 | Edward Albert Bowser - Geometry - 1890 - 418 pages
...straight line cut two other straight lines, (1) so as to make the exterior-interior angles equal, or (2) so as to make the two interior angles on the same side together equal to two right angles, then the two straight lines are parallel. xE (1) Hyp. Let the st.... | |
 | Euclid - Geometry - 1892 - 460 pages
...straight lines is based upon his twelfth Axiom, which we here repeat. AXIOM 12. If a straight line cut two straight lines so as to make the two interior angles on the same side of it together less than two right angles, these straight lines, being continually produced, will at length... | |
 | Michigan Schoolmasters' Club - Education - 1894 - 554 pages
...any center with any radius. 4. That all right angles are equal. 6. If a straight line meet two other straight lines so as to make the two interior angles on the same side of it together less than two rig~ht angles, these two straight lines being continually produced shall at... | |
 | Charles Austin Hobbs - Geometry, Plane - 1899 - 266 pages
...exterior angles are parallel. Proposition 32. Theorem. 43. If two straight lines are cut by a transversal so as to make the two interior angles on the same side of the transversal supplementary, the two straight lines are parallel. Consult Prop. 4 and Prop. 30. COB.... | |
 | Euclid, Henry Sinclair Hall, Frederick Haller Stevens - Euclid's Elements - 1900 - 330 pages
...straight lines is based upon his twelfth Axiom, which we here repeat. AXIOM 12. If a straight line cut two straight lines so as to make the two interior angles on the same side of it together less than two right angles, these straight lines, being continually produced, will at length... | |
 | Joseph John Findlay - Elementary school teaching - 1902 - 494 pages
...proposition (it is numbered as the first part of Proposition 28) : — If a straight line meet two other straight lines, so as to make the two interior angles on the same side supplementary, the lines will never meet, although produced ever so far. You can prove it by assuming... | |
 | Euclid - Euclid's Elements - 1904 - 488 pages
...straight lines is based upon his twelfth Axiom, which we here repeat. AXIOM 12. If a straight line cut two straight lines so as to make the two interior angles on the same side of it together less than two right angles, these straight lines, being continually produced, will at length... | |
 | Walter William Rouse Ball - Mathematicians - 1908 - 576 pages
...Among Euclid's axioms and postulates is one on parallel lines, which is usually stated iu the form that if a straight line meets two straight lines, so as to make the sum of the two interior angles on the same side of it taken together less than two right angles, then... | |
 | William Thompson Sedgwick, Harry Walter Tyler - Science - 1917 - 526 pages
...known as Axioms 11 and 12, — "All right angles are equal " ; and the famous parallel axiom : — "If a straight line meets two straight lines, so as...make the two interior angles on the same side of it together less than two right angles, these straight lines will meet if produced on that side." The... | |
 | Charles Austin Hobbs - Geometry, Solid - 1921 - 216 pages
...corresponding angles equal, the two lines are parallel. Prop. 41. If two lines are cut by a transversal so as to make the two interior angles on the same side of the transversal supplementary, the lines are parallel. Prop. 41, Cor. II. Two lines respectively perpendicular... | |
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If a straight line meets two straight lines, so as to make the two interior angles on the same side of it taken together lesi than two right angles... 
