 | Euclides - 1884 - 182 pages
...BGH&nd GHD. (Ax. 4) But AGH and BGH are equal to two right angles ; (1. 13) therefore BGH and GHD are less than two right angles ; "but those straight lines which, with another falling upon them, make the interior angles on the same side of it together less than two right angles,... | |
 | Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...PROPOSITION XXI. THEOREM. // two straight lines intersect a third straight line, making the sum of the interior angles on the same side less than two right angles, the two lines will meet if sufficiently produced. Let the two lines CD, IL, meet the line EF, making... | |
 | Alan Sanders - Geometry, Modern - 1901 - 260 pages
...also bisected. PROPOSITION XX. THEOREM 127. If two lines are cut by a transversal, making the sum of the interior angles on the same side less than two right angles, the lines will meet if sufficiently produced. Let AB and CD be cut by EF, making Z 1 + Z 2 < 2 KA's.... | |
 | Philosophy - 1903 - 750 pages
...to prop up the argument that proves the equality of alternate angles on parallels, viz. , that — "those straight lines which, with another straight...angles on the same side less than two right angles, do meet if continually produced." This is exactly the point to be proved, for it is only one form of... | |
 | Euclid - Mathematics, Greek - 1908 - 550 pages
...right angles are equal to one another. \ 5. 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... | |
 | Leslie Leland Locke - Mathematics - 1909 - 364 pages
...all right angles are equal to one another. 5. 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... | |
 | Jacob William Albert Young - Mathematics - 1911 - 434 pages
...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 right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than... | |
 | Jacob William Albert Young - Mathematics - 1911 - 432 pages
...fifth postulate of Euclid reads as follows: "If a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the two lines, if produced indefinitely, meet on that side on which are the angles less than two right... | |
 | Duncan M'Laren Young Sommerville - Geometry, Non-Euclidean - 1914 - 291 pages
...and the fifth is the famous ParallelPosfculate : " 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... | |
 | Robert Édouard Moritz - Mathematics - 1914 - 434 pages
...2007. Euclid's Postulate 5 [The Parallel Axiom]. 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... | |
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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. 
