| Euclides - 1874 - 342 pages
...angles; but those straight lines, which with another straight line falling upon them, make the two **interior angles on the same side less than two right...together if continually produced (Ax. 12) ; therefore** , 3. The straight lines AB, CD if produced far enough will meet towards B, D ; but they never meet,... | |
| Adrien Marie Legendre - Geometry - 1874 - 512 pages
...PROPOSITION X2I. THEOREM. If 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... | |
| Euclides - Euclid's Elements - 1881 - 236 pages
...angles. But those straight lines, which with another straight line falling upon them, make the two **interior angles on the same side less than two right angles, will meet together** (Ax. 12) if continually produced. Therefore the two straight lines AB, CD, if produced far enough,... | |
| Stewart W. and co - 1884 - 272 pages
...angles AGH, BGH, are greater than BGH, GHD ; but the angles AGH, BGH, are equal to two right angles ; **therefore the angles BGH GHD, are less than two right...angles on the same side less than two right angles,** do meet together if continually "oduced ; therefore the straight lines AB, CD, if oduced far enough,... | |
| 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 - 748 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 - 366 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... | |
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