| Euclides - 1855
...latter. Corollary 2. — All the angles of a scalene triangle are unequal. PROP. XIX. THEOREM. The **greater angle of every triangle is subtended by the greater side, or** hat the greater side opposite to it. Let ABC be a triangle, of which the angle ABC is greater than... | |
| Cambridge univ, exam. papers - 1856
...the vertex of an isosceles triangle at right angles to the base bisects the vertical angle. 2. The **greater angle of every triangle is subtended by the...greater side or has the greater side opposite to it.** 3. At a given point in a given straight line to make a given rectilineal angle equal to a given rectilineal... | |
| Euclides - 1856
...greater than another, the side opposite the greater angle is greater than the side opposite the less. **Let ABC be a triangle, of which the angle ABC is greater than** ACB ; the side AC will be greater than A B. Because the angles at the base of the triangle ABC are... | |
| Euclides - 1858
...APPLICATION. — For the demonstration of other propositions, as Prop. 19. PROP. 19. — THEOR. The **greater angle of every triangle is subtended by the...greater side, or has the greater side opposite to it.** DEMONSTRATION. — P. 5. The angles at the base of an isosceles triangle are equal. P. 18. The greater... | |
| Robert Potts - 1860 - 361 sider
...angle ABC greater than the angle ACB. Therefore the greater side, &c. QED PROPOSITION XIX. THEOREM. The **greater angle of every triangle is subtended by the...which the angle ABC is greater than the angle BCA.** Then the side AC shall be greater than the side AB. A For, if AC be not greater than AB, AC must either... | |
| Euclides - 1860
...angle (I. 17), therefore the perpendicular AB would be less than AC. PROPOSITION XIX. THEOREM. The **greater angle of every triangle is subtended by the...greater side, or has the greater side opposite to it.** Given a triangle ABC, of which the angle ABC is greater than the angle BCA ; to prove that the side... | |
| War office - 1861 - 12 sider
...plane in 30 seconds ? MATHEMATICS. Afternoon Paper. REV. WN GRIFFIN, MA EUCLID (Books 1, 2, 3). 1. The **greater angle of every triangle is subtended by the...greater side, or has the greater side opposite to it.** 2. Triangles upon the same base, and between the same parallels, are equal to one another. 3. If a... | |
| S. M. Saxby - 1861 - 112 sider
...To satisfy this it needs only that AB and CD be precisely parallel. 21. Euc. I. Prop. XIX. — The **greater angle of every triangle is subtended by the...greater side, or has the greater side opposite to it.** The arcs of the circles drawn about each of the angular points with an equal radius show at once that,... | |
| S. M. Saxby - 1862 - 179 sider
...To satisfy this it needs only that AB and CD be precisely parallel. *25. Euc. I. Prop. XIX. — The **greater angle of every triangle is subtended by the...greater side, or has the greater side opposite to it.** The arcs of the circles drawn about each of the angular Fig. 9. points with an equal radius show at... | |
| Euclides - 1862
...the angle ACB. Conclusion. — Therefore, the greater side, &c. QED PROPOSITION 19.— THEOREM. The **greater angle of every triangle is subtended by the...greater side, or has the greater side opposite to it.** (References— Prop. I. 5, 18.) Hypothesis. — Let ABC be a triangle, of which the angle A Tin is... | |
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