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
| Michael H. Whitworth - Literary Criticism - 2001 - 240 pages
...and the definition of parallelism rely upon references to infinity. Parallel straight lines are those **which, 'being in the same plane and being produced...both directions, do not meet one another in either** direction'.1 The difficulty with this definition is that it suggests one may physically demonstrate... | |
| William P. Berlinghoff, Kerry E. Grant, Dale Skrien - Mathematics - 2001 - 602 pages
...three sides unequal. Parallel straight lines are straight lines in the same plane which, if extended **indefinitely in both directions, do not meet one another in either direction.** From this simple beginning — twenty-three definitions, five Common Notions, and five Postulates —... | |
| Audun Holme - Mathematics - 2002 - 378 pages
...neither equilateral nor right-angled. And let quadrilaterals other than these be called trapezia. 22. **Parallel straight lines are straight lines which,...directions, do not meet one another in either direction.** It is interesting to note that the term line does not signify only straight line, and that the straight... | |
| Leonard Mlodinow - Science - 2010 - 320 pages
...angle, surface, and plane. He defined some of these terms quite precisely. Parallel lines, he wrote, **are "straight lines which, being in the same plane,...directions, do not meet one another in either direction."** A circle, he wrote, is "a plane figure contained by one line [ie, curve] such that all straight lines... | |
| Georgia Lynette Irby-Massie, Paul Turquand Keyser - History - 2002 - 392 pages
...these be called trapezia. 23. Parallels are straight lines which, being in the same plane and extending **indefinitely in both directions, do not meet one another in either direction.** Postulates [1-3 assert that space is continuous and infinite] 1 . Let the following be postulated:... | |
| Edward Grant - Religion - 2004 - 307 pages
...is an angle less than a right angle. 13. A boundary is that which is an extremity of anything. 23. **Parallel straight lines are straight lines which,...directions, do not meet one another in either direction.** (Euclid 1956, 1:153, 154) Euclid includes two kinds of propositions: constructional propositions and... | |
| Mathematics - 2006 - 353 pages
...multitude of primes numbers ) ( Heath, 1956, vol. II, pp. 412-413 ) ° ( postulate ) - M r^TlJÎPJ Bf 1.23: **Parallel straight lines are straight lines which,...directions, do not meet one another in either direction.** ( -f-ff a&. ad £& • ) ( Heath, 1956, vol. I, p. 154 ) IS; i£ 5: [Let the following be postulated:]... | |
| Chris Hayhurst - Biography & Autobiography - 2006 - 112 pages
...the center of the circle. The last definition in the book deals with what is meant by "parallel." 23. **Parallel straight lines are straight lines which,...directions, do not meet one another in either direction.** Parallel Lines Following the definitions, book I lists five "postulates." The postulates use the same... | |
| Giandomenico Sica - Mathematics - 2006 - 268 pages
...p. 1005]. 5 The definition concerning parallel straight lines is stated as the 23rd definition: they **are "straight lines which, being in the same plane...directions, do not meet one another in either direction"** [Heath (1956), p. 154]. 6 Euclid's fifth postulate reads as follows: "that, if a straight line falling... | |
| William Byers - Mathematics - 2010 - 424 pages
...controversial aspect of Euclidean geometry. Here is Euclid's definition of parallel lines: Definition:5 **Parallel straight lines are straight lines which,...directions, do not meet one another in either direction.** (forever) (forever) Figure 2.3. Parallel lines This definition uses the second geometric postulate,... | |
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