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" When a straight line set up on a straight line makes the adjacent angles equal to one another, each of the equal angles is right, and the straight line standing on the other is called a perpendicular to that on which it stands. "
Introduction and books 1,2 - Page 181
by Euclid, Sir Thomas Little Heath, Johan Ludvig Heiberg - 1908
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Mathematical Cranks

Underwood Dudley - Mathematics - 1992 - 372 pages
...evenly with the points on itself," we prefer to leave the term undefined — but others were just fine: When a straight line set up on a straight line makes...called a perpendicular to that on which it stands. FIGURE 15 common notions, things that are clearly true but are not restricted to geometry: two things...
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A Commentary on the First Book of Euclid's Elements

Proclus, Glenn Raymond Morrow - Mathematics - 1992 - 355 pages
...the complete and indivisible Good has primacy over the things that are plural and separated. X-XII. When a straight line set up on a straight line makes...equal to one another, each of the equal angles is a right angle and the straight line standing on the other is called a perpendicular to that on which...
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The Poincaré Half-plane: A Gateway to Modern Geometry

Saul Stahl - Mathematics - 1993 - 298 pages
...coming to any serious conclusions, and that Euclid felt the need to acknowledge their efforts. 10. When a straight line set up on a straight line makes...called a perpendicular to that on which it stands. This innocuous looking definition suffers from two difficulties. It is not at all clear what equality...
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Geometry from a Differentiable Viewpoint

John McCleary - Mathematics - 1994 - 308 pages
...straight, the angle is called rectilineal. (10) When a straight line set up on a straight line makes adjacent angles equal to one another, each of the...called a perpendicular to that on which it stands. (11) An obtuse angle is an angle greater than a right angle. (12) An acute angle is an angle less than...
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Mathematics: The Science of Patterns: The Search for Order in Life, Mind and ...

Keith Devlin - Mathematics - 1996 - 224 pages
...that lies evenly with the points on itself. Definition 10 When a straight line standing on another straight line makes the adjacent angles equal to one...called a perpendicular to that on which it stands. Definition 23 Parallel straight lines are straight lines that, being in the same plane and being produced...
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Foundations and Fundamental Concepts of Mathematics

Howard Whitley Eves - Mathematics - 1997 - 344 pages
...angle are straight lines, the angle is called a rectilinear angle. 10. When a straight line erected on a straight line makes the adjacent angles equal to one another, each of the equal angles is called a right angle, and the straight line standing on the other is called a perpendicular to that...
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Geometry: Plane and Fancy: Plane and Fancy

David A. Singer - Mathematics - 1998 - 159 pages
...to prove it. First we must review what we know about right angles. Euclid's tenth definition says: When a straight line set up on a straight line makes...called a perpendicular to that on which it stands. This should not be interpreted to mean that there actually are right angles. In fact, Euclid proves...
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Space from Zeno to Einstein: Classic Readings with a Contemporary Commentary

Nick Huggett - Philosophy - 1999 - 274 pages
...line. 9. And when the lines containing the angle are straight, the angle is called rectilineal. 10. When a straight line set up on a straight line makes...called a perpendicular to that on which it stands. 11. An obtuse angle is an angle greater than a right angle. 12. An acute angle is an angle less than...
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Mathematical Expeditions: Chronicles by the Explorers

Reinhard Laubenbacher, David Pengelley - Mathematics - 1999 - 275 pages
...parallels, and restate the parallel postulate itself. Euclid, from Elements BOOK I. DEFINITION 10. When a straight line set up on a straight line makes...called a perpendicular to that on which it stands. Note that this definition makes no reference to any units of angle measurement, as opposed to a definition...
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A Course in Modern Geometries

Judith N. Cederberg - Mathematics - 2001 - 439 pages
...line. 9. And when the lines containing the angle are straight, the angle is called rectilineal. 10. When a straight line set up on a straight line makes...one another, each of the equal angles is right, and Reprinted with permission of Cambridge University Press from The Thirteen Books of Euclid's Elements,...
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