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
| David Eugene Smith - Geometry - 1911 - 339 pages
...") in his proofs, so that he might well have omitted the definitions, as we often do. 23. PARALLELS. **Parallel straight lines are straight lines which,...directions, do not meet one another in either direction.** This definition of parallels, simplified in its language, is the one commonly used to-day. Other definitions... | |
| David Eugene Smith - Geometry - 1911 - 339 pages
...") in his proofs, so that he might well have omitted the definitions, as we often do. 23. PARALLELS. **Parallel straight lines are straight lines which, being in the same plane and being produced** indefin,tely in both directions, do not meet one another in either direction. This definition of parallels,... | |
| David Eugene Smith - Mathematics - 1958 - 736 pages
...Lines. The word "parallel"6 means "alongside one another." Euclid defined parallel straight lines as **"straight lines which, being in the same plane and...directions, do not meet one another in either direction."** Rather less satisfactory is the definition of Poseidonius (c. 100 BC) as those lines "which, in one... | |
| G.E. Martin - Mathematics - 1975 - 509 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 and the Common Notions (or Axioms) appear next in Book I. In reading these you might... | |
| Daniel Pedoe - Mathematics - 1976 - 296 pages
...circumference of the circle, and such a straight line also bisects the circle. The final Definition is: 23. **Parallel straight lines are straight lines which, being in the same plane and being produced** indeiinitely in both directions, do not meet one another in either direction. It is possible to discuss... | |
| A. Shimony - Language Arts & Disciplines - 1987 - 384 pages
...is a 'practical corollary'. Euclid's definition of parallel lines, however, is not so obliging: they **are "straight lines which, being in the same plane...directions, do not meet one another in either direction",** which offers neither a 'rule' JUDSON WEBB for constructing parallels, nor suggests any 'synthesis'... | |
| Daniel Pedoe - Mathematics - 1970 - 449 pages
...neither equilateral nor right-angled; and let quadrilaterals other than these be called trape2ia. 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.... | |
| Posidonius - Literary Criticism - 1972 - 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... | |
| Lucas Nicolaas Hendrik Bunt - Mathematics - 1988 - 299 pages
...those lying within the figure are congruent to one another. The list of definitions ends with: XX1H **Parallel straight lines are straight lines which,...indefinitely in both directions, do not meet one another in** cither direction. With the term "straight line" Euclid evidently does not think of an infinite straight... | |
| Morris Kline - Mathematics - 1990 - 390 pages
...circumference [not denned explicitly] of the circle, and such a straight line also bisects the circle. 23. **Parallel straight lines are straight lines which,...directions, do not meet one another in either direction.** The opening definitions are framed in terms of concepts that are not denned, and hence serve no logical... | |
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