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Nicomachus Of Gerasa:     more detail

The Thirteen Books of Euclid's Elements; The Works of Archimedes Including the Method; On Conic Sections; and Introduction to Arithmetic (Britannica Great Books, 11) by Euclid, Archimedes, et all 1952 The Manual of Harmonics of Nicomachus the Pythagorean by Nicomachus, Flora R. Levin, 1993-12 Nicomachus of Gerasa: An entry from Gale's <i>Science and Its Times</i> by Judson Knight, 2001 Euclid - Archimedes - Apollonius of Perga - Nicomachus of Gerasa (The Great Books of the Western World, 25th Anniversary Edition) by Euclid, Archimedes, et all 1985 The arithmetical philosophy of Nicomachus of Gerasa by George Johnson, 1916-01-01 Volume 11 Great Books of the Western World: The Thirteen Books of Euclid's Elements; the Works of Archimedes Including the Method; on Conic Sections By Apollonius of Perga and Introduction to Arithmetic By Nicomachus of Gerasa by Unknown, 1952 The Great Books of the St. John''s Program - Nicomachus of Gerasa (c.100 A.D.): Introduction to Arithmetic by Martin Luther (trans.) Nicomachus of Gerasa; D''Ooge, 1946 Nicomachus of Gerasa: Introduction to Arithmetic by Nicomachus of Gerasa. Translated by Martin Luther D'ooge., 1960 The Mathematical Writings of Euclid, Archimedes, Apollonius of Perga, Nicomachus of Gerasa (The Great Books of the Western World) by Euclid, Archimedes, et all 1985 Introduction to Arithmetic by Martin [translator] Nicomachus of Gerasa; D'Ooge, 1926 Introduction To Arithmetic by Nicomachus Of Gerasa; Translated By Martin Luther Dodge, 1960 The Thirteen Books of Euclid's Elements: The Works of Archimedes Including the Method: On Conic Sections: Introduction to Arithmetic (Great Books of the Western World, Vol. 11) by Euclid, Archimedes, et all 1987

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1. Nicomachus Of Gerasa (fl.c. 100 A.D.) Library Of Congress Citations
   Book Citations 6 Records. Author Nicomachus, of Gerasa. Uniform Title Introductio arithmetica.  
   http://www.mala.bc.ca/~mcneil/cit/citlcnico.htm
   
   Extractions: The Little Search Engine that Could Down to Name Citations LC Online Catalog Amazon Search Book Citations [6 Records] Author: Nicomachus, of Gerasa. Uniform Title: Introductio arithmetica. English Title: Introduction to arithmetic. Translated into English by Martin Luther D'Ooge, with studies in Greek arithmetic by Frank Egleston Robbins and Louis Charles Karpinski. New York, Macmillan, 1926. Published: [New York, Johnson Reprint Corp., 1972] Description: ix, 318 p. illus. 23 cm. LC Call No.: QA31 .N553 1972 Dewey No.: 513 Notes: Original ed. issued as v. 16 of University of Michigan studies. Humanistic series. Bibliography: p. 311-312. Subjects: Mathematics, Greek. Arithmetic Early works to 1900. Series Entry: University of Michigan studies. Humanistic series ; v. 16. Control No.: 73039141 //r934 Author: Nicomachus, of Gerasa. Uniform Title: Introductio arithmetica. French Title: Introduction arithmbetique / Nicomaque de Gberase ; introd., traduction, notes et index par Janine Bertier. Published: Paris : J. Vrin, 1978. Description: 254 p. ; 26 cm. Series: Histoire des doctrines de l'antiquitbe classique ; 2 LC Call No.: QA31 .N554 Dewey No.: 513 ISBN: 75.00F Notes: Translation of Introductio arithmetica. Bibliography: p. [227]-232. Includes index. Subjects: Mathematics, Greek. Arithmetic Early works to 1900. Other authors: Bertier, Janine. Control No.: 79338551 //r933

2. Nicomachus
   nicomachus of gerasa. nicomachus of gerasa is mentioned in a small number ofsources and we can date him fairly accurately from the information given.  
   http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Nicomachus.html
   
   Extractions: Nicomachus of Gerasa is mentioned in a small number of sources and we can date him fairly accurately from the information given. Nicomachus himself refers to Thrasyllus who died in 36 AD so this gives lower limits on his dates. On the other hand Apuleius , the Platonic philosopher, rhetorician and author whose dates are 124 AD to about 175 AD, translated Nicomachus's Introduction to Arithmetic into Latin so this gives an upper limit on his dates. One of the most interesting references is by Lucian , the rhetorician, pamphleteer and satirist who was born about 120 AD, who makes one of his characters say:- You calculate like Nicomachus. Clearly Nicomachus had achieved fame for his arithmetical work! In the paper [7] Dillon argues that Nicomachus died in 196 AD. His argument is based on the fact that Marinus claimed that Proclus believed that he was the reincarnation of Nicomachus. Since

3. Nicomachus
   Biography of Nicomachus (60120) nicomachus of gerasa. Born about 60 in Gerasa, Roman Syria (now Jarash, Jordan)  
   http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Nicomachus.html
   
   Extractions: Nicomachus of Gerasa is mentioned in a small number of sources and we can date him fairly accurately from the information given. Nicomachus himself refers to Thrasyllus who died in 36 AD so this gives lower limits on his dates. On the other hand Apuleius , the Platonic philosopher, rhetorician and author whose dates are 124 AD to about 175 AD, translated Nicomachus's Introduction to Arithmetic into Latin so this gives an upper limit on his dates. One of the most interesting references is by Lucian , the rhetorician, pamphleteer and satirist who was born about 120 AD, who makes one of his characters say:- You calculate like Nicomachus. Clearly Nicomachus had achieved fame for his arithmetical work! In the paper [7] Dillon argues that Nicomachus died in 196 AD. His argument is based on the fact that Marinus claimed that Proclus believed that he was the reincarnation of Nicomachus. Since

4. References For Nicomachus
   Books MLD'Ooge (trs.), nicomachus of gerasa, Introduction to Arithmetic (New York,1926). TL Heath, A History of Greek Mathematics (2 Vols.) (Oxford, 1921).  
   http://www-gap.dcs.st-and.ac.uk/~history/References/Nicomachus.html
   
   Extractions: S Brentjes, Untersuchungen zum Nicomachus Arabus, Centaurus M Crubellier and J Sip, Looking for perfect numbers, History of Mathematics : History of Problems (Paris, 1997), 389-410. J M Dillon, A date for the death of Nicomachus of Gerasa, Classical Review Rev. Histoire Sci. H R Muzafarova, Nicomachos' arithmetic in a work by Qutb ad-Din as-Shirazi (Russian), in Mathematics and the methodology of its teaching (Russian) I (Dushanbe, 1974), 124-131. Trans. Amer. Philos. Soc. Main index Birthplace Maps Biographies Index

5. - Great Books -
   nicomachus of gerasa is mentioned in a small number of sources and we can date him fairly accurately from the  
   http://www.mala.bc.ca/~mcneil/nico.htm

6. - Great Books -
   nicomachus of gerasa (c. 100), nicomachus of gerasa is mentioned in a small numberof sources and we can date him fairly accurately from the information given.  
   http://www.malaspina.com/site/person_887.asp
   
   Extractions: Nicomachus of Gerasa is mentioned in a small number of sources and we can date him fairly accurately from the information given. Nicomachus himself refers to Thrasyllus who died in 36 AD so this gives lower limits on his dates. On the other hand Apuleius, the Platonic philosopher, rhetorician and author whose dates are 124 AD to about 175 AD, translated Nicomachus's Introduction to Arithmetic into Latin so this gives an upper limit on his dates. One of the most interesting references is by Lucian , the rhetorician, pamphleteer and satirist who was born about 120 AD, who makes one of his characters say: You calculate like Nicomachus . Clearly Nicomachus had achieved fame for his arithmetical work! Nicomachus was a Pythagorean . This is obvious from his writings on numbers and music, but we are also told this by Porphyry who says that he was one of the leading members of the Pythagoreans School. Nicomachus wrote Arithmetike eisagoge (Introduction to Arithmetic) which was the first work to treat arithmetic as a separate topic from geometry. Unlike Euclid, Nicomachus gave no abstract proofs of his theorems, merely stating theorems and illustrating them with numerical examples. However Introduction to Arithmetic does contain quite elementary errors which show that Nicomachus chose not to give proofs of his results because he did not in general have such proofs. Many of the results were known by Nicomachus to be true since they appeared with proofs in Euclid, although in a geometrical formulation. Sometimes Nicomachus stated a result that is simply false and then illustrated it with an example that happens to have the properties described in the result. We must deduce from this that some of the results are merely guesses based on the evidence of the numerical examples (and in some cases perhaps even based on one example!).

7. - Great Books -
   10. nicomachus of gerasa (c. 100), Antiquity Literature/Music/Science11. Nielsen, Carl (1865-1931), Modern Music 12. Nietzsche  
   http://www.malaspina.com/site/results_iN_page1.htm

8. Figure 4 For Kappraff's "The 'Arithmetic' Of Nicomachus Of Gerasa And Its Applic
   4. Depressing the string of a monochord at its midpoint and sounding it with a bow yields a tone one octave above the fundamental tone characteristic of the whole string.  
   http://www.emis.de/journals/NNJ/Kappraff-fig04.html

9. The Arithmetic Of Nichomachus Of Gerasa By Jay Kappraff For The Nexus Network Jo
   INTRODUCTION nicomachus of gerasa (Figure 1, at left) has gained a position ofimportance in the history of ancient mathematics due in great measure to his  
   http://www.nexusjournal.com/Kappraff.html
   
   Extractions: Abstract. Mathematician Jay Kappraff discusses a pair of tables of integers found in the Nicomachus's Introduction to Arithmetic and shows how they lead to a general theory of proportion. He shows how the system of musical proportions developed by the neo-Platonic Renaissance architects Leon Battista Alberti and Andrea Palladio, the Roman system of proportions described by Theon of Smyrna, and the Modulor of Le Corbusier are derived naturally from the Nicomachus tables. The Arithmetic of Nicomachus of Gerasa N icomachus of Gerasa (Figure 1, at left) has gained a position of importance in the history of ancient mathematics due in great measure to his Introduction to Arithmetic [1]. This book is one of the only surviving documentations of Greek number theory. Little is known about the life of Nicomachus, and the period of his life can only be estimated to lie between the middle of the first century and the middle of the second century AD, making him contemporary with Theon of Smyrna and Ptolemy. I will discuss a pair of tables of integers found in the

10. Figure 8 For Kappraff's "The 'Arithmetic' Of Nicomachus Of Gerasa And
    8. A design by Mark Bak which contains S, SR, and RR at three different scales. back to text top of page  
    http://www.hms.gr/EMIS/journals/NNJ/Kappraff-fig08.html

11. Figure 5 For Kappraff's "The 'Arithmetic' Of Nicomachus Of Gerasa And Its Applic
    Click here to go to the NNJ homepage. Figures for Jay Kappraff's The Arithmeticof nicomachus of gerasa and its Applications to Systems of Proportion.  
    http://www.nexusjournal.com/Kappraff-fig05.html
    
    Extractions: and its Applications to Systems of Proportion ... Fig. 10 2, the sacred cut. Four sacred cuts mark the vertices of a regular octagon and lead to a subdivision of the square into three species of rectangles: a square of proportion 1:1; a square root rectangle of proportion 1: 2; and a rectangle of proportion 1: q, top of page back to text Top of Page

12. Figure 6 For Kappraff's "The 'Arithmetic' Of Nicomachus Of Gerasa And
    6. The algebraic properties of the Roman system can be made palpable by considering the equivalent geometric properties based on the interrelation of the proportions 1, Ö2, and q.  
    http://www.hms.gr/EMIS/journals/NNJ/Kappraff-fig06.html

13. Figure 10 For Kappraff's "The 'Arithmetic' Of Nicomachus Of Gerasa And Its Appli
    10. The exterior of Le Corbusier's Unité d'Habitation with its windows exhibiting the Modulor tiling. top of page back to text  
    http://ftp.univie.ac.at/EMIS/journals/NNJ/Kappraff-fig10.html

14. Malaspina.com - Nicomachus Of Gerasa (fl. Ca. 100 AD)
    Launch Previous Entry in New Window Malaspina Literature Database Launch NextEntry in New Window nicomachus of gerasa (fl.c. 100 AD) MacTutor.  
    http://www.mala.bc.ca/~mcneil/nico1.htm

15. Figure 5 For Kappraff's "The 'Arithmetic' Of Nicomachus Of Gerasa And Its Applic
    5. The geometrical construction referred to by Tons Brunés, a Danish engineer and student of ancient geometry, as the Sacred Cut.  
    http://ftp.univie.ac.at/EMIS/journals/NNJ/Kappraff-fig05.html
    
    Extractions: and its Applications to Systems of Proportion ... Fig. 10 2, the sacred cut. Four sacred cuts mark the vertices of a regular octagon and lead to a subdivision of the square into three species of rectangles: a square of proportion 1:1; a square root rectangle of proportion 1: 2; and a rectangle of proportion 1: q, top of page back to text Top of Page

16. Phorum - Nicomachus Of Gerasa
    nicomachus of gerasa Open Source Digital Rights Management (DRM) WRITERSWORD.COMPERSONALS.JOLLYROGER.COMMEET FELLOW BOOK LOVERS FRIENDS GREAT BOOKS  
    http://jollyroger.com/classics/cforum/list.php?f=181

17. Figure 9 For Kappraff's "The 'Arithmetic' Of Nicomachus Of Gerasa And Its Applic
    9. A square tiled in three ways with the same species of rectangles whose lengths and widths are numbers from the Red and Blue sequence. top of page back to text  
    http://webdoc.sub.gwdg.de/EMIS/journals/NNJ/Kappraff-fig09.html

18. Phorum - Nicomachus Of Gerasa
    nicomachus of gerasa WRITERSWORD.COMPERSONALS.JOLLYROGER.COM MEET FELLOW BOOKLOVERS FRIENDS GREAT BOOKS DISCUSS THE TRAGEDY OF DRAKERAFT.COM Free  
    http://jollyroger.com/classics/cforum/search.php?f=181

19. Nicomachus Of Gerasa - Britannica.com
    ENCYCLOPÆDIA BRITANNICA. nicomachus of gerasa fl. AD 100,, Gerasa,Roman Syria now Jarash, Jordan. NeoPythagorean philosopher  
    http://piano.dsi.uminho.pt/disciplinas/PAED/temas/nicomach/Nicomachus Of Gerasa
    
    Extractions: fl. AD 100,, Gerasa, Roman Syria [now Jarash, Jordan] Neo-Pythagorean philosopher and mathematician who wrote Arithm e tik e eisag o g e Introduction to Arithmetic ), an influential treatise on number theory. Considered a standard authority for 1,000 years, the book sets out the elementary theory and properties of numbers and contains the earliest-known Greek multiplication table. In his Arithm e tik e Nicomachus, unlike Euclid, gave no abstract proofs of his theorems. Instead he merely enunciated the theorems and illustrated them with specific numerical examples. A Latin translation of the Arithm e tik e by Apuleius of Madaurus ( c. AD 125) is lost, but Boethius' version survived and was used as a schoolbook up to the Renaissance. Nicomachus' Encheiridion Harmonik e s ("Handbook of Harmony") is on the Pythagorean theory of music. He also wrote

20. Index Of /disciplinas/PAED/temas/nicomach/Nicomachus Of Gerasa - Britannica_com_
    ParentIndex of /disciplinas/PAED/temas/nicomach/nicomachus of gerasa Britannica_com_files.Name Last modified Size  
    http://piano.dsi.uminho.pt/disciplinas/PAED/temas/nicomach/Nicomachus Of Gerasa
    
    Extractions: Name Last modified Size Description ... Parent Directory 29-Oct-2001 18:12 0k 22-Nov-2001 01:37 12k article;pv=article;sz.. 22-Nov-2001 01:37 1k bl_corner.gif 22-Nov-2001 01:37 1k br_corner.gif 22-Nov-2001 01:37 1k britannica.css 22-Nov-2001 01:37 4k dot.gif 22-Nov-2001 01:37 1k gline.gif 22-Nov-2001 01:37 1k hdr_logo_chnl.gif 22-Nov-2001 01:37 2k onlineopinion.js 22-Nov-2001 01:37 9k red.gif 22-Nov-2001 01:37 1k standard.js 22-Nov-2001 01:37 8k tr_corner.gif 22-Nov-2001 01:37 1k ub2asdark.gif 22-Nov-2001 01:37 1k ub2homedark.gif 22-Nov-2001 01:37 1k ub2mwdark.gif 22-Nov-2001 01:37 1k ub2storedark.gif 22-Nov-2001 01:37 1k

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