 | Euclides - 1855 - 270 pages
...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 - 252 pages
...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 - 168 pages
...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 - 248 pages
...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 - Geometry, Plane - 1860 - 380 pages
...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 - 288 pages
...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 - 714 pages
...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 - Nautical astronomy - 1861 - 140 pages
...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 - Marine engines - 1862 - 200 pages
...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 - 140 pages
...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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THE greater angle of every triangle is subtended by the greater side, or has the greater side opposite to it. 
