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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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The Teaching of Geometry

David Eugene Smith - Geometry - 1911 - 339 pages
...will pass to the next definition and consider this one in connection therewith. 9. RECTILINEAR ANGLE. When the lines containing the angle are straight, the angle is called rectilinear. This definition, taken with the preceding one, has always been a subject of criticism....
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History of Mathematics, Volume 2

David Eugene Smith - Mathematics - 1958 - 736 pages
...intersecting a straight line in space.2 Angle. Euclid's definitions of an angle are as follows : A plane angle is the inclination to one another of two...meet one another and do not lie in a straight line. And when the lines containing the angle are straight, the angle is called rectilineal. This excludes...
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The Foundations of Geometry and the Non-Euclidean Plane

G.E. Martin - Mathematics - 1997 - 512 pages
...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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Geometry and the Visual Arts

Daniel Pedoe - Mathematics - 1976 - 296 pages
...on itself. 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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Geometry: A Comprehensive Course

Daniel Pedoe - Mathematics - 1970 - 449 pages
...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, each...
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A Commentary on the First Book of Euclid's Elements

Proclus - Mathematics - 1992 - 355 pages
...send down impressions of themselves. Vili. A plane angle is the inclination to one another of two Unes in a plane which meet one another and do not lie in a straight line. Some of the ancients put the angle in the category of relation, calling it the inclination either of...
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Thinking Things Through: An Introduction to Philosophical Issues and ...

Clark Glymour - Psychology - 1997 - 382 pages
...are lines. 7. A plane surface is a surface that lies evenly with the straight lines on itself. 8. A plane angle is the inclination to one another of two lines in a plane that meet one another and do not lie in a straight line. 9. And when the lines containing the angle...
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The Poincaré Half-plane: A Gateway to Modern Geometry

Saul Stahl - Mathematics - 1993 - 298 pages
...extremities of a plane surface are straight lines and that the surface lies evenly with them. 8. A plane angle is the inclination to one another of two...angle are straight, the angle is called rectilineal. It is clear from the above two definitions that Euclid has some interest in curvilinear angles, ie,...
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Berkeley's Philosophy of Mathematics

Douglas M. Jesseph - Mathematics - 1993 - 322 pages
...that had a long history in geometry and was much discussed in Berkeley's day. According to Euclid, "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). This definition covers cases beyond the intersection of two straight lines. In...
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Geometry from a Differentiable Viewpoint

John McCleary - Mathematics - 1994 - 308 pages
...arms. The next postulate deals with angles. We first recall a few more of Euclid's definitions: (8) A plane angle is the inclination to one another of two lines in the plane that meet one another and do not lie in a straight line. (9) And when the lines containing...
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