Read complete books and articles on: Euclid

Euclid - yooˈklĭd, fl. 300 b.c., Greek mathematician. Little is known of his life other than the fact that he taught at Alexandria, being associated with the school that grew up there in the late 4th cent. b.c. He is famous for his Elements, a presentation in thirteen books of the geometry and other mathematics known in his day. The first six books cover elementary plane geometry and have served since as the basis for most beginning courses on this subject. The other books of the Elements treat the theory of numbers and certain problems in arithmetic (on a geometric basis) and solid geometry, including the five regular polyhedra, or Platonic solids. The great contribution of Euclid was his use of a deductive system for the presentation of mathematics. Primary terms, such as point and line, are defined; unproved assumptions, or postulates, regarding these terms are stated; and a series of statements are then deduced logically from the definitions and postulates. Although Euclid's system no longer satisfies modern requirements of logical rigor, its importance in influencing the direction and method of the development of mathematics is undisputed. One consequence of the critical examination of Euclid's system was the discovery in the early 19th cent. that his fifth postulate, equivalent to the statement that one and only one line parallel to a given line can be drawn through a point external to the line, can not be proved from the other postulates; on the contrary, by substituting a different postulate for this parallel postulate two different self-consistent forms of non-Euclidean geometry were deduced, one by Nikolai I. Lobachevsky (1826) and independently by János Bolyai (1832) and another by Bernhard Riemann (1854). A few modern historians have questioned Euclid's authorship of the Elements, but he is definitely known to have written other works, most notably the Optics.

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10 of the Best Books and Articles on: Euclid

as selected by Questia librarians

1.

The Great Mathematicians (Chap. III "Alexandria: Euclid, Archimedes, and Apollonius") » Read Now
by Herbert Westren Turnbull. 146 pgs.

Collections: History, Entire Library

...SCHOOL 18 III. ALEXANDRIA: EUCLID, ARCHIMEDES AND APOLLONIUS 34...just as, through the discovery of non-Euclidean systems, geometry became geometries. This...Menaechmus ?...
2.

The Infinite in the Finite (Chap. 10 "The Elements of Euclid") » Read Now
by Alistair Macintosh Wilson. 532 pgs.

Collections: Entire Library

This book is an extended history of mathematics that places mathematical development firmly in its historical context. Each section begins with a description of the geography and history of the country considered. From there, lively retelling of the creation myths and legends leads on to a...
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This book is an extended history of mathematics that places mathematical development firmly in its historical context. Each section begins with a description of the geography and history of the country considered. From there, lively retelling of the creation myths and legends leads on to a description of how its people wrote and counted. This is followed by relevant mathematical material. The book covers; * The geometry of stone circles in Europe * The area of triangles and volume of pyramids that concerned the engineers of the Pharoahs * The Babylonian sexagesimal number system and our present measures of space and time which grew out of it * The use of the abacus and remainder theory in China * Greek mathematics from Pythagoras to Pappus. Detailed accounts of the work of apollonius and Archimedes are given. * The invention of trigonometry by Arab mathematicians * The solution of quadratic equations by completing the square developed in India Each chapter has a mathematical case study which is discussed both in the context of thetimes and in th light of more recent developments. Worked examples are also included. "The author has woven together a broad historical backgrounding and some fairly detailed but accessible mathematics in amost exciting way." John Fauvel, author of Let Newton Be!
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3.

Mathematical Sorcery: Revealing the Secrets of Numbers ("The Elements of Euclid" begins on p. 42) » Read Now
by Calvin C. Clawson. 304 pgs.

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Calvin Clawson has a unique talent for opening the door, for the uninitiated, to the splendors of mathematics. In this captivating quest for pure knowledge, he takes us on a journey to the amazing discoveries of our ancient ancestors. He divulges the wisdom of the ancient Greeks, Sumerians...
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Calvin Clawson has a unique talent for opening the door, for the uninitiated, to the splendors of mathematics. In this captivating quest for pure knowledge, he takes us on a journey to the amazing discoveries of our ancient ancestors. He divulges the wisdom of the ancient Greeks, Sumerians, Babylonians, and Egyptians, whose stunning revelations have deep meaning to this day.
The secrets of the constellations, the enigma of the golden mean, and the brilliance of a proof are just some of the breakthroughs Clawson explores with unbridled delight. Enabling us to appreciate the achievements of Newton and other intellectual giants is his singular talent. But he takes us one step further. Clawson inspires us through his eloquence and zeal to actually do mathematics. Transporting us beyond an appreciation, he urges us to leap to the next level. He helps us intuitively comprehend and follow the very building blocks of the stately but mysterious edifices that too long have been forbidden, including infinity, functions, and the limit. By accompanying him on this journey, we taste the fruit of knowledge that has eluded us until now.
Mathematical Sorcery is Clawson's greatest work. By trusting in his intuitive approach, we sample the sumptuous delights of the greatest minds in the history of civilization.
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4.

Ancient Mathematics ("Euclid" begins on p. 88) » Read Now
by S. Cuomo. 290 pgs.

Collections: History, Entire Library

The theorem of Pythagoras, Euclid's "Elements", Archimedes' method to find the volume of a sphere: all parts of the invaluable legacy of ancient mathematics. But ancient mathematics was also about counting and measuring, surveying land and attributing mystical significance to the number six.This...
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The theorem of Pythagoras, Euclid's "Elements", Archimedes' method to find the volume of a sphere: all parts of the invaluable legacy of ancient mathematics. But ancient mathematics was also about counting and measuring, surveying land and attributing mystical significance to the number six.This volume offers the first accessible survey of the discipline in all its variety and diversity of practices. The period covered ranges from the fifth century BC to the sixth century AD, with the focus on the Mediterranean region. Topics include:* mathematics and politics in classical Greece* the formation of mathematical traditions* the self-image of mathematicians in the Graeco-Roman period* mathematics and Christianity* and the use of the mathematical past in late antiquity.
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5.

Studies in the History and Methods of the Sciences (Chap. III "Elements of Geometry: Euclid") » Read Now
by Arthur David Ritchie. 230 pgs.

Collections: History, Entire Library

...III. ELEMENTS OF GEOMETRY: EUCLID 24...be even more shaking of heads over Euclid Elements ; a mere textbook, mostly a...should remember Hobbes attempt to define Euclidean...
6.

History of the Sciences in Greco-Roman Antiquity (Discussion of Euclid begins on p. 66 and "The Elements of Euclid- Methods of Demonstration- Axioms and Postulates" begins on p. 150) » Read Now
by Arnold Reymond, Ruth Gheury De Bray. 248 pgs.

Collections: History, Entire Library
7.

The Art of the Infinite: The Pleasures of Mathematics (Chap. Five "Euclid Alone") » Read Now
by Ellen Kaplan, Robert Kaplan. 324 pgs.

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Robert Kaplan's The Nothing That Is: A Natural History of Zero was an international best-seller, translated into ten languages. The Times called it "elegant, discursive, and littered with quotes and allusions from Aquinas via Gershwin to Woolf" and The Philadelphia Inquirer praised it as "absolutely...
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Robert Kaplan's The Nothing That Is: A Natural History of Zero was an international best-seller, translated into ten languages. The Times called it "elegant, discursive, and littered with quotes and allusions from Aquinas via Gershwin to Woolf" and The Philadelphia Inquirer praised it as "absolutely scintillating." In this delightful new book, Robert Kaplan, writing together with his wife Ellen Kaplan, once again takes us on a witty, literate, and accessible tour of the world of mathematics. Where The Nothing That Is looked at math through the lens of zero, The Art of the Infinite takes infinity, in its countless guises, as a touchstone for understanding mathematical thinking. Tracing a path from Pythagoras, whose great Theorem led inexorably to a discovery that his followers tried in vain to keep secret (the existence of irrational numbers); through Descartes and Leibniz; to the brilliant, haunted Georg Cantor, who proved that infinity can come in different sizes, the Kaplans show how the attempt to grasp the ungraspable embodies the essence of mathematics. The Kaplans guide us through the "Republic of Numbers," where we meet both its upstanding citizens and more shadowy dwellers; and we travel across the plane of geometry into the unlikely realm where parallel lines meet. Along the way, deft character studies of great mathematicians (and equally colorful lesser ones) illustrate the opposed yet intertwined modes of mathematical thinking: the intutionist notion that we discover mathematical truth as it exists, and the formalist belief that math is true because we invent consistent rules for it. "Less than All," wrote William Blake, "cannot satisfy Man." The Art of the Infinite shows us some of the ways that Man has grappled with All, and reveals mathematics as one of the most exhilarating expressions of the human imagination.
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8.

Makers of Science: Mathematics, Physics, Astronomy ("Euclid" begins on p. 34) » Read Now
by Ivor B. Hart, Charles Singer. 324 pgs.

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...adjoining lands 33 9. Euclids Proof by Exhaustion 37...regard to the right-angled triangle Euclid I , 47 commonly referred to as the theorem of Pythagoras. The proof given...
9.

A Concise History of Mathematics (Discussion of Euclid begins on p. 58) » Read Now
by Dirk J. Struik. 302 pgs.

Collections: History, Entire Library
10.

History of Western Philosophy (Chap. 24 "Early Greek Mathematics and Astronomy") » Read Now
by Bertrand Russell. 780 pgs.

Collections: Philosophy, Entire Library

First published in 1946, History of Western Philosophy went on to become the best-selling philosophy book of the twentieth century. A dazzlingly ambitious project, it remains unchallenged to this day as the ultimate introduction to Western philosophy. Providing a sophisticated overview of the...
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First published in 1946, History of Western Philosophy went on to become the best-selling philosophy book of the twentieth century. A dazzlingly ambitious project, it remains unchallenged to this day as the ultimate introduction to Western philosophy. Providing a sophisticated overview of the ideas that have perplexed people from time immemorial, it is 'long on wit, intelligence and curmudgeonly scepticism', as the New York Times noted, and it is this, coupled with the sheer brilliance of its scholarship, that has made Russell's History of Western Philosophy one of the most important philosophical works of all time.
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