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 181by Euclid, Sir Thomas Little Heath, Johan Ludvig Heiberg - 1908Full view - About this book
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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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