41. Hippopede Coffman Deposit #12 The Hippopede of proclus. and. proclus (410 485 AD ) was a Greek mathematician who is best known for his Commentaries on the First Book of Euclid s Elements. http://curvebank.calstatela.edu/hippopede/hippopede.htm

Back to . . . Curve Bank Home Page NCB Deposit # 12 contributed by Dr. Adam Coffman Department of Mathematical Sciences Indiana University - Purdue University Fort Wayne from http://www.ipfw.edu/math/Coffman/pov/spiric.html The Hippopede of Proclus "Hippopede" means the foot of a horse and/or the shackle attached to the foot of a horse. The shackle is called a "fetter." 1. The implicit equation in the xy- plane is where a and b are positive constants. This is a curve with reflectional symmetry about both the horizontal and vertical axes. 2. Any Hippopede is the intersection of a torus with one of its tangent planes that is parallel to its axis of rotational symmetry, as demonstrated in the animation. 3. Converting the implicit equation to polar coordinates gives so the origin at r = is a solution, and the remainder of the curve is given by b a, the point at the origin is an isolated node and the balance of the solution set is a simple closed curve, also called an Elliptic Lemniscate of Booth. The b a special case is given by the rational parametrization Each of these curves is the image of an ellipse under an inversion in a circle. The circle and the ellipse must have the same center. The curve is non-convex for

42. Proclus' Axiom -- From MathWorld Foundations of Mathematics Axioms Geometry Line Geometry Lines. proclus Axiom. Eric W. Weisstein. proclus Axiom. From MathWorldA Wolfram Web Resource. http://mathworld.wolfram.com/ProclusAxiom.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index ABOUT THIS SITE About MathWorld About the Author DESTINATIONS What's New MathWorld Headline News Random Entry ... Live 3D Graphics CONTACT Email Comments Contribute! Sign the Guestbook MATHWORLD - IN PRINT Order book from Amazon Foundations of Mathematics Axioms Geometry ... Lines Proclus' Axiom If a line intersects one of two coplanar parallel lines , it must intersect the other also. This axiom is equivalent to the parallel postulate Coplanar Intersection Line-Line Intersection ... search Dunham, W. "Hippocrates' Quadrature of the Lune." Ch. 1 in Journey through Genius: The Great Theorems of Mathematics. New York: Wiley, p. 54, 1990. Eric W. Weisstein. "Proclus' Axiom." From MathWorld A Wolfram Web Resource. http://mathworld.wolfram.com/ProclusAxiom.html Wolfram Research, Inc.

43. Proclus Translate this page Retour. proclus et ses ejectas. Lorsque ce petit cratère est éclairé fortement (quelques jours autour de la pleine lune) on voit http://www.astrosurf.com/astrojb/proclus.htm

Retour Proclus et ses ejectas Le 17 aout: acquisition IRIS, une seule image, pas de traitement.

44. Spira Solaris, The Chaldean Oracles, Proclus And Kepler. Spira Solaris Archytas- From this viewpoint it was a logical step to consider next the contents of the Chaldean Oracles, held in such high esteem by proclus and others. http://www.spirasolaris.ca/sbb4e.html

PART V. SPIRA SOLARIS AND THE CHALDEAN ORACLES A. THE CHALDEAN ORACLES In considering the astronomical elements in ancients works it seemed advisable to examine the origins of later scientific advances associated in one way or another with these earlier sources. This was especially so with respect to the contributions made by both Galileo and Kepler in light of their acknowledged use of materials provided in Plato's . But this was only one facet of a much wider investigation. Another concerned technical details long-buried in the Babylonian astronomical cuneiform texts of the Seleucid Era [310 BC - 75 A.D.] - information that only surfaced during the latter part of the previous century and has yet to see the light of day even now. Irrespective of how much or how little this neglected corpus of technical knowledge is regarded, there still remains the leading question why Babylonian astronomy was so obviously concerned with synodic motion and varying orbital velocity . It was this question that generated sufficient interest in astronomy and mathematics to apply the general synodic relationship in Parts I and II of the present work. As shown in these earlier sections, this was the vital step that provided the necessary understanding to the "Golden Section" and the Phi- Series in the present astronomical context. From this viewpoint it was a logical step to consider next the contents of the

45. Plato Transformed - Proclus: Bibliography Translate this page Plato Transformed - proclus bibliography (1991-2002). The number of books and articles on proclus has increased considerably in the last few decades. http://www.hiw.kuleuven.ac.be/dwmc/plato/proclus/probiblio.htm

Home About Lectures and events Proclus ... Institute of Philosophy Plato Transformed - Proclus: bibliography (1991-2002) The number of books and articles on Proclus has increased considerably in the last few decades. Throughout this period, it has been deemed important to continue the pioneering work of N. Scotti Muth, who gathered together an extensive bibliography of Proclus from 1949 (the year of the publication of J. Rosan, The Philosophy of Proclus. The Final Phase of Ancient Thought , New York: Cosmos, 1949) to 1992: Scotti Muth, N., Proclo negli ultimi quarant' anni: Bibliografia ragionata della letteratura primaria e secondaria riguardante il pensiero procliano e i suoi influssi storici (anni 1949-1992) , introduction by W. Beierwaltes, Milano: Vita et Pensiero, 1993. Our eventual aim is to provide readers with an exhaustive annotated bibliography (1990-2004), that will be published in 2005 in Lustrum . The list below shows a very early stage of our work. A complete list will appear here shortly before the publication. Any comment or suggestion concerning the bibliography, or any additional reference should be directed to

46. Plato Transformed - Proclus Plato Transformed proclus. proclus bibliography, The number of books and articles on proclus has increased considerably in the last few decades. http://www.hiw.kuleuven.ac.be/dwmc/plato/proclus/

Home About Lectures and events Proclus ... Institute of Philosophy Plato Transformed - Proclus Proclus' bibliography The number of books and articles on Proclus has increased considerably in the last few decades. Throughout this period, it has been deemed important to continue the pioneering work of N. Scotti Muth, who gathered together ... Proclus Diadochus biography Proclus, the most important philosopher of the fifth century AD, was born in 409/10 or 411/12 AD in Byzantium, though both his parents were of Lycian origin. After a period spent in Alexandria, where he studied rhetoric, mathematics and ... Editions and translations of Proclus' works The following list contains all editions and translations of Proclus' works published after 1900. Included are also Marinus,

47. Grand Midi: Proclus Et Son Influence Translate this page ÉDITIONS DU GRAND MIDI. proclus et son Influence. Ce recueil comprend les textes de quatorze spécialistes de proclus Werner Beierwaltes http://www.grandmidi.com/l107.htm

ÉDITIONS DU GRAND MIDI Proclus et son Influence Ce recueil comprend les textes de quatorze spécialistes de Proclus: Werner Beierwaltes, Linos Benakis, Stanislas Breton, Joseph Combès, Michael Erler, Pierre Hadot, Antony C. Lloyd, H.-D. Saffrey, H.-R. Schwyzer, A. P. Segonds, Carlos Steel, Loris Sturlese, L. G. Westerink et Laura Westra Recensions Table des matières Auteurs et éditeurs Sommaire ... Nouveautés

48. Proclus - Encyclopedia Article About Proclus. Free Access, No Registration Neede encyclopedia article about proclus. proclus in Free online English dictionary, thesaurus and encyclopedia. proclus. Word Word. http://encyclopedia.thefreedictionary.com/Proclus

Dictionaries: General Computing Medical Legal Encyclopedia Proclus Word: Word Starts with Ends with Definition Proclus Lycaeus ( February 8 February 8 is the 39th day of the year in the Gregorian Calendar. There are 326 days remaining, 327 in leap years. Events 421 - Constantius III becomes co-Emperor of the Western Roman Empire 1587 - Mary, Queen of Scots is executed. 1622 - King James I of England disbands the English Parliament 1692 - A doctor in Salem Village, Massachusetts Bay Colony declares that three teenaged girls are under domination of Satan, leading to the Salem witch trials. Click the link for more information. Centuries: 4th century - 5th century - 6th century Decades: 360s 370s 380s 390s 400s - Years: 407 408 409 410 411 - Events The Visigoths move into Gaul, led by Alaric's brother Ataulf. Cyril of Alexandria becomes Patriarch of Alexandria. Ataulf marries Galla Placidia, sister of the Emperor Honorius. Lazarus, bishop of Aix en Provence, and Herod, bishop of Arles, are expelled from their sees on a charge of Manichaeism. Click the link for more information.

49. Proclus Of Constantinople - Encyclopedia Article About Proclus Of Constantinople encyclopedia article about proclus of Constantinople. proclus of Constantinople in Free online English dictionary, thesaurus and encyclopedia. http://encyclopedia.thefreedictionary.com/Proclus of Constantinople

Dictionaries: General Computing Medical Legal Encyclopedia Proclus of Constantinople Word: Word Starts with Ends with Definition Saint Proclus (d. July July is the seventh month of the year in the Gregorian Calendar, with 31 days. July was renamed for Julius Caesar; previously, it was called Quintilis in Latin, since it was the fifth month in the Roman calendar which started in March. Because of its origin, until the 18th century this month was pronounced the same as the girl's name Julie July begins on the same day of the week as April every year and also January in leap years. In the Irish Calendar the month is called Iúil and is the third and last month of the Summer season. Click the link for more information. Centuries: 4th century - 5th century - 6th century Decades: 390s 400s 410s 420s 430s - Years: 441 442 443 444 445 - Events A synod is held by Turibius of Astorga. Flavian becomes Patriarch of Constantinople Births Deaths Proclus, patriarch of Constantinople Click the link for more information. ) was a patriarch Originally a patriarch is a man who exercises autocratic authority over an extended family. See patriarchy.

50. Commentaar Van Proclus Op Propositie I-47 Commentaar van proclus op Propositie I47 (Euclides Elementen). VI-31. einde Opmerking. begin pagina proclus.htm laatste wijziging op 06-10-02. http://www.pandd.demon.nl/proclus.htm

Commentaar van Proclus op Propositie I-47 (Euclides: Elementen) Overzicht Pythagoras Elementen Meetkunde Overzicht Proclus' commentaar Propositie VI-31 (Uitgebreide Stelling van Pythagoras) Bewijs van VI-31 Zie ook de pagina " Boek VI " 1. Proclus' commentaar Vertaling uit het Grieks: Glen R. Morrow in Proclus: A Commentary on the First Book of Euclid's Elements (Princeton University Press, 1970; herdruk 1992) Zie verder ook History of Mathematics: Proclus How he proves the theorem in the sixth book will be evident there. But now let us consider how he shows the theorem before us to be true, remarking only that he does not prove the universal proposition here, since he has not yet explained similarity in rectilinear figures, nor proved anything in general about proportion. Hence many of the things here proved in a partial fashion are proved in that book more generally through the use of the above method. In the present proposition the author of the Elements proves his conclusion by means of the ordinary theory of parallelograms. There are two sorts of right-angled triangles, isosceles and scalene. In isosceles triangles you cannot find numbers that fit the sides; for there is no square number that is de double of a square number, if you ignore approximations, such as the square of seven which lacks one of being double the square of five. But in scalene triangles it is possible to find such numbers, and it has been clearly shown that the square on the side subtending the right angle may be equal to the squares on the sides containing it. Such is the triangle in the republic, in which sides of three and four contain the right angle and five subtends it, so that the square on five is equal to the squares on those sides. For this is twenty-five, and of those the square of three is nine and that of four sixteen. The statement, then, is clear for numbers.

51. Proclus; Morrow, G.R., Trans.: Proclus: A Commentary On The First Book Of Euclid of the book proclus A Commentary on the First Book of Euclid s Elements by proclus; Morrow, GR, trans., published by Princeton University Press....... http://pup.princeton.edu/titles/5166.html

PRINCETON University Press SEARCH: Keywords Author Title More Options Power Search Search Hints E-MAIL NOTICES NEW IN PRINT E-BOOKS ... HOME PAGE Proclus: A Commentary on the First Book of Euclid's Elements Proclus 406 pp. Shopping Cart Another Princeton book by Proclus: Proclus' Commentary on Plato's Parmenides Subject Area: Classics Shopping Cart: For customers in the U.S., Canada, Latin America, Asia, and Australia Paper: $35.00 ISBN: 0-691-02090-6 For customers in Europe, Africa, the Middle East, and India Prices subject to change without notice File created: 5/7/04 Questions and comments to: webmaster@pupress.princeton.edu Princeton University Press

52. Proclus; Morrow, G.R. And Dillon, J.M., Trans.: Proclus' Commentary On Plato's of the book proclus Commentary on Plato s I Parmenides /I by proclus; Morrow, GR and Dillon, JM, trans., published by Princeton University Press....... http://pup.princeton.edu/titles/2407.html

Parmenides PRINCETON University Press SEARCH: Keywords Author Title More Options Power Search Search Hints E-MAIL NOTICES NEW IN PRINT E-BOOKS ... HOME PAGE Proclus' Commentary on Plato's Parmenides Proclus Translated by Glenn R. Morrow and John M. Dillon 406 pp. Shopping Cart Another Princeton book by Proclus: Proclus: A Commentary on the First Book of Euclid's Elements. Subject Areas: Archaeology and Ancient History Philosophy Shopping Cart: For customers in the U.S., Canada, Latin America, Asia, and Australia Paper: $49.95 ISBN: 0-691-02089-2 For customers in Europe, Africa, the Middle East, and India Prices subject to change without notice File created: 5/7/04 Questions and comments to: webmaster@pupress.princeton.edu Princeton University Press

53. MSN Encarta - Proclus http://fr.encarta.msn.com/encyclopedia_761566181/Proclus.html

Accueil MSN Mon MSN Hotmail Rechercher ... S'abonner   Encarta Premium Rechercher Article accessible sur abonnement MSN Encarta Premium : Acc©dez   30 000 articles encyclop©diques avec plus de 12 000 illustrations, un atlas mondial interactif, un guide du Web et une palette compl¨te de ressources et d'outils ©ducatifs. 34,99 € par an (service d’acc¨s   Internet non compris). En savoir plus. Cet article n'est accessible que si vous ªtes abonn©   MSN Encarta Premium. Dans ce cas, connectez-vous en cliquant sur le lien Aller sur MSN Encarta Premium (ci-dessus). Proclus Proclus (v. 410-485), dernier philosophe majeur de la Gr¨ce antique et repr©sentant le plus influent de l'©cole ath©nienne du n©oplatonisme. N©  ... Encarta vous int©resse ? Abonnez-vous d¨s maintenant et b©n©ficiez de : Plus de 30 000 articles 2 000 analyses d'oeuvre Plus de 12 000 m©dias (dont des extraits sonores, des vid©os et des m©dias interactifs) Un atlas mondial interactif Une palette compl¨te de ressources et d'outils ©ducatifs Un guide du Web Plus de r©sultats pour Proclus Autres fonctionnalit©s Encarta Rechercher Proclus Accueil MSN Mon MSN ... Finances ©2004 Microsoft Corporation. Tous droits r©serv©s.

54. MSN Encarta - Résultats De La Recherche - Proclus proclus . Page 1 sur 1. *, Réservé aux abonnés MSN Encarta Premium. 1. proclus*. Encyclopédie EncartaArticle. http://fr.encarta.msn.com/Proclus.html

Accueil MSN Mon MSN Hotmail Rechercher ... S'abonner   Encarta Premium Rechercher Encarta R©sultats de la recherche pour "Proclus" Page sur 1 R©serv© aux abonn©s MSN Encarta Premium. Proclus Encyclop©die EncartaArticle Proclus (v. 410-485), dernier philosophe majeur de la Gr¨ce antique et repr©sentant le plus influent de l'©cole ath©nienne du n©oplatonisme. N©  ... n©oplatonisme Encyclop©die EncartaArticle Trouv© dans l'article n©oplatonisme mystique Encyclop©die EncartaArticle Trouv© dans l'article mystique bien (philosophie) Encyclop©die EncartaArticle Trouv© dans l'article bien (philosophie) th©ologie Encyclop©die EncartaArticle Trouv© dans l'article th©ologie Euclide (math©maticien) Encyclop©die EncartaArticle Trouv© dans l'article Euclide (math©maticien) De la nature (Parm©nide) Encyclop©die EncartaArticle Trouv© dans l'article De la nature (Parm©nide) grecque, philosophie Encyclop©die EncartaArticle Trouv© dans l'article grecque, philosophie R©serv© aux abonn©s MSN Encarta Premium. Page sur 1 R©sultats provenant de MSN Search Proclus PROCLUS de Lycie, grec, vers 410-485 Philosophe et historien n©o-platonicien. Originaire de Xanthos en Lycie (au sud de l'Asie Mineure, actuelle Anatolie, en Turquie), il s'©tablira   Alexandrie puis   Ath¨nes.

55. Chapter 3.  Proclus' Elements selections from proclus Elements of Theology, summarizing his argument for the soul s indestructible and imperishable nature. Chapter 3 proclus Elements. http://mbdefault.org/3_elements/default.asp

Home - Welcome Forums Lectures A Word of Encouragement ... E-mail the webmaster. Chapter 3 Proclus' Elements The book is Proclus' Elements of Theology . By 1017 this fifth-century text had likely made its way to Dar al-Hikma. It would have been nestled in the cabinet beside its more popular (and pseudonymous) abridgment, Aristotle's Book of Causes The Elements of Theology Elements may be the most orderly proof of immortality ever composed by a Hellenic philosopher. For readers who've not seen the text, it will be instructive at this time to study a few Elements which abstract Proclus' argument. This presentation will pass quickly to a critique. The critique brings Proclus' image of the soul into focus, as it disentangles the knot of his immortality argument. thought , in the preparatory conclusion of Chapter 7. Many readers may imagine the critical material to be unnecessary, or even pointless. It is neither; but here I think a longwinded explanation would take us too far afield, so I'll refrain. Chapter 7 will come soon enough. Only, here especially I must beg for the reader's patience and trust. We take up the seamed volume. Leather opens to paper, paper opens to words.

56. Proclus Diadochus 1560 proclus Diadochus 1560. First edition in Latin and a very fresh copy of this handsome book; this is one of proclus most important writings. http://homepage.sunrise.ch/mysunrise/geissbuehler/pic_of_the_month_042002_02.htm

Geometricum Books and Instruments from 15th to 18th Century HOME BOOKS INSTRUMENTS PIC of MONTH ... SEARCH Proclus Diadochus 1560 Proclus Diadochus In Primum Euclidis Elementorum librum Commentariorum ad Universam Mathematicam Disciplinam Principium Eruditionis Tradentium Libri IIII. Folio, Holzschnittportrait auf der Rückseite des Titels mit vielen Holzschnittdiagrammen. Die Extrakte von Euclid sind mit gestochenen Rahmen eingefasst. Neuer Pergamenteinband. Padua, Gratiosus Perchacinus, 1560 First edition in Latin and a very fresh copy of this handsome book; this is one of Proclus' most important writings. "A Venetian patrician, Barocius [Barozzi] received a humanistic education and achieved an admirable command of Greek and Latin. He studied at the University of Padua and according to his own account, lectured there about 1559 on the Sphere of Sacrobosco. Barocius' edition of Proclus' commentary on the first book of Euclid 's Elements was the first important translation of this work, for it was based on better manuscripts than previous efforts had been. The translation, published at Venice in 1560, was completed by Barocius at the age of twenty-two."D.S.B., I, p. 468.

57. Proclus proclus(Commentaire sur le Timée). Dieu bâtit une http://nitram.lsdp.net/proclus.HTML

En voici quelques unes, extraites de l'ouvrage de Flammarion: Accueil Suite

58. Proclus proclus, 410 485. proclus, a Neoplatonist, was an influence on Amos Bronson Alcott, Ralph Waldo Emerson, Margaret Fuller, as well http://www.alcott.net/alcott/home/champions/Proclus.html

Proclus, 410 - 485 Proclus, a Neoplatonist, was an influence on Amos Bronson Alcott Ralph Waldo Emerson Margaret Fuller , as well as other New England Transcendentalists. As the last major Greek philosopher, and elaborated upon by Damascius , Proclus codified later Platonism, offering not only a coherent metaphysical system but a complete pagan theology. By combining his own views with those of his teachers Plutarch , Syrianus, Porphyry , and Iamblichus

59. Siorvanes/PROCLUS proclus NeoPlatonic Philosophy and Science Lucas Siorvanes Siorvanes s extensive original research presents proclus as much more than just a metaphysician. http://www.yale.edu/yup/books/068069.htm

PROCLUS Neo-Platonic Philosophy and Science Lucas Siorvanes 1997 Philosophy 356 pp. 6 1/8 x 9 1/4 Cloth ISBN 0-300-06806-9 Proclus, head of the Philosophy School at Athens for fifty years, was one of the leading philosophical figures in Late Antiquity. Lucas Siorvanes here introduces Proclus to English-language readers, discussing his metaphysics and theory of knowledge and focusing in particular on his Neo-Platonism. Proclus lived in the turbulent fifth century A.D., a time of struggles among Christians, Jews, and pagans, the invasion of Attila the Hun, the fall of the Western Roman Empire, and the rise of the Eastern Roman Empire in Byzantium. While Late Antiquity has been regarded as a time of superstition and forbiddingly complex philosophies, recent scholarship has shown it to be full of cultural and intellectual vigor. During Proclus's tenure as head of the Philosophy School, he systematized Neo-Platonism as the summit of ancient Greek thought, brought it to its peak of influence, and became responsible for the form in which it was transmitted to the Byzantine, Western European, and Islamic civilizations. Siorvanes's extensive original research presents Proclus as much more than just a metaphysician. He surveys all of Proclus's philosophical interestsincluding religion, physics, astronomy, mathematics, and poetryrevealing the philosopher's central concern with the problems of being and knowledge and relating the ideas of Proclus to those of such other major thinkers as Plato, Aristotle, and Ptolemy. To help the newcomer, Siorvanes supplies more than 200 quotations from Proclus's works. He also traces the impact of Proclus's Neo-Platonism across cultures, religions, and centuries, in such diverse areas as Christian and Islamic theologies, Renaissance art, Kepler's astronomy, Romantic poetry, Emerson's thought, modern philosophy and science, and current popular phrases.

60. Carte Du Ciel Et Planètes Pour PROCLUS Translate this page Astrologie thème astral des célébrités, Carte du ciel et positions planétaires de proclus, né le 8 février 0412 à 09h00 à Byzance (Grèce). http://www.astrotheme.fr/portraits/jCAHRd68q3Zr.htm

L'Astrologie NEWS ** Webmasters / Services *** Marque Blanche *** ... Espace Membres Identifiant Mot de passe Mot de passe perdu ? Astrologie : thème astral des célébrités Carte du ciel et positions planétaires de PROCLUS, né le 8 février 0412 à 09h00 à Byzance (Grèce) Verseau 20°13 AS Bélier 6°04 PROCLUS Positions des planètes Soleil Verseau Lune Gémeaux Mercure Verseau Vénus Verseau Mars Capricorne Jupiter Taureau Saturne Taureau Uranus Verseau Neptune Taureau Pluton Taureau Chiron Poissons Cérès Balance Pallas Verseau Junon Scorpion Vesta Verseau Noeud Nord Scorpion Lilith Cancer Fortune Lion AS Bélier MC Capricorne Positions des maisons Maison 1 Bélier Maison 2 Taureau Maison 3 Gémeaux Maison 4 Cancer Maison 5 Cancer Maison 6 Lion Maison 7 Balance Maison 8 Scorpion Maison 9 Sagittaire Maison 10 Capricorne Maison 11 Capricorne Maison 12 Verseau Liste des aspects Mars Conjonction MC Orbe Neptune Conjonction Pluton Orbe Jupiter Conjonction Saturne Orbe Soleil Conjonction Vénus Orbe Jupiter Conjonction Pluton Orbe Jupiter Conjonction Neptune Orbe Vénus Conjonction Uranus Orbe Saturne Conjonction Pluton Orbe Saturne Conjonction Neptune Orbe Soleil Conjonction Uranus Orbe Saturne Carré Uranus Orbe Soleil Carré Neptune Orbe Soleil Carré Pluton Orbe Vénus Carré Jupiter Orbe Vénus Carré Pluton Orbe Vénus Carré Neptune Orbe Jupiter Carré Uranus Orbe Mars Carré AS Orbe Vénus Carré Saturne Orbe Soleil Carré Jupiter Orbe Uranus Carré Pluton Orbe Uranus Carré Neptune Orbe Soleil Carré Saturne Orbe Soleil Trigone Lune Orbe Lune Trigone Vénus Orbe Mercure Sextile AS Orbe Mars Sextile Uranus Orbe Uranus Sextile MC Orbe Neptune SemiCarré AS Orbe Pluton SemiCarré AS Orbe Soleil SemiCarré AS Orbe

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