M598/M700 - MATHIESEN - SPRING 2000 Music Library Reserve Books And Scores English Mathematics useful for understanding Plato / by theon of smyrna ; translatedfrom the 1892 Greek/French edition of J. Dupuis by Robert and Deborah http://www.dlib.indiana.edu/variations/reserves/old/spring00/m598m700mlo.html
Extractions: William and Gayle Cook Music Library Aristides Quintilianus. On music, in three books / Aristides Quintilianus ; translation with introduction, commentary, and annotations by Thomas J. Mathiesen. New Haven : Yale University Press, c1983. (Music theory translation series) Aristoxenus. Aristoxenou Harmonika stoicheia = The harmonics of Aristoxenus / edited with translation notes, introduction, and index of words by Henry S. Macran. Oxford : Clarendon Press, 1902. Augustine, Saint, Bishop of Hippo. cn (The Fathers of the Church) BR60.F2 A92 vol. 2 Barbera, Charles Andre. The persistence of Pythagorean mathematics in ancient musical thought / Charles Andre Barbera. 1980. Bernard Silvestris, fl. 1136. The Cosmographia of Bernardus Silvestris. A translation with introd. and notes by Winthrop Wetherbee. New York, Columbia University Press, 1973. Boethius, his life, thought, and influence / edited by Margaret Gibson. Oxford : Blackwell, 1981. Boethius, d. 524. Fundamentals of music / Anicius Manlius Severinus Boethius ; translated, with
M602 - MATHIESEN - SPRING 2003 Music Library Reserve Books And Scores Mathematics useful for understanding Plato / by theon of smyrna ; translated fromthe 1892 Greek/French edition of J. Dupuis by Robert and Deborah Lawlor and http://www.dlib.indiana.edu/variations/reserves/m602mlo.html
Extractions: William and Gayle Cook Music Library Anonymous of St. Emmeram, 13th cent. De musica mensurata / the Anonymous of St. Emmeram ; complete critical edition, translation, and commentary [by] Jeremy Yudkin. Bloomington, Ind. : Indiana University Press, c1988. xii, 385, [1] p. : music ; 29 cm. Arabische Musiktheorie von den Anfängen bis zum 6./12. Jahrhundert : Studien, Übersetzungen und Texte in Faksimile / Eckhard Neubauer. Frankfurt am Main : Institute for the History of Arabic-Islamic Science at the Johann Wolfgang Goethe University, 1998. xii, 426, 9 p. : ill. ; 25 cm. Aristides Quintilianus. On music, in three books / Aristides Quintilianus ; translation with introduction, commentary, and annotations by Thomas J. Mathiesen. New Haven : Yale University Press, c1983. xiii, 217 p. : ill. ; 24 cm. Aristoxenus. Aristoxenou Harmonika stoicheia = The harmonics of Aristoxenus / edited with translation notes, introduction, and index of words by Henry S. Macran. Oxford : Clarendon Press, 1902.
Untitled 100 NICOMACHUS ARITHMETICA. 100 MENELAUS SPHERICS. 125 theon of smyrna PLATONICMATHEMATICS. 150 PTOLEMY THE ALMAGEST. 250 DIOPHANTUS ARITHMETICA. http://www.erols.com/bram/timeline.html
Extractions: CHRONOLOGY OF MATHEMATICIANS -1100 CHOU-PEI -585 THALES OF MILETUS: DEDUCTIVE GEOMETRY PYTHAGORAS : ARITHMETIC AND GEOMETRY -450 PARMENIDES: SPHERICAL EARTH -430 DEMOCRITUS -430 PHILOLAUS: ASTRONOMY -430 HIPPOCRATES OF CHIOS: ELEMENTS -428 ARCHYTAS -420 HIPPIAS: TRISECTRIX -360 EUDOXUS: PROPORTION AND EXHAUSTION -350 MENAECHMUS: CONIC SECTIONS -350 DINOSTRATUS: QUADRATRIX -335 EUDEMUS: HISTORY OF GEOMETRY -330 AUTOLYCUS: ON THE MOVING SPHERE -320 ARISTAEUS: CONICS EUCLID : THE ELEMENTS -260 ARISTARCHUS: HELIOCENTRIC ASTRONOMY -230 ERATOSTHENES: SIEVE -225 APOLLONIUS: CONICS -212 DEATH OF ARCHIMEDES -180 DIOCLES: CISSOID -180 NICOMEDES: CONCHOID -180 HYPSICLES: 360 DEGREE CIRCLE -150 PERSEUS: SPIRES -140 HIPPARCHUS: TRIGONOMETRY -60 GEMINUS: ON THE PARALLEL POSTULATE +75 HERON OF ALEXANDRIA 100 NICOMACHUS: ARITHMETICA 100 MENELAUS: SPHERICS 125 THEON OF SMYRNA: PLATONIC MATHEMATICS PTOLEMY : THE ALMAGEST 250 DIOPHANTUS: ARITHMETICA 320 PAPPUS: MATHEMATICAL COLLECTIONS 390 THEON OF ALEXANDRIA 415 DEATH OF HYPATIA 470 TSU CH'UNG-CHI: VALUE OF PI 476 ARYABHATA 485 DEATH OF PROCLUS 520 ANTHEMIUS OF TRALLES AND ISIDORE OF MILETUS 524 DEATH OF BOETHIUS 560 EUTOCIUS: COMMENTARIES ON ARCHIMEDES 628 BRAHMA-SPHUTA-SIDDHANTA 662 BISHOP SEBOKHT: HINDU NUMERALS 735 DEATH OF BEDE 775 HINDU WORKS TRANSLATED INTO ARABIC 830 AL-KHWARIZMI: ALGEBRA 901 DEATH OF THABIT IBN - QURRA 998 DEATH OF ABU'L - WEFA 1037 DEATH OF AVICENNA 1039 DEATH OF ALHAZEN
Extractions: Abstract. Martin Euser researches the factor root-(2N - 1) and its interesting relations between musical proportions and Pythagorean triangles. The simple scheme N +/- root-N is also interesting as a generative set of pairs of numbers. This set looks like a prototype for the generative set of pairs of numbers discussed in a previous article by the author. The findings are presented summarily and it is left to the reader to elaborate upon them. Pythagorean Triangles and Musical Proportions Martin Euser S ince writing a previous article on Sacred Geometry I have done a little research on the factor root-(2N - 1) and found some interesting relations between musical proportions and Pythagorean triangles. Furthermore, I have looked into the matter of the 'root-factor' scheme a bit further and found that the simple scheme N +/- root-N is also interesting as a generative set of pairs of numbers. This set looks like a prototype for the generative set of pairs of numbers I have discussed in a previous article. I will present these findings summarily and leave it to the reader to elaborate upon them.
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
130 . ( 130 190 ) theon of smyrna, (1013-1054) Hermann of R. (1364-1436) QadiZada. ( 130 BC - 70 BC ) Geminus, (1019-1066) Sripati, (1390-1450) al'Kashi. http://www.sanalhoca.com/matematik/matematikci1.htm
Extractions: sanal hoca Ana Sayfa Kimya Matematik Fizik ... E-Posta ( 130 - 190 ) Theon of Smyrna (1013-1054) Hermann of R. (1364-1436) Qadi Zada ( 130 BC - 70 BC ) Geminus (1019-1066) Sripati (1390-1450) al'Kashi ( 150 BC - 70 BC ) Zeno of Sidon (1031-1095) Shen (1393-1449) Ulugh Beg ( 200 - 284 ) Diophantus (1048-1122) Khayyam (1401-1464) Cusa ( 240 - 300 ) Sporus (1070-1130) Abraham (1404-1472) Alberti ( 290 350 ) Pappus (1075-1160) Adelard (1412-1486) Qalasadi ( 300 360) Serenus (1092-1167) Ezra (1412-1492) Francesca ( 335 - 395 ) Theon (1114-1185) Bhaskara (1423-1461) Peurbach ( 370 - 415 ) Hypatia (1114-1187) Gherard (1424-1484) Borgi ( 60 AD - 120AD ) Nicomachus (1168-1253) Grosseteste (1436-1476) Regiomontanus ( 65 AD - 125AD ) Heron (1170-1250) Fibonacci (1445-1500) Chuquet ( 70 AD - 130AD ) Menelaus (1195-1256) Sacrobosco (1445-1517) Pacioli ( 78 AD - 139AD ) Heng (1200-1280) Albertus (1452-1519) Leonardo ( 85 AD - 165AD ) Ptolemy (1201-1274) Tusi (1462-1498) Widman (160 BC - 100 BC) Theodosius (1202-1261) Ch'in (1465-1526) Ferro (1680BC-1620BC) Ahmes (1219-1292) Bacon
DIOPTASE c. AD zoo), nor by theon of smyrna (c. AD 130), nor does Greek arithmetic as representedby these authors and by lamblichus (end of 3rd century) show any trace http://30.1911encyclopedia.org/D/DI/DIOPTASE.htm
Extractions: protection of trees generally (according to Pherecydes in C. W. MUller, Frag. HISt. Graec. iv. p. 637, the word rikra signified tree). It is suggested that the cult of Dionysus absorbed that of an old tree-spirit. He was figured also, like Hermes, in the form of a pillar or term surmounted by his head. For the connexion of Dionysus with Greek tragedy see DRAMA. See Farnell, Cults of the Greek States, v. (1910); also 0. Rap Beziehungen des Dionysuskulius zu Thrakien (1882); 0. Ribbec Among the great variety of problems solved are problems leading to determinate equations of the first degree in one, two, three or four variables, to determinate quadratic equations, and to indeterminate equations of the first degree in one or more variables, which are, however, transformed into determinate equations by arbitrarily assuming a value for one of the required numbers, Diophantus being always satisfied with a rational, even if fractional, result and not requiring a solution in integers. But the bulk Of the work consists of problems leading to indeterminate eq,uations of the second degree, and these universally take the form that one or two (and never more) linear or quadratic functions of one variable x are to be made rational square numbers by finding a suitable value for x. A few problems lead to indeterminate equations of the third and fourth degrees. an easy indeterminate equation of the sixth degree being Several varieties, depending on differences in structure and chemical composition, have been distinguished, viz. coccolite
Chapter 8 Updates - Dissections: Plane & Fancy continued fraction technique for solving the Pell equation b 2 + 1 = 2a 2 . About130 AD theon of smyrna gave the recursive formulas for a i and b i . They had http://www.cs.purdue.edu/homes/gnf/book/Booknews/ch8.html
Extractions: in , by Greg N. Frederickson Katharina Huber pointed out that the roles of x and y are reversed when reducing Fibonacci's formula to Diophantus's formula on page 73. As suggested by Puzzle 8.3, the Penta class can include identities produced using nonintegral values for p and q. This observation also applies to the Penta-penta class. There are two typos in the specification of Method 5. In the second line of step 2, the first expression should be y - q - 1 rather than z - q - 1 and the second expression should be y - x rather than z - x (These are corrected in the paperback edition.) Using Method 2C, I gave 5-piece dissections for all squares in the PP-plus class. One solution in the PP-plus class is 9 , for which L. P. Mochalov gave a 5-piece dissection in Vladimir Belov's 1992 book. (See the updates to chapter 1.) Mochalov's method can be generalized to handle all squares in the PP-plus class. I should have written Cossali's name as Pietro Cossali.
Greek Musical Writings - Cambridge University Press Rhythmica Book III; 8. The Euclidean Sectio Canonis; 9. Minor authors quoted by Theonand Porphyry; Passages from theon of smyrna; Passages from Porphyry; 10. http://books.cambridge.org/052130220X.htm
Extractions: For updates on new titles in: Volume 2 , Harmonic and Acoustic Theory In stock This second volume of Greek Musical Writings contains important texts on harmonic and acoustic theory, illustrating the progress of these sciences from their beginnings in the sixth century BC over the subsequent thousand years. Writers represented include Philolaus, Plato, Aristotle, Theophrastus, Aristoxenus, Ptolemy, Aristides, Archytas, and Quintilianus. All the Greek texts are newly translated by the editor. Some replace inadequate existing translations; other significant portions of the book include much that is essential for an understanding of medieval and Renaissance musicology. Dr Barker provides detailed and authoritative commentary and annotations to all the texts. Each section is prefaced by an introductory essay and some of the more complex issues are discussed further in appendices. Acknowledgements; Abbreviations, texts and typographic conventions; General introduction; 1. Pythagoras and Early Pythagoreanism; Appendix: the scalar Divisions of Archytas; 2. Plato; 3. Aristotle; 4. The Aristotelian Problemata; 5. The Peripatetic De Audibilibus; 6. Theophrastus; 7. Aristoxenus Elementa Harmonica; Book I; Book II; Book III; Appendix: Aristoxenus Elementa Rhythmica Book III; 8. The Euclidean Sectio Canonis; 9. Minor authors quoted by Theon and Porphyry; Passages from Theon of Smyrna; Passages from Porphyry; 10. Nicomachus Enchiridion; 11. Ptolemy Harmonicas; Book I; Book II; Appendix to Book II; Book III; 12. Aristides and Quintilianus De Musica; Book I; Book II; Book III; Bibliography; Index.
T Index of Miletus (2091*) Theaetetus of Athens (1320) Theodorus of Cyrene (673) Theodosiusof Bithynia (1044) Theon of Alexandria (1135) theon of smyrna (655) Thiele http://math.ichb.ro/History/Indexes/T.html
Theosophy Library Online - Great Teacher Series - ALBINUS Albinus was the contemporary of theon of smyrna, who wrote a mathematical introductionto Plato, a compilation of quotations on Platonic philosophy which http://theosophy.org/tlodocs/teachers/Albinus.htm
Extractions: Plato's doctrine of Fate is something like this: all things, he says, are in Fate, but not everything is fated. For though Fate holds the rank of law, it does not decree that one person shall do this and another suffer that, for if it did, it would go on ad infinitum producing infinite things and infinite accidents associated with them. Moreover, there would be nothing in our power, and praise and blame as well as everything like that would vanish. Rather, Fate decrees that if a soul selects a life of this kind, and does certain acts, then certain things will follow upon the selection. The soul then is without a master, and it rests with itself to do or to refrain from an act: it is not forced to do this or that. Nonetheless, whatever follows from doing something is accomplished by Fate. For example, if a Paris carries off a Helen, he freely does so, but it follows that Greeks will war with Trojans for her sake. Didaskalikos XXVI ALBINUS The rise of Stoic philosophy, austere and admirable in its demanding way of life, but metaphysically limited from a Platonic perspective, eventually attracted the attention of the Academy. Whilst the Old Academy dealt with questions raised by Plato, the Middle Academy, marked by the election of Crates in 270 B.C., focussed on detailed responses to Stoic philosophy. This critical and even negative use of dialectic resulted in a steady drift towards scepticism, a reaction to all dogmatic schools which propounded specific doctrines. With the election of Carneades, who died in 128 B.C., the New Academy was rigidly sceptical; Carneades emphasized
RE: "completed Infinite" 1088 a 6), but only the beginning of number (theon of smyrna says the same thing,p.24,23) According as this view numbers are multitudes composed of http://hhobel.phl.univie.ac.at/phlo/200009/msg00089.html
Extractions: Date Prev Date Next Thread Prev Thread Next ... Thread Index To phil-logic@bucknell.edu Subject : RE: "completed infinite" From : "Daniel M. Kervick" < dkervick@nh.ultranet.com Date : Fri, 8 Sep 2000 21:24:03 -0400 Importance : Normal In-Reply-To 00c301c019e4$8b8d3920$4718fea9@desynre Reply-To phil-logic@bucknell.edu Sender owner-phil-logic@bucknell.edu Follow-Ups Re: "completed infinite" From: "Drake O'Brien" <dobrien@lightspeed.bc.ca> References Re: "completed infinite" From: "Drake O'Brien" <dobrien@lightspeed.bc.ca> Prev by Date: Re: diagonalization Next by Date: Re: "completed infinite" Prev by thread: Re: "completed infinite" Next by thread: Re: "completed infinite" Index(es): Date Thread
Re: "completed Infinite" 1088 a 6), but only the beginning of number (theon of smyrna says the same thing,p.24,23) According as this view numbers are multitudes composed of units http://hhobel.phl.univie.ac.at/phlo/200009/msg00085.html
Extractions: Date Prev Date Next Thread Prev Thread Next ... Thread Index To phil-logic@bucknell.edu Subject : Re: "completed infinite" From : "Drake O'Brien" < dobrien@lightspeed.bc.ca Date : Fri, 8 Sep 2000 15:30:15 -0700 References LPBBINAMNFBBPMAFKNNPIEGFCDAA.dkervick@nh.ultranet.com Reply-To phil-logic@bucknell.edu Sender owner-phil-logic@bucknell.edu Follow-Ups RE: "completed infinite" From: "Daniel M. Kervick" <dkervick@nh.ultranet.com> References RE: "completed infinite" From: "Daniel M. Kervick" <dkervick@nh.ultranet.com> Prev by Date: RE: "completed infinite" Next by Date: Re: diagonalization Prev by thread: RE: "completed infinite" Next by thread: RE: "completed infinite" Index(es): Date Thread
Extractions: BOULLIAU Concerning Enfranchised People . These two writings were condemned by the Inquisition. In 1649 he published at the Louvre the history of Ducas in Greek, with a Latin translation and his Notes. His works on philosophy and on mathematics include a treatise on the nature of light, presented in 1638; the translation of Theon of Smyrna, the Platonist, with his notes, which appeared in 1644; a treatise on spiral lines, in 1657. In 1663 he brought to light the treatise of Ptolemy On the Faculty of Judgment ; and some time later, a large work in folio entitled
Level 3 - 100 A.D. theon of smyrna was a Greek mathematical astronomer who was calles Theon the Mathematician by this person. Try Hipparchus theon of smyrna. On to Level 4. http://www.coe.ufl.edu/webtech/Timemachine/Math/100/103.htm
Extractions: Level - 3 This early mathematicians works were based on trigonometric ideas, or using triangles to find out distances on Earth and in Space. Many star charts were used to prove the geocentric (Earth centered) theory based on observations that lasted from March 26, 127 to February 2, 147. To increase the amount of data used this mathematician also used the star charts developed by the earlier mathematical astronomer Hipparchus. Theon of Smyrna was a Greek mathematical astronomer who was calles "Theon the Mathematician" by this person. This mathematician's work and the geocentric theory was not challenged until 1543 when Copernicus proved the heliocentric (Sun centered) rotation of the Universe.
New Page 3 70 BC); Clepcosmological work On the Cyclic motions of the celestial bodies; andtheon of smyrna (first half of second century AD), who wrote the Manual of http://jrider.web.wesleyan.edu/wescourses/2001f/fren234/01/handbooktradition.htm
Extractions: contemporary Home Excerpts pertaining to the history of the handbook tradition From pages 11-12, and 14 of Foundations of Modern Science in the Middle Ages by Edward Grant. Any "bold faced" words were not bold faced in the original text. "The achievements of the first six centuries of the Christian era were typical of the manner in which Greek science and natural philosophy had developed and advanced. Always the product of a small number of gifted scholars concentrated in a few centers, Greek science was a fragile enterprise, able to advance and preserve itself just so long as the intellectual environment was favorable, or at least not overtly antagonistic. Greek science at its traditional best in the Roman Empire was but a continuation of the progress already made in the physical and biological sciences of classical Greece and the Hellenistic world, when the works of Plato, Aristotle, Hipparchus, Eudoxus, Euclid, Archimedes, Appollonius of Perga, Hipparchus, Theophrastus, Herophilus, and Erastistratus established the highest levels of achievement.
- Great Books - lost. However, some details of these calculations appear in worksby other authors such as Cleomedes, theon of smyrna and Strabo. http://www.malaspina.com/site/person_515.asp
Extractions: Eratosthenes was born in Cyrene which is now in Libya in North Africa. His teachers included the scholar Lysanias of Cyrene and the philosopher Ariston of Chios who had studied under Zeno, the founder of the Stoic school of philosophy. Eratosthenes also studied under the poet and scholar Callimachus who had also been born in Cyrene. Eratosthenes then spent some years studying in Athens. Eratosthenes made a surprisingly accurate measurement of the circumference of the Earth. Details were given in his treatise On the measurement of the Earth which is now lost. However, some details of these calculations appear in works by other authors such as Cleomedes, Theon of Smyrna and Strabo . Eratosthenes compared the noon shadow at midsummer between Syene (now Aswan on the Nile in Egypt) and Alexandria. He assumed that the sun was so far away that its rays were essentially parallel, and then with a knowledge of the distance between Syene and Alexandria, he gave the length of the circumference of the Earth as 250,000 stadia. [Adapted from MacTutor Eratosthenes was the second librarian of the Great Library of Alexandria, so called to distinguish it from the smaller or "daughter" library in the Serapeum, was a foundation of the first Ptolemies for the purpose of aiding the maintenance of Greek civilization in the midst of the conservative Egyptians. If the removal of Demetrius Phalereus to Alexandria, in 296-295 B.C., was connected with the organization of the library, at least the plan for this institution must have been formed under Ptolemaios Soter (died c. 284 B.C.), but the completion of the work and its connection with the Museum was achievement of his successor, Ptolemaios Philadelphos. As
Mathematicians Nicomachus of Gerasa (c. 100) *SB. Zhang Heng (78139). theon of smyrna (c. 125).Ptolemy (Claudius Ptolemaeus) (c. 100-c. 170) *SB *MT. Marinus of Tyre (c. 150). http://www.chill.org/csss/mathcsss/mathematicians.html
Extractions: List of Mathematicians printed from: http://aleph0.clarku.edu:80/~djoyce/mathhist/mathhist.html 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) Socrates (469-399) Philolaus of Croton (d. c. 390) *SB Democritus of Abdera (c. 460-370) *SB *mt 400 B.C.E. Hippasus of Metapontum (or of Sybaris or Croton) (c. 400?) Archytas of Tarentum (of Taras) (c. 428-c. 347) *SB *mt Plato (427-347) *SB *MT Theaetetus of Athens (c. 415-c. 369) *mt Leodamas of Thasos (fl. c. 380) *SB
Esoteric Science theon of smyrna declares that this array of ten dots, the tetractys of Pythagoras,was a symbol of the greatest importance, to the discerning mind it revealed http://www.prs.org/gallery-science.htm
Extractions: By far the most remarkable conception of the atom evolved during the last century is that produced by the genius of Dr. Edwin D. Babbitt. MPH The Problem of Diversity From Kircher's Ars Magna Sciendi In this diagram Kircher arranges 18 objects in two vertical columns and then determines the number of arrangements in which they can be combined. By the same method Kircher further estimates that fifty objects may be arranged in 1,273, 726,838,815,420,339, 851,343,083, 767,005,515,293, 749,454,795,473,408,000,000, 000,000 combinations. From this it will be evident that infinite diversity is possible, for the countless parts of the universe may be related to each other in an in-calculable number of ways. MPH Pythagoras, the First Philosopher
Spring 2003 Sectional Meeting Of The Allegheny Mountain Section In the first century AD, the Introduction to Arithmetic, by Nicomachus of Gerasaand Mathematics Useful for Understanding Plato by theon of smyrna were one the http://mallard.ds.psu.edu/~ecb5/MAA-Spring-03/tattersall.html
