Parallel straight lines are straight lines which, being in the same plane and being produced indefinitely in both directions, do not meet one another in either direction. Introduction and books 1,2 - Page 190by Euclid, Sir Thomas Little Heath, Johan Ludvig Heiberg - 1908Full view - About this book
| Howard Whitley Eves - Mathematics - 1997 - 344 pages
...but is neither equilateral nor right-angled. Quadrilaterals other than these are called trapezia. 23. **Parallel straight lines are straight lines which,...directions, do not meet one another in either direction.** Postulates Let the following be postulated: 1. A straight line can be drawn from any point to any point.... | |
| Plato, Reginald E. Allen - Philosophy - 1998 - 336 pages
...of the assumption of angle measurement. This postulate is the foundation for Book I, Definition 23: **"Parallel straight lines are straight lines which,...directions, do not meet one another in either direction."** Once again, a potentialist formulation: the lines are not infinite, but may be produced as far as you... | |
| David A. Singer - Mathematics - 1998 - 159 pages
...The language of this statement is tricky. What does the word "parallel" mean? According to Euclid: **Parallel straight lines are straight lines which,...directions, do not meet one another in either direction.** which, (being) in one plane, neither converge nor diverge, but have all the perpendiculars equal which... | |
| Keith Devlin - Mathematics - 2000 - 352 pages
...perpendicular to that on which it stands. Definition 23. Parallel straight lines are straight lines that, **being in the same plane and being produced indefinitely...directions, do not meet one another in either direction.** To the mathematician of today, the first three of the above definitions are unacceptable; they simply... | |
| Posidonius, I. G. Kidd - Philosophy - 2004 - 432 pages
...Elementa, p. 176.5-17 (Friedlein) Context: Proclus is commenting on Euclid, Def. xxxv (xxm Heiberg): **parallel straight lines are straight lines which,...directions, do not meet one another in either direction.** After giving Posidonius' definition, Proclus criticises Euclid's definition by objecting that the absence... | |
| Nick Huggett - Philosophy - 1999 - 274 pages
...neither equilateral nor right-angled. And let quadrilaterals other than these be called trapezia. 23. **Parallel straight lines are straight lines which,...directions, do not meet one another in either direction.** Postulates Let the following be postulated: 1. To draw a straight line from any point to any point.... | |
| Reinhard Laubenbacher, David Pengelley - Mathematics - 1999 - 275 pages
...angles ACD and DCB are equal if they lie on top of each other when we fold along DC. DEFINITION 23. **Parallel straight lines are straight lines which, being in the same plane and being produced** indefinitelv in both directions, do not meet one another in either direction. POSTULATE 5. That, if... | |
| Judith N. Cederberg - Mathematics - 2001 - 439 pages
...neither equilateral nor rightangled. And let quadrilaterals other than these be called trapezia. 23. **Parallel straight lines are straight lines which,...directions, do not meet one another in either direction.** The Postulates 1 . To draw a straight line from any point to any point. 2. To produce a finite straight... | |
| Victor J. Katz - Mathematics - 2000 - 261 pages
...were also some who tried to resolve the problem by altering Euclid's definition of parallel lines: 23. **Parallel straight lines are straight lines which,...directions, do not meet one another in either direction.** They exchanged the last sentence with this one: have the same distance between them in both directions... | |
| Ivor Grattan-Guinness - Mathematics - 2000 - 817 pages
...another.' The last one bore upon parallelism: Euclid defined 'parallel straight lines' as those which **being produced indefinitely in both directions, do not meet one another in either direction',** and then formulated a postulate in terms of «o«-parallelism: That, if a straight line falling on... | |
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