Euklids of elements
Euklids of elements or the elements (in the original Stoicheia) was into the second half 19. Century the work of the world literature usually common after the Bible. It gives us a good overview of the mathematical level of knowledge of the Greekstoward end 4. Century v. Chr..
With the elements it concerns a text book of mathematics, which consists of 13 books. Today one that these books come from several authors and on older sources is partly based, knows Euklid here thus mainlyas Systematisierer and a publisher served.
Table of contents |
books
the list gives an overview of the treated topics in the individual books (and over those contents after assumed sources):
- Book 1-6: Surfacesgeometry, and. A. congruent and similar figures
- book 1: From the definitions to the set of the Pythagoras (source (n): Pythagoräer)
- book 2: Geometrical algebra (Pythagoräer)
- book 3: Circle teachings (Pythagoräer)
- book 4: Polygons (Pythagoräer)
- book 5: Irrational one Sizes of (Eudoxos of kneeling DOS)
- book 6: Proportions (source (n) unknown)
- book 7-9: Arithmetic, and. A. Number theory and proportion teachings
- book 7: Divisibility and prime numbers (Pythagoräer)
- book 8: Square/Kubikzahl and geometrical rows (Pythagoräer)
- book 9: Straight one andodd numbers, and. A. also the sentence of Euklid (Pythagoräer)
- book 10: Geometry for inkommensurable sizes of (Theaitetos)
- book 11-13: Space geometry (geometry of solids), and. A. the five even bodies (Platonic bodies)
- book 11: Elementary to space geometry
- Book 12: Exhaustionsmethode (Eudoxos of kneeling DOS)
- book 13: the five even bodies (Platonic bodies) (Theaitetos)
to these books later even still two further books were added:
- Book 14: a book of the Hypsikles (in 2. Century v. Chr.)
- Book 15: a book probably coming from Damaskios (in 5. Century)
structure
the work prepares the bases of geometry and arithmetic and shows exemplary the structure of an accurate science. Most statements become from a limited supply of definitions, Deduced and proved to postulates and axioms. This procedure affected to today not only the mathematicians, but also many physicists, philosophers and theologians with its attempt to develop their science on axioms.
see also: Euclidean geometry
excessive quantity
the oldestreceived handwriting originates from the Byzanz of the yearly 888 and today in the Bodleian LIBRARY (Oxford) is kept. A translation of the Boethius from the Greek one in latin (over 500) is today only partial, receive and also only in later working on.
Of thatnumerous Arab translations and comments were particularly for the excessive quantity the two translations of the aluminium-Haggag toward end 8. Century and those of Ishaq ibn Hunain/Tabit ibn Qurra (end of 9. Century) and/or. of Nasi aluminum DIN aluminium-Tusi (1248) of importance.
The first medievalTranslation of the elements in latin we owe to the Englishman aristocracy pool of broadcasting corporations von Bath. This roamed across in 12. Century Europe on the search for handwriting and transferred so around 1120 also this work from the Arab one. Of it the elements became independent then in the same century in Spain also from at least two further famous translators from the Arab one transfer: of Hermann of Kärnten and of Gerhard of Cremona.
Likewise in 12. Century, however in South Italies or on Sicilies and of an unknown author, is a further translation of the elements from thatGreek ones developed. Because of the style for the translation the assumption is appropriate close that it concerns with this unknown author the same, which translated around (1160) also the Almagest of the Ptolemäus.
Naturally the elements belonged to the first works, which one wanted to have printed.The preparing treatment of the Regiomontanus remained unfinished into the 1460er year. A complete translation from the Greek one of Zamberti could be printed then 1505. From this time after the invention of the printing some us most important the works are only emphasized here: the translation of theCommandinus from the Greek one (1572), which commentated in detail expenditure of Christoph Clavius (1574), the translation of F. Peyrard in the French (1814 - 1818), the translation (the first parts) of Xu Guangqi and Matteo Ricci in the Chinese (1607)and not least the German translation of Cl. Thaer after the text of Heiberg (1933 - 1937).
literature
Euklid: The elements, ISBN 3-8171-3413-4
Web
- the Web on the left of Euclid's of element adapted tons by D. E. Joyce.
- On theprincipal edition and translation OF the text