 | Sandhurst roy. military coll - 1859 - 672 pages
...condition in italics is not fulfilled, where would the construction for this proposition fail ? 3. In obtuse-angled triangles, if a perpendicular be drawn from either of the acute nngles to the opposite side produced, the square of the side subtending the obtuse angle is greater... | |
 | John Playfair - Geometry - 1860 - 332 pages
...the square of AH. PROP. XII. THEOR. In obtuse angled triangles, if a perpendicular be drawn from any of the acute angles to the opposite side produced,...squares of the sides containing the obtuse angle, by twee the rectangle contained by the side upon which, when produced, the perpendicular falls, and the... | |
 | Robert Potts - Geometry, Plane - 1860 - 380 pages
...square on AH. QEF • PROPOSITION XII. THEOREM. In obtuse-angled triangles, if a perpendicular be drawtt 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... | |
 | War office - 1861 - 714 pages
...other, the base of that which lias the greater angle shall be greater than the base of the other. 2. In obtuse-angled triangles, if a perpendicular be drawn...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... | |
 | War office - 1861 - 260 pages
...opposite sides and angles of parallelograms are equal to one another, and the diameter bisects them. 2. In obtuse-angled triangles, if a perpendicular be drawn...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... | |
 | Euclides - 1862 - 140 pages
...H, so that the rectangle AB . BH, is equal to the square on AH. QEF PROPOSITION 12.— THEOKEM. In obtuse-angled triangles, if a perpendicular be drawn...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... | |
 | Euclides - 1862 - 172 pages
...in H, so that the rectangle AB, BH, is equal to the square of AH. Q. R F. PROP. XII — THEOREM. In obtuse-angled triangles, if a perpendicular be drawn...of the acute angles to the opposite side produced; then the square of the side subtending the obtuse angle is greater than the squares of the sides containing... | |
 | University of Oxford - Education, Higher - 1863 - 328 pages
...be equal to a given triangle, and have one of its angles equal to a given rectilineal angle. 6. In obtuse-angled triangles, if a perpendicular be drawn...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... | |
 | Euclides - 1864 - 448 pages
...divided in H, so that the rectangle AB, BH is equal to the square on AH. QEF PROPOSITION XII. THEOREM. 2n obtuse-angled triangles, if a perpendicular be drawn...from either of the acute angles to the opposite side produved, the square on the side subtending the obtuse angle, is greater than the squares on the sides... | |
 | Robert Potts - 1865 - 528 pages
...divided in H, so that the rectangle AB, BHlB equal to the square on AH. QEF PROPOSITION X1L THEOREM. In obtuse-angled triangles, if a perpendicular be drawn...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... | |
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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... 
