101. Cryptozoology.com The statement euclid s geometry is an accurate description of the real But euclid s geometry itself only says that IF euclid s axioms are true in a http://www.cryptozoology.com/forum/topic_view_thread.php?tid=11&pid=241027

102. KEGP According to Kant, therefore, euclid s geometrical system is a transcendental abstraction from actual experience, and only because of this factnot because http://www.hkbu.edu.hk/~ppp/srp/arts/KEGP.html

KANT ON EUCLID: GEOMETRY IN PERSPECTIVE by Stephen Palmquist stevepq@hkbu.edu.hk I. The Perspectival Aim of the first Critique There is a common assumption among philosophers, shared even by many Kant-scholars, that Kant had a naive faith in the absolute valid­ity of Euclidean geometry, Aristotelian logic, and Newtonian physics, and that his primary goal in the Critique of Pure Reason was to pro­vide a rational foundation upon which these classical scientific theories could be based. This, it might be thought, is the essence of his attempt to solve the problem which, as he says in a footnote to the second edition Preface, "still remains a scandal to philosophy and to human reason in general"namely, "that the existence of things outside us...must be accepted merely on faith , and that if anyone thinks good to doubt their existence, we are unable to counter his doubts by any satisfactory proof" [K2:xxxix]. This assumption, in turn, is frequently used to deny the validity of some or all of Kant's philosophical projector at least its relevance to modern philosophi­cal understandings of scientific knowledge. Swinburne, for instance, asserts that an acceptance of the views expressed in Kant's first Critique "would rule out in advance most of the great achievements of science since his day."

103. Saccheri S Solution To Euclid S BLEMISH euclid s flaw . The discovery of these two geometries resulted from a (euclid Freed of Every Flaw A geometrical work in which are established the http://www.faculty.fairfield.edu/jmac/sj/sacflaw/sacflaw.htm

104. Euclid Book I of 1847; David Joyce s Java edition of euclid. Elizabeth Tuttle s wonderful guide to reading reading euclid in Greek; The Perseus project s Greek text of http://www.math.ubc.ca/~cass/Euclid/

Oliver Byrne's edition of 1847 David Joyce's Java edition of Euclid Elizabeth Tuttle's wonderful guide to reading reading Euclid in Greek The Perseus project's Greek text of Euclid The Perseus project's collection of Heath's comments from his English edition of Euclid The integrated text (Byrne, Joyce, and Heath) at UBC Introduction Book I Book II Book III ... Book XIII A local collection of proofs of Pythagoras' Theorem in Java A Latin dictionary A precursor - YBC 7289 The Oxyrhynchus papyrus with the diagram for II.5 Euclid in the Middle Ages , including a complete copy of a survey article and a list of extant manuscripts by Dr. Menso Folkerts. On Erhard Ratdolt , publisher of the 1482 edition of Euclid (the very first, based on the somewhat faulty medieval edition produced by Campanus) Images from Ratdolt's edition Images from the first English edition of 1582 Selections from Sir Charles Thomas-Stanford's commentary on editions of Euclid Ralph Abraham's Visual elements The Euclid collection at University College, London

105. Greek Mathematics And Its Modern Heirs euclid s Optics is the earliest surviving work on geometrical optics, and is generally found in Greek manuscripts along with elementary works on spherical http://www.ibiblio.org/expo/vatican.exhibit/exhibit/d-mathematics/Greek_math.htm

Greek Mathematics and its Modern Heirs Classical Roots of the Scientific Revolution Euclid, Elements In Greek, Ninth century Euclid's "Elements," written about 300 B.C., a comprehensive treatise on geometry, proportions, and the theory of numbers, is the most long-lived of all mathematical works. This manuscript preserves an early version of the text. Shown here is Book I Proposition 47, the Pythagorean Theorem: the square on the hypotenuse of a right triangle is equal to the sum of the squares on the sides. This is a famous and important theorem that receives many notes in the manuscript. Vat. gr. 190, vol. 1 fols. 38 verso - 39 recto math01 NS.01 Archimedes, Works In Latin, Translated by Jacobus Cremonensis, ca. 1458 In the early 1450's, Pope Nicholas V commissioned Jacobus de Sancto Cassiano Cremonensis to make a new translation of Archimedes with the commentaries of Eutocius. This became the standard version and was finally printed in 1544. This early and very elegant manuscript may have been in the possession of Piero della Francesca before coming to the library of the Duke of Urbino. The pages displayed here show the beginning of Archimedes' "On Conoids and Spheroids" with highly ornate, and rather curious, illumination. Urb. lat. 261 fol. 44 verso - 45 recto math02 NS.17

106. Non-Euclidean Geometries, Discovery History of the dicovery of noneuclidean geometries. So Riemann modified euclid s Postulates 1, 2, and 5 to. Two distinct points determine at least one http://www.cut-the-knot.com/triangle/pythpar/Drama.shtml

Username: Password: Sites for teachers Sites for parents Awards Interactive Activities ... Sites for parents Non-Euclidean Geometries Drama of the Discovery Four names - C.F.Gauss N.Lobachevsky J.Bolyai (1802-1860), and B.Riemann (1826-1846) - are traditionally associated with the discovery of non-Euclidean geometries. In non-Euclidean geometries, the fifth postulate is replaced with one of its negations : through a point not on a line, either there is none (B) or more than 1 (C) line parallel to the given one. Carl Friedrich Gauss was apparently the first to arrive at the conclusion that no contradiction may be obtained this way. In a private letter of 1824 Gauss wrote: The assumption that (in a triangle) the sum of the three angles is less than 180 o leads to a curious geometry, quite different from ours, but thoroughly consistent, which I have developed to my entire satisfaction. From another letter of 1829, it appears that Gauss was hesitant to publish his research because he suspected the mediocre mathematical community would not be able to accept a revolutionary denial of Euclid's geometry. Gauss invented the term "Non-Euclidean Geometry" but never published anything on the subject. On the other hand, he introduced the idea of surface curvature on the basis of which Riemann later developed Differential Geometry that served as a foundation for Einstein's General Theory of Relativity.

107. Adventures In CyberSound: Euclid euclid s The Optics is the earliest surviving work on geometrical optics, and is generally found in Greek manuscripts along with elementary works on http://www.acmi.net.au/AIC/EUCLID_BIO.html

A D V E N T U R E S in C Y B E R S O U N D Euclid (alt: Euklid, Eucleides) : 365 - 300 BC Euclid's The Optics is the earliest surviving work on geometrical optics, and is generally found in Greek manuscripts along with elementary works on spherical astronomy. There were a number of medieval Latin translations, which became of new importance in the fifteenth century for the theory of linear perspective. This technique is beautifully illustrated in the miniature of a street scene in this elegant manuscript from the library of the Duke of Urbino. It may once have been in the possession of Piero della Francesca, who wrote one of the principal treatises on perspective in painting. Source: The Vatican Library Euclid , Greek Eucleides (fl. c. 300 BC, Alexandria), the most prominent mathematician of Greco-Roman antiquity, best known for his treatise on geometry, the Elements Life and work Of Euclid's life it is known only that he taught at and founded a school at Alexandria in the time of Ptolemy I Soter , who reigned from 323 to 285/283 BC. Medieval translators and editors often confused him with the philosopher

108. NonEuclid - Hyperbolic Geometry Article + Software Applet NonEuclid is a software simulation offering straightedge and compass constructions in hyperbolic geometry. http://math.rice.edu/~joel/NonEuclid/

NonEuclid NonEuclid is Java Software for Interactively Creating Ruler and Compass Constructions in both the for use in High School and Undergraduate Education. Hyperbolic Geometry is a geometry of Einstein's General Theory of Relativity and Curved Hyperspace. NonEuclid has moved. The new location is: http://cs.unm.edu/~joel/NonEuclid/

109. People In The History Of Astronomy Short biographies of Pythagoras, Ptolemy, Copernicus, Kepler, Galileo, Newton, Halley, Einstein, and Hawking. http://www.geocities.com/CapeCanaveral/Launchpad/4515/HISTORY.html

People In The History Of Astronomy Background Pythagoras Ptolemy Copernicus ... Stephen Hawking Background          One of the most powerful creations of Greek science was the mathematical astronomy created by Hipparchus in the second century B.C. and given final form by Ptolemy in the second century A.D. Ptolemy's work was known in the Middle Ages through imperfect Latin versions. In fifteenth-century Italy, however, it was brought back to life. George Trebizond, a Cretan emigre in the curia, produced a new translation and commentary. These proved imperfect and aroused much heated criticism. But a German astronomer, Johannes Regiomontanus, a protege of the brilliant Greek churchman Cardinal Bessarion, came to Italy with his patron, learned Greek, and produced a full-scale "Epitome" of Ptolemy's work from which most astronomers learned their art for the next century and more. Copernicus was only one of the celebrities of the Scientific Revolution whose work rested in large part on the study of ancient science carried out in fifteenth-century Italy. (The Revival Of An Ancient Science) Pythagoras (582–c.507 B.C)

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