thirteen contemporary geometry textbooks, demonstrating how each in turn is either inferior to or functionally identical to that of Euclid's Elements.
Euclid's and books
According to Pappus, " Apollonius, having completed Euclid's four books of conics and added four others, handed down eight volumes of conics.
Euclid's Elements ( Stoicheia ) is a mathematical and geometric treatise consisting of 13 books written by the Greek mathematician Euclid in Alexandria c. 300 BC.
It has been customarily said that the Pythagoreans discovered most of the material in the first two books of Euclid's Elements.
Euclid's and several
Unfortunately, Euclid's original system of five postulates ( axioms ) is not one of these as his proofs relied on several unstated assumptions which should also have been taken as axioms.
In addition, through several of his works, most notably Philosophy from Oracles and Against the Christians, he was involved in a controversy with a number of early Christians, and his commentary on Euclid's Elements was used as a source by Pappus of Alexandria.
Euclid's and languages
Roger Ascham thought that his pupil Robert had an uncommon talent for languages and writing, " exceed almost all other by nature ", and regretted that he had done himself harm by preferring " Euclid's pricks and lines " ( mathematics ).
Euclid's and English
In 1077, Khayyám wrote Sharh ma ashkala min musadarat kitab Uqlidis ( Explanations of the Difficulties in the Postulates of Euclid ) published in English as " On the Difficulties of Euclid's Definitions ".
In 1756, appeared, both in Latin and in English, the first edition of his Euclid's Elements.
( Euclid's original definition and some English dictionaries ' definition of rhombus excludes squares, but modern mathematicians prefer the inclusive definition.
The Book frontispiece | frontispiece of Sir Henry Billingsley's first English version of Euclid's Elements, 1570
He therefore bought an English edition of Euclid's Elements which included an index of propositions, and, having turned to two or three which he thought might be helpful, found them so obvious that he dismissed it " as a trifling book ", and applied himself to the study of René Descartes ' Geometry.
The Book frontispiece | frontispiece of Sir Henry Billingsley's first English version of Euclid's Elements, 1570
Euclid's and German
In geometry, Pasch's theorem, stated in 1882 by a German mathematician Moritz Pasch, is a result of plane geometry which cannot be derived from Euclid's postulates.
Euclid's and Arabic
The frontispiece of an Adelard of Bath Latin translation of Euclid's Elements, c. 1309 – 1316 ; the oldest surviving Latin translation of the Elements is a 12th-century translation by Adelard from an Arabic version.
The frontispiece of an Adelard of Bath Latin translation of Euclid's Elements, c. 1309 – 1316 ; the oldest surviving Latin translation of the Elements is a 12th century work by Adelard, which translates to Latin from the Arabic.
Pappus also wrote commentaries on Euclid's Elements ( of which fragments are preserved in Proclus and the Scholia, while that on the tenth Book has been found in an Arabic manuscript ), and on Ptolemy's Ἁρμονικά ( Harmonika ).
His works include Rekhaganita, a translation of Euclid's Elements made from Nasir al-Din al-Tusi's Arabic recension of same ; Siddhantasarakaustubha, a translation of the Almagest from Arabic ; and two works on astronomical instruments such as the astrolabe, Siddhanta-samrat and Yantraprakara, which also record astronomical observations made by Jagannatha.
In the 10th century, Arabic mathematicians used geometric dissections in their commentaries on Euclid's Elements.
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