 | Mathematics - 1836 - 488 pages
...opposite side produced, the square of the side subtending the obtuse angle is greater than the squares of the sides containing the obtuse angle, by twice the...perpendicular falls, and the straight line intercepted between the perpendieu lar and the obtuse angle. XIII. In every triangle the square of the side subtending... | |
 | John Playfair - Euclid's Elements - 1836 - 488 pages
...opposite side produced, the square of the side subtending the obtuse angle is greater than the squares of the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, tchen produced, the perpendicular falls, and the straight line intercepted between the perpendicular... | |
 | Euclides - Euclid's Elements - 1837 - 112 pages
...opposite side produced, the square of the side subtending the obtuse angle is greater than the squares of the sides containing the obtuse angle, by twice the...triangle, between the perpendicular and the obtuse angle. Obs. This proposition is so short, and each step so necessary to the proof, that to attempt to simplify... | |
 | Charles Reiner - Geometry - 1837 - 254 pages
...opposite side produced, the square of the side subtending the obtuse angle is greater than the squares of the sides containing the obtuse angle, by twice the...triangle, between the perpendicular and the obtuse angle. Obs.—While it is, of course, not to be expected, that the pupils can express the result of a demonstration... | |
 | John Playfair - Euclid's Elements - 1837 - 332 pages
...opposite side produced, the square, of the side subtending the obtuse angle is greater than the squares of the sides containing the obtuse angle, by twice the...perpendicular falls, and the straight line intercepted between the perpendicular and the obtuse angle. Let ABC be an obtuse angled triangle, having the obtuse... | |
 | Euclid - Geometry - 1838 - 470 pages
...opposite side produced, the square of the side subtending the obtuse angle is greater than the squares of the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, wnen produced, the perpendicular falls, and the straight line intercepted without the triangle between... | |
 | Euclides - 1840 - 82 pages
...obtuse-angled triangle, the square of the side subtending the obtuse angle exceeds the sum of the squares of the sides containing the obtuse angle, by twice the rectangle contained by either of those sides and the produced part of it intercepted between the perpendicular let fall on... | |
 | Euclides - Geometry - 1841 - 378 pages
...opposite side produced, the square of the side subtending the obtuse angle, is greater than the squares of the sides containing the obtuse angle, by twice the...triangle between the perpendicular and the obtuse angle. obtuse angle ACB, and from the point A let AD be drawn* perpendicular to BC produced: the square of*... | |
 | John Playfair - Euclid's Elements - 1842 - 332 pages
...opposite side produced, the square of the side subtending the obtuse angle is greater than the squares of the sides containing the obtuse angle, by twice the...perpendicular falls, and the straight line intercepted between the perpendicular and the obtuse angle. Let ABC be an obtuse angled triangle, having the obtuse... | |
 | Euclides - 1842 - 316 pages
...subtending the obtuse angle is greater than the squares of the sides containing the obtuse angle, by twiee the rectangle contained by the side upon which, when...perpendicular falls, and the straight line intercepted on the exterior of the triangle between the perpendicular and the obtuse angle. Let ABC be an obtuse-angled... | |
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In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square on the side subtending the obtuse angle is greater than the squares on the sides containing the obtuse angle, by twice the... 
