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
| Proclus - Mathematics - 1992 - 355 pages
...speculative reflections to those who seek knowledge of the intelligible and invisible world. 175 XXXV.1"2 **Parallel straight lines are straight lines which,...directions, do not meet one another in either direction.** The basic propositions about parallels and the attributes by which they are recognized we shall learn... | |
| Clark Glymour - Psychology - 1997 - 382 pages
...triangle is that which has its three sides equal. 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.** Common notions 1. Things that are equal to the same thing are also equal to one another. 2. If equals... | |
| Alan Musgrave - Philosophy - 1993 - 310 pages
...enables one to prove that when the two angles sum to exactly 180° the lines A and B are parallel. **('Parallel straight lines are straight lines which,...directions, do not meet one another in either direction'** (Euclid I956,i: 154)-) The early geometers did not seriously question the truth of Euclid's axiom of... | |
| Saul Stahl - Mathematics - 1993 - 298 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 Euclid's book is an attempt to systematize the many geometrical theorems produced by his... | |
| Morris Raphael Cohen, Ernest Nagel, John Corcoran - Philosophy - 1993 - 232 pages
...23), are 2 The Thirteen Books of Euclid's Elements, tr. by Sir TL Heath, 1926 S vols., Vol. I, p. 203. **"straight lines which, being in the same plane and...directions, do not meet one another in either direction."** The following are the five postulates: Postulate 1. "To draw a straight line from any point to any... | |
| John McCleary - Mathematics - 1994 - 308 pages
...area in order to prove the Pythagorean theorem (1.47). Euclid defines parallel lines as follows: (23) **Parallel straight lines are straight lines which,...directions, do not meet one another in either direction.** The first important result about parallels in the Elements is the following proposition. Proposition... | |
| Dan Pedoe - Mathematics - 1995 - 102 pages
...angles are less than two right angles (Figure 10°). 7 FIG. 10° If we now define parallel lines as **straight lines which, being in the same plane and...directions, do not meet one another in either direction,** we obtain the equal angles shown in Figure 11°. A FIG. 11° The interior angles on the same side of... | |
| Philip J. Davis, Reuben Hersh, Elena Anne Marchisotto - Mathematics - 1995 - 488 pages
...occur in it. The word parallel is expanded in Euclid under Definition 23. "Parallel straight lines are **lines which being in the same plane and being produced...directions do not meet one another in either direction."** The reason for our calling Euclid's Fifth the parallel axiom is that it is totally equivalent to any... | |
| Keith Devlin - Mathematics - 1996 - 224 pages
...Parallel straight lines are straight lines that, being in the same plane and being produced [ie extended] **indefinitely in both 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... | |
| 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.... | |
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