 | University of Oxford - Education, Higher - 1863 - 316 pages
...line made up of the half and the part produced. 10. 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 subtending the obtuse angle is greater than the squares of the sides containing the obtuse... | |
 | Euclides - 1864 - 448 pages
...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,...squares on the sides containing the obtuse angle, by twive the rectangle contained by the side upon which, when produved, the perpendicular falls, and the... | |
 | Euclides - 1864 - 262 pages
...to the square on A HQBF PROPOSITION XII. THEOREM. In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square on the aide subtending the obtuse angle, is greater than the squares on the sides containing the obtuse angle,... | |
 | Robert Potts - 1865 - 528 pages
...to the square on AH. QEF PROPOSITION X1L THEOREM. In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite...angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle... | |
 | Architecture - 1865 - 276 pages
...gnomon of a parallelogram ? 6. Prop. 12. Theorem. 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 subtending the obtuse angle is greater than the squares of the sides containing the obtuse... | |
 | Euclides - 1865 - 402 pages
...equal to the square of the other part. Prop. 12. 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 subtending the obtuse angle is greater thau the squares of the sides containing the obtuse... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...line AB ii divided at H, so that the rectangle AB, BH is equal to the square on AH. QEF PKOPOSITION 12. THEOREM. In obtuse-angled triangles, if a perpendicular...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... | |
 | 1868 - 876 pages
...triangle are together greater than the third side 20 4. In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite...angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle... | |
 | 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...angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and t/ie straight line intercepted without the... | |
 | 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... | |
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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... 
