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" A plane angle is the inclination to one another of two lines in a plane which meet one another and do not lie in a straight line. "
Introduction and books 1,2 - Page 176
by Euclid, Sir Thomas Little Heath, Johan Ludvig Heiberg - 1908
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Mathematical Logic

G. T. Kneebone
...breadthless length. 3. A straight line is a line which lies evenly with the points on itself. 8. A plane angle is the inclination to one another of two...meet one another and do not lie in a straight line. 10. When a straight line set up on a straight line makes adjacent angles equal to one another, each...
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Geometry: Our Cultural Heritage

Audun Holme - Mathematics - 2002 - 378 pages
...and breath only. 6. A plane surface is that which lies evenly with the straight lines on itself. 7. A plane angle is the inclination to one another of two...meet one another and do not lie in a straight line. 8. And when the lines containing the angle are straight, the angle is caller rectilinear. 9. When a...
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Greek Science of the Hellenistic Era: A Sourcebook

Georgia Lynette Irby-Massie, Paul Turquand Keyser - History - 2002 - 392 pages
We all want to understand the world around us, and the ancient Greeks were the first to try and do so in a way we can properly call scientific. Now their work is accessible to ...
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A History of Analysis

Hans Niels Jahnke - Mathematics - 422 pages
...rectilineal angle (Elements I, Def. 2), which can be subsumed under the more general definition: "A plane angle is the inclination to one another of two...meet one another and do not lie in a straight line" (Elements I, Def. 8). Nevertheless, this special case is that one Euclid considers in his work. In...
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Interpreting Avicenna: Science And Philosophy In Medieval Islam-Proceedings ...

Avicenna Study Group. Conference - Philosophy - 2004 - 262 pages
...Euclid's definition of a plane angle, which is the following: "A plane angle is the inclination to one or another of two lines in a plane which meet one another and do not lie in a straight line (Elements, def. I, 8)." 7 But there is an essential difference. In their definitions of a plane angle...
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此零非彼O

洪萬生 - Mathematics - 2006 - 353 pages
...BC TIJ ФЁ ? ' J9fliA ' Г ^ H r^j ^: ^ift ) Й <HPMJ1IR> 3(1 1X2000): 2-20 Itt : A plane angle is the inclination to one another of two...meet one another and do not lie in a straight line. ' "Hne"yFJl*flL^ ( straight line ) And when the lines containing the angle are straight, the...
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The Pythagorean Theorem: A 4,000-year History

Eli Maor - Mathematics - 2007 - 259 pages
...length"), a straight line ("a line which lies evenly with the points on itself"), and a plane angle ("the inclination to one another of two lines in a...which meet one another and do not lie in a straight line").2 These are followed by ten statements that Euclid regarded as self-evident, as so clear and...
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The Thirteen Books of Euclib's Elements.

Euclid - Geometry - 1925
...are lines. 7. A plane surface is a surface which lies evenly with the straight lines on itself. 8. A plane angle is the inclination to one another of two...angle are straight, the angle is called rectilineal. 10. When a straight line set up on a straight line makes the adjacent angles equal to one another,...
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Euclid in Greek

...(cXto-is 8vo ypa/jpuv, the 'inclination of two lines to one another.' We translate therefore: 'A pkne angle is the inclination to one another of two lines...meet one another and do not lie in a straight line.' The words TV -ypa/x/xv before кЛип s are unnecessary and should be ignored; they were no doubt...
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Euclid in China: The Genesis of the First Chinese Translation of Euclid's ...

Peter M. Engelfriet - Mathematics - 1998 - 488 pages
...controversy, rooted in Antiquity, about the nature of such angles. In I.Def. 8 a plane angle is defined as the inclination to one another of two lines in a plane which meet one another and do not He in a straight line, and I.Def. 9 calls such an angle "rectilineal" when the lines containing the...
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