1. VIVIANI, Vincenzo., De Locis Solidis Secunda Divinatio Geometrica In Quinque Lib attempted restoration of a work by aristaeus the elder, De locis solidis secunda divinatio geometrica was twentyfour. Aristaeus' work is believed to have been the first methodical http://www.polybiblio.com/phillips/748.html

Nigel Phillips VIVIANI, Vincenzo. De Locis Solidis Secunda Divinatio Geometrica in quinque libros iniuria temporum amissos Aristaei Senioris Geometrae... Opus Conicum continens elementa tractatuum ejusdem Viviani... Florentiae: Typis Regiae Celsistudinis apud Petrum Antonium Brigonci, [1701]. Folio, 12 leaves, pp. 164, 128, 3 engraved plates (two double-page). Half-title, numerous woodcut diagrams in the text. Short (3 cm.) tear in lower margin of K2, very small stain in lower corner of last leaves, a few leaves slightly foxed, but a very clean copy. Contemporary limp vellum, lower corners neatly repaired, a few holes in the vellum of the lower cover, upper inner hinge becoming loose. This item is listed on Bibliopoly by Nigel Phillips ; click here for further details.

2. Biography-center - Letter A www.pixiport.com/bioarieh.htm. aristaeus the elder, www-history.mcs.st-and.ac.uk/~history/ Mathematicians history/biographies/arvirag.html. Aryabhata the Elder, www-history.mcs.st-and 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 602 biographies 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.cfm/351.html Aase, Jon Morton www.whonamedit.com/doctor.cfm/334.html Abadie, Joseph Louis Irénée Jean www.whonamedit.com/doctor.cfm/35.html Abate, Nicolò dell www.getty.edu/art/collections/bio/a672-1.html Abbad ibn Bishr, www.usc.edu/dept/MSA/history/biographies/sahaabah/bio.ABBAD_IBN_BISHR.html Abbado, Claudio www.emiclassics.com/artists/biogs/abbab.html Abbat, Agnes Dean

3. Kepler's Model author of the work sometimes known as "Euclid Book XIV". Apparently this result is due to aristaeus the elder, ca 320 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.

4. History Of Mathematics: Chronology Of Mathematicians 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. c. 335) *SB http://aleph0.clarku.edu/~djoyce/mathhist/chronology.html

Chronological List of Mathematicians Note: there are also a chronological lists of mathematical works and mathematics for China , and chronological lists of mathematicians for the 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, *W, *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

5. Conic Sections In Ancient Greece Appendix B. Approximate Time line of Major Figures. 350 BC Menaechmus 310 BCaristaeus the elder 300 BC Euclid 287212 BC Archimedes 262-? BC Apollonius 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.

6. Aristaeus aristaeus the elder. Born about 370 BC in Greece Died about 300 BC. Aristaeusthe Elder was probably older than, but still a contemporary of, Euclid. http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Aristaeus.html

Aristaeus the Elder Born: about 370 BC in Greece Died: about 300 BC Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Aristaeus the Elder was probably older than, but still a contemporary of, Euclid . We know practically nothing of his life except that Pappus refers to him as Aristaeus the Elder which presumably means that Pappus was aware of another later mathematician also named Aristaeus. We have no record of such a person but we do point out below a possible confusion which may result from there being two mathematicians called Aristaeus. Pappus gave Aristaeus great credit for a work entitled Five Books concerning Solid Loci which was used by Pappus but has now been lost. 'Solid loci' is the Greek name for conic sections so it is rather confusing that there is another reference by a later writer to a work by Aristaeus called Five Books concerning Conic Sections . However these two works are now thought to be the same. Pappus describes the work as:- ... five books of Solid Loci connected with the conics. and also claims (if this is not a latter addition to the text) that Euclid compiled elementary results on conics in his treatise Conics while Aristaeus's results, much deeper, original and specialised, were not included by

7. Aristaeus Biography of Aristaeus (370BC300BC) aristaeus the elder. Born about 370 BC in Greece aristaeus the elder was probably older than, but still a contemporary of, Euclid http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Aristaeus.html

Aristaeus the Elder Born: about 370 BC in Greece Died: about 300 BC Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Aristaeus the Elder was probably older than, but still a contemporary of, Euclid . We know practically nothing of his life except that Pappus refers to him as Aristaeus the Elder which presumably means that Pappus was aware of another later mathematician also named Aristaeus. We have no record of such a person but we do point out below a possible confusion which may result from there being two mathematicians called Aristaeus. Pappus gave Aristaeus great credit for a work entitled Five Books concerning Solid Loci which was used by Pappus but has now been lost. 'Solid loci' is the Greek name for conic sections so it is rather confusing that there is another reference by a later writer to a work by Aristaeus called Five Books concerning Conic Sections . However these two works are now thought to be the same. Pappus describes the work as:- ... five books of Solid Loci connected with the conics. and also claims (if this is not a latter addition to the text) that Euclid compiled elementary results on conics in his treatise Conics while Aristaeus's results, much deeper, original and specialised, were not included by

8. 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.dcs.st-and.ac.uk/~history/Search/historysearch.cgi?SUGGESTION=dis

9. TMTh:: ARISTAEUS THE ELDER MATHEMATICIAN. aristaeus the elder (fl. c. 320 BC) Life Aristaeus wasa native of Croton, a Greek colony in southern Italy. He succeeded http://www.tmth.edu.gr/en/aet/1/15.html

Home Ancient Greek Scientists AGRICULTURALISTS ARCHITECTS ... PHYSICISTS MATHEMATICIAN ARISTAEUS THE ELDER (fl. c. 320 BC) Life Aristaeus was a native of Croton, a Greek colony in southern Italy. He succeeded Eudoxus of Cnidus as the head of his school in Cyrene, and worked closely with Euclid and Apollonius on a treatise entitled "Analysis of Locus", a method of geometry for advanced students, now lost. Work His main writings are: "Geometric loci" "Elements of conic sections": 5 books. "On regular solids ": Unlike Apollonius of Perga, Aristaeus considered the three conics as sections of acute-angled, right-angled and obtuse-angled cones perpendicular to the generatrix. Lost. "On the five regular solids": Proved that the pentagon of a dodecahedron is inscribed in the same circle as the triangle of an icosahedron inscribed in the same sphere. Lost. "Solid loci": 5 books. This treatise is considered more important than Euclid's work of the same name. "On geometrical loci with respect to three and four lines". Contact the Technology Museum

10. Aristaeus aristaeus the elder. Born about 360 BC in GreeceDied about 300 BC. Show birthplace location http://intranet.woodvillehs.sa.edu.au/pages/resources/maths/History/rsts.htm

Aristaeus the Elder Born: about 360 BC in Greece Died: about 300 BC Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Welcome page Aristaeus was a contemporary of Euclid and Euclid gave him great credit for a work Solid Loci , the Greek name for conics, which is now lost. The work of both Aristaeus and Euclid on conics was, almost 200 years later, further developed by Apollonius References (2 books/articles) Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Welcome page History Topics Index Famous curves index ... Search Suggestions JOC/EFR December 1996 The URL of this page is: http://www-history.mcs.st-andrews.ac.uk/history/Mathematicians/Aristaeus.html

11. References For Aristaeus References for aristaeus the elder. Biography in Dictionary of ScientificBiography (New York 19701990). Books JL Coolidge, A history http://intranet.woodvillehs.sa.edu.au/pages/resources/maths/History/~DZ772B.htm

References for Aristaeus the Elder Biography in Dictionary of Scientific Biography (New York 1970-1990). Books: J L Coolidge, A history of the conic sections and quadric surfaces (Oxford, 1945). Close this window or click this link to go back to Aristaeus Welcome page Biographies Index History Topics Index Famous curves index ... Search Suggestions JOC/EFR December 1996 The URL of this page is: http://www-history.mcs.st-andrews.ac.uk/history/References/Aristaeus.html

12. ThinkQuest : Library : A Taste Of Mathematic Thymaridas (c. 350); Dinostratus (c. 350); Speusippus (d. 339); Aristotle(384322); aristaeus the elder (fl. c. 350-330); Eudemus of http://library.thinkquest.org/C006364/ENGLISH/history/historygreece.htm

Index Math A Taste of Mathematic Welcome to A Taste of Mathematics.You will find the taste of mathematics here.The history of Mathematics,famous mathematicians,cxciting knowledge,the world difficult problems and also mathematics in our life... Browsing,thinking,enjoying,and have a good time here! Visit Site 2000 ThinkQuest Internet Challenge Languages English Chinese Students fangfei Beijing No.4 High School, Beijing, China ziyan Beijing No.4 High School, Beijing, China Coaches Tife Zesps3 Szks3 Ogslnokszta3c9cych Numer 1, Beijing, China xueshun Beijing No.4 High School, Beijing, China Want to build a ThinkQuest site? The ThinkQuest site above is one of thousands of educational web sites built by students from around the world. Click here to learn how you can build a ThinkQuest site. Privacy Policy

13. History Of Mathematics: Greece Aristotle (384322) aristaeus the elder (fl. c. 350-330 http://aleph0.clarku.edu/~djoyce/mathhist/greece.html

Greece Cities Abdera: Democritus Alexandria : Apollonius, Aristarchus, Diophantus, Eratosthenes, Euclid , Hypatia, Hypsicles, Heron, Menelaus, Pappus, Ptolemy, Theon Amisus: Dionysodorus Antinopolis: Serenus Apameia: Posidonius Athens: Aristotle, Plato, Ptolemy, Socrates, Theaetetus Byzantium (Constantinople): Philon, Proclus Chalcedon: Proclus, Xenocrates Chalcis: Iamblichus Chios: Hippocrates, Oenopides Clazomenae: Anaxagoras Cnidus: Eudoxus Croton: Philolaus, Pythagoras Cyrene: Eratosthenes, Nicoteles, Synesius, Theodorus Cyzicus: Callippus Elea: Parmenides, Zeno Elis: Hippias Gerasa: Nichmachus Larissa: Dominus Miletus: Anaximander, Anaximenes, Isidorus, Thales Nicaea: Hipparchus, Sporus, Theodosius Paros: Thymaridas Perga: Apollonius Pergamum: Apollonius Rhodes: Eudemus, Geminus, Posidonius Rome: Boethius Samos: Aristarchus, Conon, Pythagoras Smyrna: Theon Stagira: Aristotle Syene: Eratosthenes Syracuse: Archimedes Tarentum: Archytas, Pythagoras Thasos: Leodamas Tyre: Marinus, Porphyrius Mathematicians Thales of Miletus (c. 630-c 550)

14. Section One Chapter Four The Republicv. Hippopodej. Quadriviumw. Menaechmusk. Ideal Formsx. Conic Sectionsl. Platonic Solidsy. aristaeus the elder http://ivihsm.cua.edu/teaching_guide/20001129_Section_One_Chapter_Four.pdf

15. Full Alphabetical Index Translate this page Arbuthnot, John (251*) Archimedes of Syracuse (3190*) Archytas of Tarentum (1366*)Arf, Cahit (1452*) Argand, Jean (81) aristaeus the elder (588) Aristarchus 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)

16. À§´ëÇѼöÇÐÀÚ ¸ñ·Ï Argand Born 18 July 1768 in Geneva, Switzerland Died 13 Aug 1822 in Paris, FranceAristaeus, aristaeus the elder Born about 360 BC in Greece Died about 300 http://www.mathnet.or.kr/API/?MIval=people_seek_great&init=A

17. Pappus Of Alexandria, (fl. C. 300-c. 350) Among many others he mentions aristaeus the elder, Carpus of Antioch, Conon of Samos, Demetrius of Alexandria http://www.math.tamu.edu/~dallen/masters/Greek/pappus.pdf

18. 8th Grade Aristotle (384322) *SB *MT ·. aristaeus the elder (fl. c http://mslombardo.freehosting.net/catalog.html

Free Web site hosting - Freeservers.com Web Hosting - GlobalServers.com Choose an ISP NetZero High Speed Internet ... Dial up $14.95 or NetZero Internet Service $9.95 8th Grade Info Home Page 5th Grade 6th Grade 7th Grade ... Guest Book Page Your project You need to hand me a 2 page paper on the mathematician of your choice by May 31st. You must have 3 sources. I have compiled a list of "MaThMaGiCiAnS" you can choose from. Mathmaticians 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

19. Dictionary Of The History Of Ideas of Pappus who attributes the elaboration of two methods to the work of Euclid,Apollonius of Perga, and aristaeus the elder (MR Cohen and IE Drabkin, pp. http://etext.lib.virginia.edu/cgi-local/DHI/dhi.cgi?id=dv3-48

20. Aa, Personal , Ahmet Kaya ,Þebnem Ferah , Göksel , Ebru Gündeþ Arbuthnot, John (251*) Archimedes of Syracuse (3190*) Archytas of Tarentum (1366*)Arf, Cahit (1452*) Argand, Jean (951) aristaeus the elder (588) Aristarchus http://www.newturk.net/index111.html

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