Cubes In Babylonia The consecutive terms 18272 and 49920 give AN=571/780, and so 3 = 1351/780.According to neugebauer (neugebauer,otto. Mathematical Cuneiform Texts. http://hem.passagen.se/ceem/babyloni.htm
Extractions: In ancient (about 2000 BC) Babylonia, algebraic problems leading to equations of higher degree are found. The Babylonians calculated cubic roots from tables, it is however not completely clear which method they used for calculating the values. It is anyhow known that they used a method of root extraction involving only integer additions. To find a rational approximation for the square root of an integer A, let N be the largest integer such that N is less than A. Then construct a sequence of integers using the recurrence formula s [j] = 2N s [j-1] + (A-N ) s [j-2] The value of ( A-N ) (s [i] /s [i+1] approaches A- N as j goes to infinity. As an example, to find we have A=3 and N=1 , so the recurrence formula is simply s [j] [i-1] [i-2] . If the initial values are chosen to be s[0]=0 and s[1]=1 , the subsequent values in the sequence are The consecutive terms and give A-N=571/780 , and so According to Neugebauer (Neugebauer,Otto. Mathematical Cuneiform Texts. New Haven, American Oriental Society, 1953), there is strong evidence that they, In order to compute cubic roots used a method of iterations, of the same kind as they used for computing square roots. They had tables of square roots, squares and cubes. They also had tables over
Biography-center - Letter N Mathematicians/Neuberg.html; neugebauer, otto wwwhistory.mcs.st-and.ac.uk/~history/Mathematicians/neugebauer.html;Neuman, Herman http://www.biography-center.com/n.html
Extractions: random biography ! Any language Arabic Bulgarian Catalan Chinese (Simplified) Chinese (Traditional) Croatian Czech Danish Dutch English Estonian Finnish French German Greek Hebrew Hungarian Icelandic Indonesian Italian Japanese Korean Latvian Lithuanian Norwegian Polish Portuguese Romanian Russian Serbian Slovak Slovenian Spanish Swedish Turkish 192 biographies Nabokov, Vladimir
History Of Mathematics: Babylonia neugebauer, otto. The Exact Sciences in Antiquity. Reprint Dover, New York,1969. neugebauer, otto, and AJ Sachs, eds. Mathematical cuneform texts. http://aleph0.clarku.edu/~djoyce/mathhist/babylonia.html
Extractions: They wrote on clay: the Babylonian tablets speak today. Univ. of Chicago Pr., Chicago, 1938. Hoyrup, Jens. Babylonian algebra from the view-point of geometrical heuristics: investigation of terminology, methods, and patterns of thought. Roskilde University Centre, Roskilde, Denmark, 1984. Neugebauer, Otto. The Exact Sciences in Antiquity. Princeton University Press, Princeton, 1951. Reviewed: Isis 43 (1952), 67-73. Reprint: Brown University Press, Providence, 1957. Second edition: Harper and Row, New York, 1962. Reprint: Dover, New York, 1969. Neugebauer, Otto, and A. J. Sachs, eds. Mathematical cuneform texts. American Oriental Series, vol. 29. American Oriental Society, New Haven, 1946. Institute for Advanced Study, Princeton, 1955. Reprint: Sources in the History of Mathematics and the Physical Sciences 5, Springer-Verlag, New York-Berlin, 1983. Reviewed: MR 84c:01005. Thanks to the Xerox Map server for the map.
Bibliography - General - History Of Scienc to date, Cambridge, 1954 . neugebauer, otto. The ExactSciences inAntiquity, Providence,RI, 1957. neugebauer, otto. The ExactSciences inAntiquity, 2nd. http://web.clas.ufl.edu/users/rhatch/pages/03-Sci-Rev/SCI-REV-Teaching/HIS-SCI-S
Extractions: S E L E C T B I B L I O G R A P H Y General Reference Edwards, Paul, Editor-in-Chief. The Encyclopedia of Philosophy , 8 vols., New York and London: Macmillan and The Free Press, 1967. Authoritative articles on major concepts in philosophy, arranged alphabetically. Gillispie, Charles Coulston, Editor-in-Chief. The Dictionary of Scientific Biography Whitrow, Martha, ed. The Isis Cumulative Bibliography , 1913-65, 3 vols., London: Mansell, 1971-76. The Isis Cumulative Bibliography , 1966-1975, 1 vol., London: Mansell, 1980, and others to follow. Comprehensive listing of scholarly books and articles in the history of science; arranged by person, institution, and subject. The best single starting place. Wiener, Phillip, ed. The Dictionary of the History of Ideas , 4 vols. and index, New York: Charles Scribner, 1973-74. Excellent accounts of major ideas in the Western tradition.
Percy Ernst Schramm Art. Sources of Information in the Humanities, no. 2. Chicago AmericanLibrary Association, 1982, p. 73; neugebauer, otto. Sense http://www.lib.duke.edu/lilly/artlibry/dah/schrammp.htm
Extractions: HName: Schramm, Percy Ernst DateBorn: 1894 Placeborn: Hamburg, Germany Datedied: 1970 Placedied: Göttingen, Germany HDescrip: Historian and portraiture scholar of the German medieval era. Schramm's father had once been the mayor of Hamburg. The younger Schramm obtained his doctorate from the University of Heidelberg in 1922. He focused on a career in teaching history. His Contemporary Portraits of Charlemagne ) appeared in 1928. In 1932 he was awarded the Benjamin D. Shreve Fellowship at Princeton University for his study of Germany, the first foreign scholar to earn the award. Back in Germany, Schramm joined the army in Nazi Germany, eventually attaining the rank of major in the German high command. He was assigned the personal diarist to Adolf Hitler. After the war, Schramm used this experience to write several books on Hitler's Germany. He never abandoned medieval history, however, and in 1962 began publishing with Florentine Mütherich (q.v.) an inventory of royal portraits of kings and queens of Germany. Schramm was also and authority on regalia and insignia, his Herrschaftszeichen und Staatssymbolik began appearing the following year.
Walther Wolf Schramm (qv). HCountry Germany. HBiography Who s Who in the World,2nd ed. 197475, pp. 1071; neugebauer, otto. Sense or Nonsense http://www.lib.duke.edu/lilly/artlibry/dah/wolfw.htm
Extractions: HName: Wolf, Walther DateBorn: 1900 Placeborn: Hildesheim, Germany Datedied: 1973 Placedied: ? HDescrip: Wolf was the son of Peter and Mathilde Stinde (Wolf). After spending the final year of World War I with the German Marines, he attended the University of Heidelberg between 1919-22. Wolf spent the year 1923 at the University in Berlin before completing his dissertation at Göttingen. He was an assistant at the Berliner Museum 1922-28. In 1928 he became a privatdozent associated with the University in Leipzig, acceding to a professorship there in 1934. He also held a joint appointment as director of Egyptology Institute. During World War II, he joined the Luftwaffe 1939-45. After the war he spent a period of time outside academics, like many faculty associated with Nazi government appointments. In 1949 he received a position to teach at the university of Munster. He remained the the next twenty years, retiring emeritus in 1969. Wolf was devoted to stylistic analysis in his art history. His use of scientific language for art was attacked in 1960 by Otto Neugebauer (1899-1990) as meaningless appropriation of scientific jargon, with whom Neugebauer also lumped Percy Schramm (q.v.). HCountry: Germany HBiography: Who's Who in the World , 2nd ed. 1974-75, pp. 1071; Neugebauer, Otto. "Sense or Nonsense in Scientific Jargon."
Chronological Literature 1, chronology general, neugebauer, otto, Chronological Concepts, HAMA,p 10611075, Springer-Verlag, Berlin-Heidelberg-New York, 1975, 1, chronology http://ourworld.compuserve.com/homepages/cplawassist/paper/99999body.html
Extractions: chronology general Adler W. Time Immorial "Washingtron, D.C." no UBVU chronology general Alsted Thesaurus chronologiae Herbor chronology general AICAC Astroem P.J.(ed.) High:Middle or Low? Acts of an International Colloquium on Absolute Chronology held at the University of Gothenburg 20th-22nd August 1987. part 1 and part 2 (Studies in Mediterranean Archaeology and Literature) SMAL Paul Astroem Foerlag Gothenburg ISBN 91-86098-64=-0/65-9 chronology general Bernays J. Joseph Justus Scaliger Berlin chronology general Beroaldus M. Chronicum scripturae sacrae autoritatae constitutum Geneva chronology general Bodin Jean Methodus ad facilem historiarum cognitionem in OPh Paris no UBVU chronology general Bodin Jean Method for the Easy Comprehension of History-Reynolds Beatrice New York no UBVU chronology general Boeckh no UBVU chronology general Calvisius Sethus Opus chronologicum Frankfurt a.M.
Research Sources For Astrology neugebauer, otto, Astronomy and History. Selected Essays (NY SpringerVerlag, 1983) {An excellent collection of neugebauer s essays. http://www.smoe.org/arcana/astrol4.html
Extractions: prev contents ... next Astrology began in Mesopotamia. The horoscope was a late invention, but it was derived from much older practices, notably looking into the sky for omens, i.e., messages from the gods, and using astronomy to create a lunisolar calendar. Mesopotamian astrology was based upon observation, without the scientific theory which Greek astrologers used.
Brown University otto neugebauer. For over thirty years, Brown s History of Mathematicsdepartment, the only one in the world, was virtually synonymous http://www.brown.edu/webmaster/about/history/neugebauer.shtml
Extractions: Brown University Providence RI 02912 Feedback Brown home Get to know Brown firsthand by visiting any time of year. Tours led by undergraduates are offered regularly. Schedules are available on the College Admission Web site Another way to get a feel for Brown is to browse through our online viewbook or Voices, Faces, Brown , an online showcase of undergraduates. The Brown campus is situated in a historic residential neighborhood overlooking downtown Providence, a prime example of urban renaissance in the Northeast. Cultural opportunities abound, not only in Providence but also throughout the state. A variety of scenic and historic sites are just minutes away by car; Boston, New York City, the Cape and mountains of New England are easily reached as well. back to the top Directions to Brown By car (Note: Construction projects in the city may require adjustments to the routes below.) From the east: Follow I-195 West, exit at South Main Street (exit 2), and proceed to the traffic light at College Street (large courthouse at corner), where you will turn right. When College Street ends at Prospect Street, you will be facing the Brown campus. From the west, north and south:
History Of Constellation And Star Names neugebauer, otto. and Parker, Richard. (19601969). neugebauer, otto. (1955). The Egyptian Decans. (Vistas in Astronomy, Volume 1, Pages 47-51). http://members.optusnet.com.au/~gtosiris/page4.html
Extractions: An Annotated Bibliography Of Studies of Occidental Constellations and Star Names to the Classical Period Compiled by Gary D. Thompson Go to: Egyptian Jewish Persian Arabic ... Return To Site Contents Page Egyptian Books/Pamphlets: Antoniadi. Eugène. (1934). L'Astronomie Egyptienne. [Note: Based on (late) Greek texts and somewhat unreliable, especially regarding the identification of Egyptian constellations. An English-language translation by (Sir) Patrick Moore remains unpublished. See the Correspondence in The Observatory "Egyptian Astronomy" comprising a letter by Eugène Antoniadi (Volume 63, 1940, Pages 13-14), and a reply by Herbert Chatley (Volume 63, 1940, Pages 14-15). See the (English-language) biographical entry by Giorgio Abetti in Dictionary of Scientific Biography, edited by Charles Gillispie, Volume 1, Page 17; and the "Historical Note" by Reginald Marriott in Journal of the British Astronomical Association, Volume 101, Number 3, June, 1991, Page 195. Life dates: 1870-1944.] Brugsch, Heinrich. (1978). Astronomical and Astrological Inscriptions on Ancient Egyptian Monuments. [Note: The book is a translation by George Chamberlain of "Thesaurus Inscriptionum Aegyptiacarum," (Volume 1, 1883), by Heinrich Brugsch. The translation was originally published as a series of 18 articles (from April 1978 through January 1980) in the monthly journal the Griffith Observer (published by the Griffith Observatory). As the title indicates the book does not deal with issues of astronomical alignments in monumental architecture. Volume 2 of "Thesaurus Inscriptionum Aegyptiacarum" dealt with calendars (and has never been translated into English).]
History Of Constellation And Star Names neugebauer, otto. (1975). Bibliographical Abbreviations. In A Historyof Ancient Mathematical Astronomy. Part Three. (Pages 11651203). http://members.optusnet.com.au/~gtosiris/page6.html
Extractions: An Annotated Bibliography Of Studies of Occidental Constellations and Star Names to the Classical Period Compiled by Gary D. Thompson Go to: Star Maps References With Extensive Bibliographies Return To Site Contents Page Star Maps Books/Pamphlets: Grasshoff, Gerd. (1990). The History of Ptolemy's Star Catalogue. [Note: Based on the author's doctoral thesis. See the (English-language) book review by James Evans in Journal for History of Exact Sciences, Volume 43, Pages 133-144.] Knoel, E[?]. (1877). "The Chronology of Star Catalogues." (Memoirs of the Royal Astronomical Society, Volume 43, Pages 1-74). [Note: Comprehensive.] Stott, Carole. (1991). Celestial Charts: Antique Maps of the Heavens. [Note: Well illustrated but poorly organised. See the (English-language) book review by Elly Dekker in Annals of Science, Volume 49, Number 6, 1992, Pages 598-599.] Warner, Deborah. (1979). The Sky Explored: Celestial Cartography 1500-1800. [Note: Excellent.] Whitfield, Peter. (1995). The Mapping of the Heavens. [Note: At times uncritical and unreliable.] Articles/Entries: Berggren, J[?]. [Len]. (1991/1992). "Ptolemy's Maps of Earth and the Heavens: A New Interpretation." (Archive for History of Exact Sciences, Volume 43, Pages 133-144).
UFG-Wien: Urban Translate this page Vater otto Josef Urban, staatlich geprüfter Privatdetektiv Mutter GertrudeUrban Oppidazeit, in JW neugebauer, Die Kelten im Osten Österreichs, Wiss. http://www.univie.ac.at/urgeschichte/pers/urban.html
Alibris - Click Here To Find Books By This Author! Translate this page Bonnie ~ neugebauer, Charise ~ neugebauer, Fritz ~ neugebauer, Janet M. ~ neugebauer,Michael ~ neugebauer, O. ~ neugebauer, otto ~ neugebauer, Wolfgang http://www.alibris.com/authors/authors0298.html
The Opinion Of A Man Named Harris: Otto Neugebauer Says April 20, 2004. otto neugebauer Says. The common belief that we gain historical perspective with increasing distance seems to me http://www.misterchristopher.com/opinion/archives/000043.html
Extractions: Main "The common belief that we gain 'historical perspective' with increasing distance seems to me to utterly misrepresent the actual situation. What we gain is merely confidence in generalization that we would never dare to make if we had access to the real wealth of contemporary evidence." Cynical, but it sounds about right. Maybe history is like Dr. Christoe's infinite plane of charge. The E field is constant, regardless of the distance from the field. When an event occurs, there's a lot of coverage and a lot of confusion. After the dust settles, everyone settles on a single account of the event, which is less comprehensive (and possibly a "generalization") but usually better than having all of different accounts. Anyway, interesting quote. I hadn't heard it before. TrackBack
Neue Seite 1 Translate this page 21.08.03, D + M, Skotton Eugen / Grammel Peter, 6, 6, neugebauer Helmut / WolfLeo, 2, 3, 28. 08. 03, A + S, Steinecker otto, 6, 6, neugebauer Helmut, 4, 2,06. 09. http://www.sportanlage.jku.at/neue_seite_11.htm
Extractions: Ranglistenspiele 2003 Datum Klasse Spieler 1. Satz 2. Satz 3. Satz A + S Steinecker Otto Wolf Leo A + S Neugebauer Helmut Wolf Leo A Berger Roman Rakuscek Andreas A Sarlay Harald Rakuscek Andreas D + M Lichtenberger Anna / Lichtenberger Franz Burgstaller Monika / Burgstaller Peppo D Wolf Leo / Masarie Rene Berger Roman / Rakuscek Andreas A + S Grammel Peter Steinecker Otto D + M Neugebauer Helmut / Wolf Leo Burgstaller Monika / Burgstaller Peppo A + S Neugebauer Helmut Lichtenberger Franz A + S Steinecker Otto Neugebauer Helmut D + M Neugebauer Helmut / Wolf Leo Lichtenberger Anna / Lichtenberger Franz D + M Sarlay Harald / Jaksch Christoph Berger Roman / Rakuscek Andreas D + M Sarlay Harald / Jaksch Christoph Neugebauer Helmut / Wolf Leo D + M Rakuscek Andreas / Rakuscek Michael Sarlay Jürgen / Sarlay Harald D + M Haberfellner Waltraud / Skotton Eugen Lichtenberger Anna / Lichtenberger Franz A + S Grammel Peter Neugebauer Helmut D M Lichtenberger Franz / Jaksch Christoph Neugebauer Helmut / Wolf Leo A + S Grammel Peter Jaksch Christoph D + M Skotton Eugen / Grammel Peter Sarlay Harald / Jaksch Christoph D + M Masarie Rene / Skotton Eugen Lichtenberger Anna / Lichtenberger Franz D + M Sarlay Harald / Jaksch Christoph Haberfellner Waltraud / Skotton Eugen A + S Steinecker Otto Jaksch Christoph w.o.
À§´ëÇѼöÇÐÀÚ ¸ñ·Ï Jean Baptiste Neuberg Born 30 Oct 1840 in Luxembourg Died 22 March 1926 in Liège,Belgium neugebauer, otto neugebauer Born 26 May 1899 in Austria Died 19 http://www.mathnet.or.kr/API/?MIval=people_seek_great&init=N
KÖNYVTÁRI ÁLLOMÁNY - 510 510 N 70 neugebauer, otto Egzakt tudományok az ókorban / otto neugebauer. Bp. Gondolat, 1984. - 260 p., 16 t. ill. ; 23 http://www.kia.hu/konyvtar/egyeb/k510.htm
Otto otto Robert Frisch (19041979) Austrian physicist. otto neugebauer (?-1990)Austrian-American astronomer and mathematical historian. http://www.geocities.com/edgarbook/names/o/otto.html
Biografisk Register Translate this page 76) Möbius, August Ferdinand (1790-1868) Napier, John (1550-1617) Needham, Joseph(1900-95) Neper, John (se Napier) neugebauer, otto (1899-1990) Neumann, John http://www.geocities.com/CapeCanaveral/Hangar/3736/biografi.htm
