| Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...square on AH. QEF PKOPOSITION 12. THEOREM. In obtuse-angled triangles, if a perpendicular lie 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... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 424 pages
...sides containing the acute angle. 127. The square on the side subtending an obtuse angle of a triangle **is greater than the squares on the sides containing the obtuse angle.** 128. If the square on one side of a triangle bo less than the squares on the other two sides, the angle... | |
| Robert Potts - 1868 - 434 pages
...obtuse-angled triangles, if a perpendicular be drawn from either of the mute angles to the opposite tide **produced, the square on the side subtending the obtuse...which, when produced, the perpendicular falls, and** t/ie straight line intercepted without the triangle between the perpendicular and the obtuse angle.... | |
| James Maurice Wilson - Geometry - 1868 - 132 pages
...-2CBxBD (by Theorem 26). Therefore A C" = AB* + BC* - 2 CB x BD. THEOREM 31. In an obtuse-angled triangle **the square on the side subtending the obtuse angle...is greater than the squares on the sides containing** that angle by twice the rectangle contained by either of these sides and the projection on it of the... | |
| 1868 - 344 pages
...triangle, if a perpendicular be drawn from either of the acute angles to the opposite side prsrtuced, **the square on the side subtending the obtuse angle is greater than the** sqnares on the sides containing the obtuse angle, by twice the rectangle contained by the side upon... | |
| Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...and XIH. of Book II. Thus the enunciation of Prop. xn. might be : — " In oblique.angled triangles, **the square on the side subtending the obtuse angle...is greater than the squares on the sides containing** that angle, by twice the rectangle contained by one of these sides and the projection of the other... | |
| Euclid, Charles Peter MASON - Geometry - 1872 - 216 pages
...In an obtuse-angled triangle the square on the side subtending the obtuse angle exceeds the sum of **the squares on the sides containing the obtuse angle by twice the rectangle contained by** either of them and the distance between a perpendicular drawn to that side produced from the opposite... | |
| Henry Major - Student teachers - 1873 - 592 pages
...is equal to the square of AIL XII. — In obtuse-angled triangles, if a perpendicular be drawn from **either of the acute angles to the opposite side produced, the square** of the side sub' tending the obtuse angle, is greater than the squares of the sides containing the... | |
| Edward Atkins - 1874 - 424 pages
...on AH. QEF Proposition 12. — Theorem. In obtuse-angled triangles if a perpendicular be drawn from **either of the acute angles to the opposite side produced,...angle, by twice the rectangle contained by the side** on which, when produced, the perpendicular falls, and the straight line intercepted without th« triangle,... | |
| Euclides - 1874 - 120 pages
...section.' medial PROPOSITION 12. THEOREM. In obtuse-angled triangles, if a perpendicular be drawn from **either of the acute angles to the opposite side produced,...angle, by twice the rectangle contained by the side** on which, when produced, the perpendicular falls, and the staight line intercepted without the triangle,... | |
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