61. High School Euclid Paper euclid is Data , concerning the solution of problems through geometric analysis, 7 Lobachevsky s geometry grew out of his unsuccessful attempts to http://www.obkb.com/dcljr/euclidhs.html

High school Euclid paper jump to... text of paper Endnotes Bibliography bottom of page Euclid and his Elements One of the most influential mathematicians of ancient Greece, Euclid flourished around 300 B.C. Not much is known about the life of Euclid. One story which reveals something about Euclid's character concerns a pupil who had just completed his first lesson in geometry. The pupil asked what he would get from learning geometry. So Euclid told his slave to give the pupil a coin so he would be gaining something from his studies. Included in the many works of Euclid is Data , concerning the solution of problems through geometric analysis, On Divisions (of Figures) , the Optics , the Phenomena , a treatise on spherical geometry for astronomers, several lost works on higher geometry, and the Elements , a thirteen volume textbook on geometry. The Elements , which surely became a classic soon after its publication, eventually became the most influential textbook in the history of civilization. In fact, it has been said that apart from the Bible , the Elements is the most widely read and studied book in the world.

62. Euclid euclid s decision to make this a postulate led to euclidean geometry. euclid s geometric solution of a quadratic equation; The five regular polyhedra http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Euclid.html

Euclid of Alexandria Born: about 325 BC Died: about 265 BC in Alexandria, Egypt Click the picture above to see six larger pictures Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Version for printing Euclid of Alexandria is the most prominent mathematician of antiquity best known for his treatise on mathematics The Elements . The long lasting nature of The Elements must make Euclid the leading mathematics teacher of all time. However little is known of Euclid's life except that he taught at Alexandria in Egypt. Proclus , the last major Greek philosopher, who lived around 450 AD wrote (see [1] or [9] or many other sources):- Not much younger than these pupils of Plato is Euclid, who put together the "Elements", arranging in order many of Eudoxus 's theorems, perfecting many of Theaetetus 's, and also bringing to irrefutable demonstration the things which had been only loosely proved by his predecessors. This man lived in the time of the first Ptolemy; for Archimedes , who followed closely upon the first Ptolemy makes mention of Euclid, and further they say that Ptolemy once asked him if there were a shorted way to study geometry than the Elements, to which he replied that there was no royal road to geometry. He is therefore younger than Plato 's circle, but older than

63. References For Euclid E Filloy, geometry and the axiomatic method. IV euclid (Spanish), Mat. SR Palmquist, Kant on euclid geometry in perspective, Philos. Math. http://www-groups.dcs.st-and.ac.uk/~history/References/Euclid.html

References for Euclid Version for printing Biography in Dictionary of Scientific Biography (New York 1970-1990). Biography in Encyclopaedia Britannica. Books: J L Berggren and R S D Thomas, Euclid's 'Phaenomena' : A translation and study of a Hellenistic treatise in spherical astronomy (Princeton, NJ, 1996). H L L Busard, The Latin translation of the Arabic version of Euclid's 'Elements' commonly ascribed to Gerard of Cremona (Leiden, 1984). H L L Busard (ed.), The Mediaeval Latin translation of Euclid's 'Elements' : Made directly from the Greek (Wiesbaden, 1987). C B Glavas, The place of Euclid in ancient and modern mathematics (Athens, 1994). D H Fowler, The mathematics of Plato's academy : a new reconstruction (Oxford, 1987). P M Fraser, Ptolemaic Alexandria (3 vols.) (Oxford, 1972). T L Heath, A history of Greek mathematics (Oxford, 1931). T L Heath, The Thirteen Books of Euclid's Elements (3 Volumes) (New York, 1956). J Itard, (Paris, 1962). S Ito, The medieval Latin translation of the 'Data' of Euclid (Boston, Mass., 1980).

64. 10.8. Euclid (330?-275? B.C.) euclid replied, There is no royal road to geometry and sent the king to study. euclid s fame comes from his writings, especially his masterpiece Elements. http://www.shu.edu/projects/reals/history/euclid.html

10.8. Euclid (330?-275? B.C.) IRA Euclid is one of the most influential and best read mathematician of all time. His prize work, Elements , was the textbook of elementary geometry and logic up to the early twentieth century. For his work in the field, he is known as the father of geometry and is considered one of the great Greek mathematicians. Very little is known about the life of Euclid. Both the dates and places of his birth and death are unknown. It is believed that he was educated at Plato's academy in Athens and stayed there until he was invited by Ptolemy I to teach at his newly founded university in Alexandria. There, Euclid founded the school of mathematics and remained there for the rest of his life. As a teacher, he was probably one of the mentors to Archimedes Personally, all accounts of Euclid describe him as a kind, fair, patient man who quickly helped and praised the works of others. However, this did not stop him from engaging in sarcasm. One story relates that one of his students complained that he had no use for any of the mathematics he was learning. Euclid quickly called to his slave to give the boy a coin because "he must make gain out of what he learns." Another story relates that Ptolemy asked the mathematician if there was some easier way to learn geometry than by learning all the theorems. Euclid replied, "There is no royal road to geometry" and sent the king to study. Euclid's fame comes from his writings, especially his masterpiece

65. Euclid It was only in the 19th century that the limitation of euclid s geometry as euclid raised geometry to the highest level and he published 13 books called http://www.angelfire.com/ks/learning/euclid.html

setAdGroup('67.18.104.18'); var cm_role = "live" var cm_host = "angelfire.lycos.com" var cm_taxid = "/memberembedded" Search: Lycos Angelfire Aeon Flux Share This Page Report Abuse Edit your Site ... Next **EUCLID** [334? - 280 B.C.] or [325 - 270 B.C.] By Arun Kumar Tripathi Darmstadt University of Technology, Germany WHO has not heard of Euclid during his first lessons in geometry in the School? He created the geometry of the universe on which Newton built his laws of gravitation and motion. It was only in the 19th century that the limitation of Euclid's geometry as applied to space was first discovered by Nicholas Lobatchevsky, and later by Einstein who completely repudiated the Euclidean geometry in his Relativity Theory. However, Euclidean geometry and the Newtonian laws are the one which are most valid on earth. The great Greek mathematician Euclid, whose book on geometry has struck fear into teenagers' hearts for two millennia. Although he apparently studied at Plato's Academy in Athens, Euclid's home was Alexandria, Egypt, where he worked during the reign of King Ptolemy one of many Egyptian kings of the same name. (By the way, Ptolemy was not the astronomer Claudius Ptolemaeus known for the "Ptolemaic system" that identified the Earth as the center of the universe.) EARLY DAYS Euclid seemed to have studied in Plato's Academy, the then best known school of Mathematics a "Cambridge of Greece". He was believed to be a "Phoenician" with a "Greek outlook". It was the period when Alexander of Macedonia, after his world conquest, had established the township of Alexandria in Egypt. Ptolemy, the governor of Alexandria in Egypt, was a great learned man and he founded the great university of Alexandria which surpassed even Plato's Academy. There Euclid was invited to teach geometry.

66. Euclid (c. 300 BC) Library Of Congress Citations Subjects geometry Early works to 1800. euclid s Elements. English References euclid. euclides elements of geometry the first VI books euclid. http://www.mala.bc.ca/~mcneil/cit/citlceuclid1.htm

Euclid (c. 300 BC) : Library of Congress Citations The Little Search Engine that Could Down to Name Citations LC Online Catalog Amazon Search Book Citations [First 20 Records] Author: Byrne, Oliver. Title: The first six books of the elements of Euclid, in which coloured diagrams and symbols are used instead of letters for the greater ease of learners. By Oliver Byrne ... Published: London, W. Pickering, 1847. Description: xxix, 268 p. col. illus. 25 cm. LC Call No.: QA451 .B99 Subjects: Euclid. Elements. Control No.: 03019358 //r84 Author: Euclid. Uniform Title: Elements. French Title: Les belbemens de gbeombetrie d'Euclide, traduits littberalement, et suivis d'un traitbe du cercle, du cylindre, du ccone et de le sphaere, de la mesure des surfaces et des solides, avec des notes. Edition: 2. bed., augm. du cinquiaeme livre, par F. Peyrard ... Ouvrage approvbe par l'Institut, et adoptbe par le gouvernement pour les bibliothaeques des lycbees ... Published: Paris, F. Louis, 1809. Description: xii, 578 p. 270 diagr. on 9 fold. pl. 20 cm. LC Call No.: QA31 .E8755 1809 Other authors: Peyrard, F. (Franpcois), 1760-1822, ed. Control No.: 03020858 //r90 Author: Rabinovitch, Israel Euclid, b. 1861. Title: The foundations of the Euclidian geometry as viewed from the standpoint of kinematics ... by Israel Euclid Rabinovitch ... Published: New York, The author, 1903. Description: xi, 116 p. diagrs. 23 cm. LC Call No.: QA681 .R14 Notes: Thesis (Ph.D.)Johns Hopkins university. "Autobiography." "List of works quoted in the introduction or consulted by the author in preparing the dissertation": p. x-xi. Subjects: Geometry Foundations. Control No.: 04001882 //r882

67. Euclid, Greek Mathematician. The Columbia Encyclopedia, Sixth Edition. 2001-05 The first six books cover elementary plane geometry and have served since as The great contribution of euclid was his use of a deductive system for the http://www.bartleby.com/65/eu/Euclid.html

Select Search All Bartleby.com All Reference Columbia Encyclopedia World History Encyclopedia Cultural Literacy World Factbook Columbia Gazetteer American Heritage Coll. Dictionary Roget's Thesauri Roget's II: Thesaurus Roget's Int'l Thesaurus Quotations Bartlett's Quotations Columbia Quotations Simpson's Quotations Respectfully Quoted English Usage Modern Usage American English Fowler's King's English Strunk's Style Mencken's Language Cambridge History The King James Bible Oxford Shakespeare Gray's Anatomy Farmer's Cookbook Post's Etiquette Bulfinch's Mythology Frazer's Golden Bough All Verse Anthologies Dickinson, E. Eliot, T.S. Frost, R. Hopkins, G.M. Keats, J. Lawrence, D.H. Masters, E.L. Sandburg, C. Sassoon, S. Whitman, W. Wordsworth, W. Yeats, W.B. All Nonfiction Harvard Classics American Essays Einstein's Relativity Grant, U.S. Roosevelt, T. Wells's History Presidential Inaugurals All Fiction Shelf of Fiction Ghost Stories Short Stories Shaw, G.B. Stein, G. Stevenson, R.L. Wells, H.G. Reference Columbia Encyclopedia PREVIOUS NEXT ... BIBLIOGRAPHIC RECORD The Columbia Encyclopedia, Sixth Edition. Euclid, Greek mathematician

68. Nrich.maths.org::Mathematics Enrichment::How Many Geometries Are There? Just over 2000 years ago the Greek geometer euclid laid down the foundations of geometry, and it is clear that euclid s geometry will not work there. http://nrich.maths.org/public/viewer.php?obj_id=1386&part=index&refpage=monthind

69. Greek For Euclid euclid s geometry is not the only geometry. Even euclid knew that geometry on the surface of a sphere was different, but he had a concrete idea of http://www.du.edu/~etuttle/classics/nugreek/lesson17.htm

The postulates are the basis on which the whole structure of the Elements is built, and they must be carefully constructed. Euclid gave five postulates, of which the first three are of remarkable simplicity. The final two actually contain the essential specification of Euclidean space. Many commentators have moved them erroneously to common notions, or have tried to prove them from the other postulates. These are misguided efforts that miss the point completely. Euclid's geometry is not the only geometry. Even Euclid knew that geometry on the surface of a sphere was different, but he had a concrete idea of three-dimensional space that his geometry was to represent. In fact, it does so very well. The departures from Euclidean geometry in the neighbourhood of the Earth are extremely small, less than those arising from drawing figures on a portion of the Earth's surface close to us. Euclid's results, are, eminently, true in a very practical sense. The fourth postulate is equivalent to a statement that angles and distances are unchanged by an arbitrary rotation or translation in space, and the fifth postulate that space is "flat" in a sense well-known in Riemannian geometry. These postulates are stated by Euclid in a form that is applicable to the course of reasoning in the Elements, and allow the proof of the necessary results. It is idle to try to prove these postulates; non-Euclidean geometries are well-known. The ai)th/mata are the things demanded, the postulates. The third-person imperative has no expressed subject; it means "let it be conceded that". The verb

70. Euclid, Greek Mathematician More on Greek mathematician euclid from Infoplease. geometry Types of geometry Types of geometry euclidean geometry, elementary geometry of two and http://www.infoplease.com/ce6/people/A0817817.html

in All Infoplease Almanacs Biographies Dictionary Encyclopedia Daily Almanac for Sep 21, 2005 Skip Navigation Home Almanacs ... Word of the Day Editor's Favorites Hispanic Heritage Month Hurricane Katrina Daylight Saving Time Ramadan ... Mississippi Infoplease Tools Periodic Table Conversion Tool Perpetual Calendar Year by Year ... Site Map College Center Scholarship Search College Resources Career Center Job Search Post Your Resume Continuing Ed. more . . . Search: Infoplease Info search tips Search: Biographies Bio search tips google_ad_client = 'pub-1894504138907931'; google_ad_width = 120; google_ad_height = 240; google_ad_format = '120x240_as'; google_ad_type = 'text'; google_ad_channel =''; google_color_border = ['336699','B4D0DC','DFF2FD','B0E0E6']; google_color_bg = ['FFFFFF','ECF8FF','DFF2FD','FFFFFF']; google_color_link = ['0000FF','0000CC','0000CC','000000']; google_color_url = ['008000','008000','008000','336699']; google_color_text = ['000000','6F6F6F','000000','333333']; Encyclopedia Euclid [y OO Pronunciation Key Euclid , fl. 300 B.C.

71. Drew R. McCoy | An "Old-Fashioned" Nationalism: Lincoln, Jefferson, And The Clas 11 Specifically, euclid s geometry had become, by Jefferson s time, Like euclid s geometry, Newton s natural science was predicated on a set of axioms http://jala.press.uiuc.edu/23.1/mccoy.html

An "Old-Fashioned" Nationalism: Lincoln, Jefferson, and the Classical Tradition DREW R. MCCOY In 1870 the former vice-president of the Confederacy, Alexander H. Stephens, offered what has surely become the best-known characterization of Abraham Lincoln's nationalism. In Lincoln, Stephens suggested, the sentiment of Union "rose to the sublimity of a religious mysticism." A century later, in his entry for "nationalism" in The Abraham Lincoln Encyclopedia , Mark E. Neely, Jr., cited Stephens's famous comment but was quick to add that there was, in fact, "little that was mystical" about Lincoln's love for the Union. It was important to remember, Neely suggested, that Lincoln's political thought "never departed from the old Lockean universe of natural rights." His idea of American nationality was, therefore, not rooted in the mystical soil of nineteenth-century romanticism; it was solidly grounded in the principled bedrock of Thomas Jefferson's eighteenth-century preamble to the Declaration of Independence, and to that extent, Neely suggested, Lincoln's nationalism was "distinctly old-fashioned." Using Neely's caveat about Stephens's observation as its point of departure, this essay seeks to explore the "old-fashioned" character of Lincoln's nationalism from an unlikely, and fresh, perspective: its connection, via the Enlightenment, to classical antiquity.

72. Overview - Relativity - Emc2 For 2200 years euclid s geometry provided the best natural description of spatial relationships. Isaac Newton s laws of motion, his inverse square law of http://www.eequalsmcsquared.auckland.ac.nz/sites/index.cfm?64D27949-D632-1D26-2F

73. Projects 1993 euclid geometry Theorems Prover (co-author S.Kordic); the program euclid proves theorems of geometry in a human-oriented way and gives their proofs http://www.matf.bg.ac.yu/~janicic/projects.htm

Projects "Acting of Planar Discontinuous Isometry Groups - Computer Approach", including a software package HYP 1-2-3 with the full realisation of Poincare's model of a hyperbolical plane (C). "EUCLID - Geometry Theorems Prover" (co-author S.Kordic); the program EUCLID proves theorems of geometry in a human-oriented way and gives their proofs in a natural language form (PROLOG). "BonaParta - a Model of the Multitasking System" (co-author Vlado Keselj) (C). "Pentomino"; a program for the intellect-game of Pentomino (including a new, "gamma" algorithm for game-tree searching) ) (C). "GCLC"; The Geometry Constructions Language -> LaTeX format Converter (GC Language is a new language for defining pictures, especially those usual in geometry) (C). "Game-Maker"; a software shell for intellect game programs (including modules for the games of reversi and chess) (C). "EUCLID Geometry Theorems Prover C-version" (the second, improved release of the prover EUCLID) (C). "PNA-DP"; a program for using different decision procedures for Presburger arithmetic in the proof planner CLaM (PROLOG). "EPM"; a package for integrating decision procedures into the proof planner CLaM (PROLOG).

74. Euclid - Books I-IX According to Stobaeus10 , “some one who had begun to read geometry with euclid, when he had learnt the first theorem, asked euclid, ‘But what shall I http://www.headmap.org/unlearn/euclid/before/tradition.htm

@import url(../../../ul-css/3-col-nn4-new-main.css); the teS Euclids elements BOOKS I-IX translated by T.L. Heath BACKGROUND euclid and the traditions about him. euclid's other works. greek commentators on the elements ... modern algebraic interpretations [see also: equations - Diophantus; conics - Appolonius] HEADMAP home unlearning EUCLID BOOK I BOOK II BOOK III BOOK IV ... BOOK IX OVERVIEW book 1, triangles book 2, quadratics books 3 and 4, circles book 5, theory of proportion book 6, geometry and the theory of proportion books 7, 8 and 9 ,number theory GEOMETRICAL ALGEBRA book II identities gemetrical solution of quadratics application of areas transformation of areas ... Book V notes Book VII notes Book VIII notes Book IX notes Volume 1 [p. 1] CHAPTER I. EUCLID AND THE TRADITIONS ABOUT HIM. As in the case of the other great mathematicians of Greece, so in Euclid's case, we have only the most meagre particulars of the life and personality of the man. Most of what we have is contained in the passage of Proclus' summary relating to him, which is as follows “Not much younger than these (sc. Hermotimus of Colophon and Philippus of Medma) is Euclid, who put together the Elements, collecting many of Eudoxus' theorems, perfecting many of Theaetetus', and also bringing to irrefragable demonstration the things which were only somewhat loosely proved by his predecessors. This man lived

75. Geometry CHANGING SYSTEMS OF geometry FROM euclid TO KLEIN S PROGRAMME. Introduction. geometry. Origins of geometry The Golden Age of Greek Mathematics http://scitsc.wlv.ac.uk/university/scit/modules/mm2217/geometry.htm

CHANGING SYSTEMS OF GEOMETRY FROM EUCLID TO KLEIN'S PROGRAMME Introduction Geometry: Origins of Geometry The Golden Age of Greek Mathematics Projective Geometry New Geometry, New Worlds ... Module Leader These pages are maintained by M.I.Woodcock.

76. Nineteenth Century Geometry Klein s names for the geometries of euclid and Lobachevsky were one may say that the truth of the geometry of euclid is not incompatible with the truth http://plato.stanford.edu/entries/geometry-19th/

version history HOW TO CITE THIS ENTRY Stanford Encyclopedia of Philosophy A ... Z This document uses XHTML/Unicode to format the display. If you think special symbols are not displaying correctly, see our guide Displaying Special Characters last substantive content change MAR The Encyclopedia Now Needs Your Support Please Read How You Can Help Keep the Encyclopedia Free Nineteenth Century Geometry 1. Lobachevskian geometry 2. Projective geometry 3. Klein's Erlangen program 4. Axiomatics perfected ... Related Entries 1. Lobachevskian geometry Euclid (fl. 300 b.c.) placed at the head of his Elements aitemata 1. To draw a straight line from any point to any point. 3. To draw a circle with any center and any radius. Figure 1 In the darker ages that followed, Euclid's sense of mathematical freedom was lost and philosophers and mathematicians expected geometry to rest on self-evident grounds. Now, if a is perpendicular and b is almost perpendicular to PQ, a and b approach each other very slowly on one side of PQ and it is not self-evident that they must eventually meet somewhere on that side. After all, the hyperbole indefinitely approaches its asymptotes and yet, demonstrably, never meets them. Through the centuries, several authors demanded-and attempted-a proof of Euclid's Postulate. John Wallis (b. 1616, d. 1703) derived it from the assumption that there are polygons of different sizes that have the same shape. But then this assumption needs proof in turn. Girolamo Saccheri (b. 1667, d. 1733) tried

77. Philosophy Department Faculty University of Illinois at Chicago, April, 2001; Kant on the practice of euclid s geometry presented at University of Illinois, UrbanaChampaign, http://philosophy.osu.edu/people/person.cfm?ID=1338

78. The Beginnings Of Mathematics In Greece, Part 2 crisis that faced the Pythagoreans, and a bit of euclid s geometry. theory shifted from the Pythagoreans number theory to euclid s geometry. http://public.csusm.edu/DJBarskyWebs/330CollageSep03.html

The Beginnings of Mathematics in Greece, Part 2 Today's discussion was a continuation of the last discussion on mathematics in ancient Greece. Dr. Barsky started off with a general overview of what was going on in the world during the fifth century B.C.E. He spoke briefly of the Greek Persian Wars and how they established Greece as a major political power in the world. Dr. Barsky also talked about the Peloponnesian wars, which pitted Athens against Sparta, the assassination of Philip of Macedonia, and the rise to power of Alexander the Great. Alexander was a student of Aristotle, who was, in turn, a student of Plato. We then spent a little time talking about Aristotle. Aristotle, being a logician more than anything, stressed that mathematicians are more interested not in what is known, but rather how it is known. Next on the agenda was the Pythagoreans. Dr. Barsky told us that the Pythagoreans found incommensurability a crisis. They felt that, when measuring things, there should exist a single unit that could be used in such a way that anything being measured could be divided evenly by this unit. They didn't deal with irrational numbers. The Pythagoreans differentiated between number and magnitude. Numbers were theoretical; magnitudes were geometric. Dr. Barsky then did a proof of the statement "the square root of two is irrational." We then returned to the Pythagorean theorem, and a proof of it based on similarity of triangles. What intrigued me was how similar Euclid's proof was to Dr. Barsky's, yet at the same time how different the proofs were. They were both based on drawing a perpendicular from the side of the square on the hypotenuse to the vertex of the right triangle, and then showing that each rectangle created by this perpendicular had area equal to that of the square on one of the legs. But from that point, the proofs diverged, with Dr. Barsky's proof being very simple and Euclid's getting very involved and complex. The reason Euclid used such a difficult method was to avoid using the similarity of triangles. He had to do this because of the differentiation between number and magnitude.

79. The Freedom In Education Magazine Taking up a double side each month is a proposition of euclid s geometry. Written with great clarity, they prove through utterly simple logic that the world http://www.jamboree.freedom-in-education.co.uk/magazine/home education magazine.

The Freedom in Education magazine The Freedom in Education magazine can be ordered on our freedom-in-education website. Here is some information about it: What it is Freedom in Education is a monthly magazine which has been running for one and a half years. It combines the recipes, craft projects, gardening tips and cartoons which can be seen on this site, with the main article, on education, from the freedom-in-education site , plus letters, puzzles, news items, a literature page and Euclid's geometry. It is twenty-four sides long, with a colour cover, and black and white on the inside. It costs £12.00 for twelve issues. How it came about A magazine was an idea we had long been contemplating. In 2002 my father, Gareth, started his website and began a free e-newsletter, which quickly gained 1000 subscribers. It simply contained an article on education, but the response back was so encouraging, we decided to publish a printed version, with all the puzzles and cartoons which the medium of the internet didn't allow. It now has about 200 subscribers, and the letters we receive back from it are overwhelmingly positive. It has been called "

80. What Is Science? Summaries And Reviews By Joan Hughes Poincare demonstrates that euclid s geometry does not depend on experiment. euclid s geometry is deduced from three axioms which cannot be proved. http://www.mdx.ac.uk/www/study/Science.htm

A Middlesex University resource provided Joan Hughes and Andrew Roberts Joan Hughes is a retired experimental chemist investigating the epistemological theories of physical and social science. Click here for poems by Joan Hughes Social Science History by Andrew Roberts Empiricism, Theory and Imagination The Ideas of Locke, Hume and Wollstonecraft ... What is Science? Summaries and Reviews by Joan Hughes A summary from a Chemistry book Physical Chemistry by W. J. Moore, 1972 Science, Geometry, Imagination and Experiment A summary and review of: Science and Hypothesis by Henri Poincare Experience and Inference A summary and review of: Human Knowledge By Bertrand Russell (1948) Deductive Testing A summary and review of: The Logic of Scientific Discovery by Karl Popper (1934) Science, Technology and Engineering The word Originally, it just meant knowledge: scientia being Latin for knowledge. In medieval Europe, science might be theoretical understanding of truth as distinct from the moral understanding of one's conscience. Science could be any knowledge learnt by study. The different branches of study were also known as sciences. Medieval universities taught seven sciences, in two groups:

A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X  Y  Z

Page 4     61-80 of 109    Back | 1  | 2  | 3  | 4  | 5  | 6  | Next 20