 That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.  Introduction and books 1,2 - Страница 188написао/ла Euclid - 1908Пуни преглед - О овој књизи
 | Georgia Lynette Irby-Massie, Paul Turquand Keyser - 2002 - 440 страница
...equal one to another, [space is homogenous] 5. If a straight line intersecting two straight lines makes the interior angles on the same side less than two right angles, die two straight lines, extended indefinitely, intersect on die side of die angles less than two right... | |
 | David C. Lindberg, Mary Jo Nye, Roy Porter, Ronald L. Numbers - 2003 - 714 страница
...non-Euclidean geometries led through Euclid's fifth, or paralled postulate, which states: "That, if a straight line falling on two straight lines make...on that side on which are the angles less than the two right angles."30 This statement fits Aristotle's criteria for a postulate: It is the kind of statement... | |
 | I. Grattan-Guinness - 2003 - 980 страница
...one of them came to be increasingly discussed - the parallel postulate. This is the claim 'that, if a straight line falling on two straight lines make...produced indefinitely, meet on that side on which the angles are less than two right angles'. While the other assumptions of Book I alone enabled Euclid... | |
 | Gilles Fauconnier, Mark Turner - 2008 - 464 страница
...require what is known as the parallel axiom: "If a straight line falling on two straight lines makes the interior angles on the same side less than two...produced indefinitely, meet on that side on which the angles are less than two right angles." This axiom seemed to many geometers, probably including... | |
 | Marcel Berger - 2007 - 852 страница
...If a straight line falling on two straight lines makes two interior angles on the same side with sum less than two right angles, the two straight lines,...produced indefinitely, meet on that side on which the angles are less than two right angles. By the end of the 18th century, Euclidean geometry's structure... | |
 | J. W. A. Young - 2004 - 440 страница
...stated by Euclid in his Postulate 5 as follows: " If a straight line falling on two straight lines makes the interior angles on the same side less than two...straight lines, if produced indefinitely, meet on that L 7 side on which are the angles less than the two right angles." This is a consequence of our assumption,... | |
 | Constance Reid - 2004 - 306 страница
...right angles are equal to one another. 5. That if a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the straight lines, if produced indefinitely, will meet on that side on which the angles are less than... | |
 | Frank Morgan - 218 страница
...Tac Suo euOeiaç ETC ometpov aujamuTEiv, ecp a ¡aspr] EIOIV at icov ouo opucov EXaaaoveç. [That, if a straight line falling on two straight lines make...on that side on which are the angles less than the two right 169 angles.] Incidentally, notice how the Greek letter sigma at the end of a word is written... | |
 | James A. Arieti - 2005 - 420 страница
...other. The fifth postulate is quite different: if a straight line falling on two straight lines makes the interior angles on the same side less than two...produced indefinitely, meet on that side on which the angles are less than the two right angles. In the figure, angles a and b are less than right angles,... | |
 | Chris Hayhurst - 2005 - 118 страница
...The last two postulates in book I are as follows: 4. All right angles are equal to one another. 5. If a straight line falling on two straight lines make...on that side on which are the angles less than the two right angles. Euclid followed up his postulates with a list of "common notions." The common notions... | |
| |
