21. Conic Sections In Ancient Greece We next come to the (again, lost) works of Aristaeus `the elder and of thecelebrated 350 BC Menaechmus; 310 BC aristaeus the elder; 300 BC Euclid http://www.math.rutgers.edu/~cherlin/History/Papers1999/schmarge.html

Conic Sections in Ancient Greece Ken Schmarge History of Mathematics Term Paper, Spring 1999 Introduction The knowledge of conic sections can be traced back to Ancient Greece. Menaechmus is credited with the discovery of conic sections around the years 360-350 B.C.; it is reported that he used them in his two solutions to the problem of "doubling the cube". Following the work of Menaechmus, these curves were investigated by Aristaeus and of Euclid. The next major contribution to the growth of conic section theory was made by the great Archimedes. Though he obtained many theorems concerning the conics, it does not appear that he published any work devoted solely to them. Apollonius, on the other hand, is known as the "Great Geometer" on the basis of his text Conic Sections , an eight-"book" (or in modern terms, "chapter") series on the subject. The first four books have come down to us in the original Ancient Greek, but books V-VII are known only from an Arabic translation, while the eighth book has been lost entirely. In the years following Apollonius the Greek geometric tradition started to decline, though there were developments in astronomy, trigonometry, and algebra (Eves, 1990, p. 182). Pappus, who lived about 300 A.D., furthered the study of conic sections somewhat in minor ways. After Pappus, however, conic sections were nearly forgotten for 12 centuries. It was not until the sixteenth century, in part as a consequence of the invention of printing and the resulting dissemination of Apollonius' work, that any significant progress in the theory or applications of conic sections occurred; but when it did occur, in the work of Kepler, it was as part of one of the major advances in the history of science.

22. Full Alphabetical Index Translate this page aristaeus the elder (588) Aristarchus of Samos (1548) Aristotle (3445*) Arnauld,Antoine (179*) Aronhold, Siegfried (234*) Artin, Emil (475*) http://www.maththinking.com/boat/mathematicians.html

Full Alphabetical Index Click below to go to one of the separate alphabetical indexes A B C D ... XYZ The number of words in the biography is given in brackets. A * indicates that there is a portrait. A Abbe , Ernst (602*) Abel , Niels Henrik (2899*) Abraham bar Hiyya (641) Abraham, Max Abu Kamil Shuja (1012) Abu Jafar Abu'l-Wafa al-Buzjani (1115) Ackermann , Wilhelm (205) Adams, John Couch Adams, J Frank Adelard of Bath (1008) Adler , August (114) Adrain , Robert (79*) Adrianus , Romanus (419) Aepinus , Franz (124) Agnesi , Maria (2018*) Ahlfors , Lars (725*) Ahmed ibn Yusuf (660) Ahmes Aida Yasuaki (696) Aiken , Howard (665*) Airy , George (313*) Aitken , Alec (825*) Ajima , Naonobu (144) Akhiezer , Naum Il'ich (248*) al-Baghdadi , Abu (947) al-Banna , al-Marrakushi (861) al-Battani , Abu Allah (1333*) al-Biruni , Abu Arrayhan (3002*) al-Farisi , Kamal (1102) al-Haitam , Abu Ali (2490*) al-Hasib Abu Kamil (1012) al-Haytham , Abu Ali (2490*) al-Jawhari , al-Abbas (627) al-Jayyani , Abu (892) al-Karaji , Abu (1789) al-Karkhi al-Kashi , Ghiyath (1725*) al-Khazin , Abu (1148) al-Khalili , Shams (677) al-Khayyami , Omar (2140*) al-Khwarizmi , Abu (2847*) al-Khujandi , Abu (713) al-Kindi , Abu (1151) al-Kuhi , Abu (1146) al-Maghribi , Muhyi (602) al-Mahani , Abu (507) al-Marrakushi , ibn al-Banna (861) al-Nasawi , Abu (681) al-Nayrizi , Abu'l (621) al-Qalasadi , Abu'l (1247) al-Quhi , Abu (1146) al-Samarqandi , Shams (202) al-Samawal , Ibn (1569) al-Sijzi , Abu (708) al-Tusi , Nasir (1912) al-Tusi , Sharaf (1138) al-Umawi , Abu (1014) al-Uqlidisi , Abu'l (1028) Albanese , Giacomo (282) Albategnius (al-Battani) (1333*)

23. A Index 87) Arbuthnot, John (251*) Archimedes of Syracuse (467*) Archytas of Tarentum (103)Arf, Cahit (1452*) Argand, Jean (81) aristaeus the elder (44) Aristarchus http://intranet.woodvillehs.sa.edu.au/pages/resources/maths/History/Progr.htm

24. User:Gerritholl/mathematicians - Wikipedia, The Free Encyclopedia Tarentum Cahit Arf - Jean Argand - Eizens Arins - aristaeus the elder -Aristarchus of Samos - Aristotle - Antoine Arnauld - Siegfried Aronhold - Emil http://en.wikipedia.org/wiki/User:Gerritholl/mathematicians

Wikimedia needs your help in its 21-day fund drive. See our fundraising page Over US$ 125,000 has been donated since the drive began on 19 August. Thank you for your generosity! User:Gerritholl/mathematicians From Wikipedia, the free encyclopedia. User:Gerritholl edit Mathematicians Ernst Abbe Niels Henrik Abel Abraham bar Hiyya Max Abraham ... Antoni Zygmund Retrieved from " http://en.wikipedia.org/wiki/User:Gerritholl/mathematicians Views User page Discussion Edit this page History Personal tools Create account / log in Navigation Main Page Community portal Current events Recent changes ... Donations Search Toolbox What links here Related changes Upload file Special pages ... Permanent link This page was last modified 01:33, 19 August 2005. All text is available under the terms of the GNU Free Documentation License (see for details). About Wikipedia

25. A Index Archimedes of Syracuse (3190*) Archytas of Tarentum (1366*) Arf, Cahit (1452*),Argand, Jean (951) Arins, Eizens (784*) aristaeus the elder (588) Aristarchus of http://www.gap-system.org/~history/Indexes/A.html

Names beginning with A The number of words in the biography is given in brackets. A * indicates that there is a portrait. Abbe , Ernst (602*) Abbott , Edwin (1456) Abel , Niels Henrik (2899*) Abraham bar Hiyya Abraham, Max Abu Kamil Shuja (1012) Abu Jafar Abu'l-Wafa al-Buzjani (1115) Ackermann , Wilhelm (205*) Adams, John Couch Adams, J Frank Adelard of Bath (1008) Adleman , Leonard (3314*) Adler , August (114) Adrain , Robert (1317*) Adrianus , Romanus (419) Aepinus , Franz (822*) Agnesi , Maria (2018*) Ahlfors , Lars (725*) Ahmed ibn Yusuf (660) Ahmes Aida Yasuaki (696) Aiken , Howard (665*) Airy , George (2362*) Aitken , Alec (1220*) Ajima , Naonobu (144) Akhiezer , Naum Il'ich (248*) al-Baghdadi , Abu (947) al-Banna , al-Marrakushi (861) al-Battani , Abu Allah (1333*) al-Biruni , Abu Arrayhan (3002*) al-Farisi , Kamal (1102) al-Haitam , Abu Ali (2490*) al-Hasib Abu Kamil (1012) al-Haytham , Abu Ali (2490*) al-Jawhari , al-Abbas (627) al-Jayyani , Abu (892) al-Karaji , Abu (1789) al-Karkhi al-Kashi , Ghiyath (1725*) al-Khazin , Abu (1148) al-Khalili , Shams (677) al-Khayyami , Omar (2140*) al-Khwarizmi , Abu (2847*) al-Khujandi , Abu (713) al-Kindi , Abu (1151) al-Kuhi , Abu (1146) al-Maghribi , Muhyi (602) al-Mahani , Abu (507) al-Marrakushi , ibn al-Banna (861) al-Nasawi , Abu (681) al-Nayrizi , Abu'l (621) al-Qalasadi , Abu'l (1247) al-Quhi , Abu (1146) al-Samarqandi , Shams (202) al-Samawal , Ibn (1569) al-Sijzi , Abu (708) al-Tusi, Nasir

26. Search Results For Dispute* Aristaeus Heath s opinion that the Aristaeus referred to by Hypsicles this isaristaeus the elder has been disputed by some historians, and there is a http://www.gap-system.org/~history/Search/historysearch.cgi?SUGGESTION=dispute*&

27. À§´ëÇѼöÇÐÀÚ ¸ñ·Ï Aristaeus, aristaeus the elder Born about360 BC in Greece Died about 300 BC; Aristarchus, Aristarchus of Samos http://www.mathnet.or.kr/API/?MIval=people_seek_great&init=A

28. History Of Mathematics Text It is written by three men Eculid the Elementarist, Apollonius of Perga, andaristaeus the elder, and its approach is by analysis and synthesis . http://www.brown.edu/Facilities/University_Library/exhibits/math/textfr.html

Euclid Brown University Library possess a copy of each sixteenth-century translation of Euclid's Elements of Geometry into a modern language. These vernacular editions, grouped around the first Latin edition of 1482, are displayed in chronological sequence, from 1533 (Greek) to 1594 (Arabic). All copies are opened at Book I, proposition 47, "Pythagoras' Theorem," which asserts: "In right-angled triangles the square of the side opposite the right angle is equal to the sum of the squares of the sides containing the right angle." Most of the translations provide proof of this equation (a + b = c using a geometrical construction known as "the bride's chair." Other first translations into modern European languages were published in the seventeenth and eighteenth centuries: Dutch (1602), Russian (1739), Swedish (1744), and Danish (1745). Latin Editions Euclid (ca. 326-ca. 265 BC) Preclarissimus liber elementorum Euclidis perspicacissimi: in artem geometrie incipit ... Venice: Erhard Ratdolt, [25 May] 1482. Euclid's Elements of Geometry has been a primary mathematics text for more than two thousand years. It is a compilation of early Greek mathematical knowledge, synthesized and systematically presented by Euclid in ca. 300 BC. Books I-IV are devoted to plane geometry, Book V deals with the theory of proportions, and Book VI with the similarity of plane figures. Books VII-IX are on number theory, Book X on commensurability and incommensurability, Books XI-XII explore three dimensional geometric objects, and Book XIII deals with the construction of the five regular solids. Later non-Euclidian additions include, Book XIV, which is thought to have been contrbuted by Hypsciles (ca. 200 BC), and Book XV, which may have been added by John of Damascus, or by a 6th-century pupil of Isadoros of Miletos.

29. Full Alphabetical Index Translate this page aristaeus the elder (588) Aristarchus of Samos (1548) Aristotle (3445*) Arnauld,Antoine (179) Aronhold, Siegfried (234*) Artin, Emil (475*) http://alas.matf.bg.ac.yu/~mm97106/math/alphalist.htm

Full Alphabetical Index The number of words in the biography is given in brackets. A * indicates that there is a portrait. A Abbe , Ernst (602*) Abel , Niels Henrik (2899*) Abraham bar Hiyya (641) Abraham, Max Abu Kamil Shuja (1012) Abu Jafar Abu'l-Wafa al-Buzjani (1115) Ackermann , Wilhelm (205) Adams, John Couch Adams, J Frank Adelard of Bath (1008) Adler , August (114) Adrain , Robert (79*) Adrianus , Romanus (419) Aepinus , Franz (124) Agnesi , Maria (2018*) Ahlfors , Lars (725*) Ahmed ibn Yusuf (660) Ahmes Aida Yasuaki (696) Aiken , Howard (665*) Airy , George (313*) Aitken , Alec (825*) Ajima , Naonobu (144) Akhiezer , Naum Il'ich (248*) al-Baghdadi , Abu (947) al-Banna , al-Marrakushi (861) al-Battani , Abu Allah (1333*) al-Biruni , Abu Arrayhan (3002*) al-Farisi , Kamal (1102) al-Haitam , Abu Ali (2490*) al-Hasib Abu Kamil (1012) al-Haytham , Abu Ali (2490*) al-Jawhari , al-Abbas (627) al-Jayyani , Abu (892) al-Karaji , Abu (1789) al-Karkhi al-Kashi , Ghiyath (1725*) al-Khazin , Abu (1148) al-Khalili , Shams (677) al-Khayyami , Omar (2140*) al-Khwarizmi , Abu (2847*) al-Khujandi , Abu (713) al-Kindi , Abu (1151) al-Kuhi , Abu (1146) al-Maghribi , Muhyi (602) al-Mahani , Abu (507) al-Marrakushi , ibn al-Banna (12)

30. History Of Mathematics: Chronology Of Mathematicians 339); Aristotle (384322) *SB *MT; aristaeus the elder (fl. c. 350-330) *SB *mt;Eudemus of Rhodes (the Peripatetic) (fl. c. 335) *SB http://homepages.feis.herts.ac.uk/~comqcln/chronology_math.html

Chronological List of Mathematicians Note: there are also a chronological lists of mathematical works and mathematics for Arabic sphere Europe Greece India , and Japan Table of Contents 1700 B.C.E. 100 B.C.E. 1 C.E. To return to this table of contents from below, just click on the years that appear in the headers. Footnotes (*mt, *MT, *RB. *SB) are explained below List of Mathematicians 1700 B.C.E. Ahmes (c. 1650 B.C.E.) *mt 700 B.C.E. Baudhayana (c. 700) 600 B.C.E. Thales of Miletus (c. 630-c 550) *MT Apastamba (c. 600) Anaximander of Miletus (c. 610-c. 547) *SB Pythagoras of Samos (c. 570-c. 490) *SB *MT Anaximenes of Miletus (fl. 546) *SB Cleostratus of Tenedos (c. 520) 500 B.C.E. Katyayana (c. 500) Nabu-rimanni (c. 490) Kidinu (c. 480) Anaxagoras of Clazomenae (c. 500-c. 428) *SB *mt Zeno of Elea (c. 490-c. 430) *mt Antiphon of Rhamnos (the Sophist) (c. 480-411) *SB *mt Oenopides of Chios (c. 450?) *SB Leucippus (c. 450) *SB *mt Hippocrates of Chios (fl. c. 440) *SB Meton (c. 430) *SB Hippias of Elis (fl. c. 425) *SB *mt Theodorus of Cyrene (c. 425)

31. Pappus It is the work of three men, Euclid the writer of the Elements , Apollonius ofPerga and aristaeus the elder, and proceeds by the method of analysis and http://202.38.126.65/mirror/www-history.mcs.st-and.ac.uk/history/Mathematicians/

32. Search Results For Dispute* Aristaeus (in a new window) Heath s opinion that the Aristaeus referred to byHypsicles this is aristaeus the elder has been disputed by some historians, and http://202.38.126.65/mirror/www-history.mcs.st-and.ac.uk/history/Search/historys

33. Biography-center - Letter A Arieh, Ben ww w.pixiport.com/bioarieh.htm; aristaeus the elder,www-history.mcs.st-and.ac.uk/~history/Mathematicians/Aristaeus.html; Aristarchus ofSamos, http://www.biography-center.com/a.html

Visit a 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 A 615 biographies A rnoldson, Klas Pontus www.nobel.se/peace/laureates/1908/arnoldson-bio.html Aachen, Hans von www.kfki.hu/~arthp/bio/a/aachen/biograph.html Aachen, Hans von www.getty.edu/art/collections/bio/a3241-1.html Aamodt, Kjetil Andre www.olympic.org/uk/athletes/heroes/bio_uk.asp?PAR_I_ID=74486 Aaron, Henry L. www.hickoksports.com/biograph/aaronhen.shtml Aarons, Ruth Hughes www.hickoksports.com/biograph/aaronsrh.shtml#other Aarskog, Dagfinn www.whonamedit.com/doctor.cf m/351.html Aase, Jon Morton www.whonamedit.com/doctor.cfm/334.html Abadie, J oseph Louis Ir©n©e Jean www.whonamedit.com/doctor.cfm/35.html Abate, Nicol² dell www.getty.edu/art/collections/bio/a672-1.html Abbad ibn Bishr,

34. Short Biographies An aristaeus the elder 350 BC 330 BC Greek He is a contemporary of Euclid and Euclidgives him great credit for a work Solid Loci , the Greek name for conics http://www.grammar.net.nz/dept_html/dept_common/scotch_college/maths/An.htm

35. Kepler's Model Apparently this result is due to aristaeus the elder, ca 320 BCE, in his work,Comparison of the five regular solids. See (Heath, 1960; v.3, p. 438). http://www.visual-kepler.org/model/description/description.html

Description of Kepler's 3D model To Kepler, the six planets (Copernican paradigm) orbited crystalline spheres. The thickness of a sphere was the minimum to contain the elliptical orbit of its planet. The five gaps between these six concentric spheres were spaced by the Platonic solids. Gap #1: Saturn/Jupiter, the cube harmonic ratio = sqrt(3) ~= 1.732 Gap #2: Jupiter/Mars, the tetrahedron harmonic ratio = 3 Gap #3: Mars/Earth, the dodecahedron harmonic ratio ~= 1.258 Gap #4: Earth/Venus, the icosahedron harmonic ratio ~= 1.258 Gap #5: Venus/Mercury, the octahedron harmonic ratio = sqrt(3) ~= 1.732 The cube and the octahedron, having the same harmonic ratio, might be interchanged. Ditto the dodecahedron and icosahedron. However, Kepler argued that the order listed above was the correct order. The sympathy of the cube and octahedron (that is, sharing the same harmonic ratio) is elementary. The sympathy of the dodecahedron and icosahedron is not elementary, but will be familiar to students of Euclid (are there any still alive?) as the second proposition of Hypsicles, author of the work sometimes known as "Euclid Book XIV". Apparently this result is due to Aristaeus the Elder, ca 320 BCE, in his work, Comparison of the five regular solids.

36. Jonathan A. Hill Catalogue Selections - Section 19, Items 950 - 968 $3,250.00 First edition and a lovely copy. Viviani s first project was an attemptedrestoration of a work by aristaeus the elder, De locis solidis secunda http://bookmarque.net/J.Hill/PageGenerator.cfm?CFID=153561&CFTOKEN=30582525&D=Jo

37. A Index Arbuthnot, John (251*) Archimedes of Syracuse (3190*) Archytas of Tarentum (1366*)Arf, Cahit (1452*) Argand, Jean (81) aristaeus the elder (588) Aristarchus http://www.bg-rams.ac.at/intranet/Physik/history/A.html

Names beginning with A The number of words in the biography is given in brackets. A * indicates that there is a portrait. Abbe , Ernst (602*) Abel , Niels Henrik (2899*) Abraham bar Hiyya (641) Abraham, Max Abu Kamil Shuja (1012) Abu Jafar Abu'l-Wafa al-Buzjani (1115) Ackermann , Wilhelm (205) Adams, John Couch Adams, J Frank Adelard of Bath (1008) Adler , August (114) Adrain , Robert (79*) Adrianus , Romanus (419) Aepinus , Franz (124) Agnesi , Maria (2018*) Ahlfors , Lars (725*) Ahmed ibn Yusuf (660) Ahmes Aida Yasuaki (696) Aiken , Howard (665*) Airy , George (313*) Aitken , Alec (825*) Ajima , Naonobu (144) Akhiezer , Naum Il'ich (248*) al-Baghdadi , Abu (947) al-Banna , al-Marrakushi (861) al-Battani , Abu Allah (1333*) al-Biruni , Abu Arrayhan (3002*) al-Farisi , Kamal (1102) al-Haitam , Abu Ali (2490*) al-Hasib Abu Kamil (1012) al-Haytham , Abu Ali (2490*) al-Jawhari , al-Abbas (627) al-Jayyani , Abu (892) al-Karaji , Abu (1789) al-Karkhi al-Kashi , Ghiyath (1725*) al-Khazin , Abu (1148) al-Khalili , Shams (677) al-Khayyami , Omar (2140*) al-Khwarizmi , Abu (2847*) al-Khujandi , Abu (713) al-Kindi , Abu (1151) al-Kuhi , Abu (1146) al-Maghribi , Muhyi (602) al-Mahani , Abu (507) al-Marrakushi , ibn al-Banna (12) al-Nasawi , Abu (681) al-Nayrizi , Abu'l (621) al-Qalasadi , Abu'l (1247) al-Quhi , Abu (1146) al-Samarqandi , Shams (202) al-Samawal , Ibn (1569) al-Sijzi , Abu (708) al-Tusi , Nasir (1912) al-Tusi , Sharaf (1138) al-Umawi , Abu (1014) al-Uqlidisi , Abu'l (1028) Albanese , Giacomo (282) Albategnius (al-Battani) (1333) Albert, A Adrian

38. Greek Math Menaechmus (c. 350) Theudius of Magnesia (c. 350?) Thymaridas (c. 350) Dinostratus(c. 350) Speusippus (d. 339) Aristotle (384322) aristaeus the elder (fl. http://www.radessays.com/link.php?site=re&aff=r2c2&dest=viewpaper.php?request=17

39. VietReader! Forums John (251*) Archimedes of Syracuse (3190*) Archytas of Tarentum (1366*) Arf, Cahit(1452*) Argand, Jean (951) aristaeus the elder (588) Aristarchus of Samos http://vietreader.com/forums/forum.php?id=F20021108075031NX&fid=23

40. }EL1T3{ - )JYD( BULLDOG c. 350) *SB Speusippus (d. 339) Aristotle (384322) *SB *MT aristaeus the elder(fl. c. 350-330) *SB *MT Eudemus of Rhodes (the Peripatetic) (fl. http://elit3clan.net/forum/index.php?s=6ee5ca39e03737c02dada4000987dbe9&showtopi

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