 | New Hampshire College of Agriculture and the Mechanic Arts - 1892 - 316 pages
...extremity on its own side of the perpendicular. 5. Demonstrate that if two lines are cut by a third, making the sum of the interior angles on the same...equal to two right angles, the two lines are parallel. 6. Demonstrate that in the same or equal circles two incommensurable arcs are to each other as the... | |
 | American fiction - 1906 - 560 pages
...in the non-euclidean field. Euclid assumed as axiomatic, that, "if two lines are cut by a third, and the sum of the interior angles on the same side of the cutting line is less than two right angles, the lines will meet on that side when sufficiently produced."... | |
 | Webster Wells - Geometry - 1894 - 400 pages
...angles, it is perpendicular to the other diagonal. 79. If two lines are cut by a third so as to make the sum of the interior angles on the same side of the secant.line less than two right angles, the lines will meet if sufficiently produced. 80. If exterior... | |
 | Webster Wells - Geometry - 1898 - 264 pages
...BGH= Z CHG, and the theorem follows by § 40.) 76. Cor. II. If two parallels are cut by a transversal, the sum of the interior angles on the same side of the transversal is equal to two riyht angles. (Fig. of Prop. XXI.) Given IIs AB and CD cut by transversal... | |
 | New Hampshire - New Hampshire - 1899 - 1242 pages
...extremity on its own side of the perpendicular. o. Demonstrate that if two lines are cut by a third, making the sum of the interior angles on the same...equal to two right angles, the two lines are parallel. 6. Demonstrate that in the same or equal circles two incommensurable arcs are to each other as the... | |
 | Webster Wells - Geometry - 1899 - 424 pages
...BGH= Z CHG, and the theorem follows by § 40.) 76. Cor. II. If two parallels are cut by a transversal, the sum of the interior angles on the same side of the transversal is equal to two right angles. (Fig. of Prop. XXI.) Given IIs AH and CD cut by transversal... | |
 | Webster Wells - Geometry - 1899 - 450 pages
...equal, AB II CD ? 79. Cor. II. (Converse of § 76.) If two straight lines are cut by a transversal, and the sum of the interior angles on the same side of the transversal is equal to two right angles, the two lines are parallel. (Fig. of Prop. XXII.) Given lines... | |
 | Henry Parker Manning - Geometry, Non-Euclidean - 1901 - 120 pages
...to be, like the rest, a simple elementary fact. It is this : * If two lines are cut by a third, and the sum of the interior angles on the same side of the cutting line is less than two right angles, the lines will meet on that side when sufficiently produced.... | |
 | Henry Parker Manning - Geometry, Non-Euclidean - 1901 - 116 pages
...to be, like the rest, a simple elementary fact. It is this : * If two lines are out by a third, and the sum, of the interior angles on the same side of the cutting line is less than two right angles, the lines will meet on that side when sufficiently produced.... | |
 | Edward Brooks - Geometry, Modern - 1901 - 278 pages
...the lines AB and CD are parallel, as was shown in Case II. Therefore, etc. COR. — If two straight lines are cut by a third line, making the sum of the two interior angles on the same side of the transversal less or greater than two right angles, the... | |
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If two lines are cut by a third, and the sum of the interior angles on the same side of the cutting line is less than two right angles, the lines will meet on that side when sufficiently produced. 
