 ... 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, when produced, the perpendicular falls, and the straight line intercepted without...  Annual Report - Page 361868Full view - About this book
 | Joseph Charles Parkinson - 1860 - 154 pages
...the square of the straight line which is made up of the half and the part produced. 8. PROP. XII. — In obtuse-angled triangles, if a perpendicular be...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... | |
 | War office - 1861 - 714 pages
...given rectilineal figure and have an angle equal to a given rectilineal angle. 3. In obtuse angled triangles, if a perpendicular be drawn from either...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 - 1862 - 172 pages
...divided 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...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 - 316 pages
...half the line bisected and of the square of the line made up of the half and the part produced. 10. In obtuse-angled triangles, if a perpendicular be...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 - 262 pages
...divided in H, so that the rectangle AB, BH is equal to the square on A HQBF PROPOSITION XII. THEOREM. In obtuse-angled triangles, if a perpendicular be...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,... | |
 | 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... | |
 | Architecture - 1865 - 276 pages
...5. What is the definition of the gnomon of a parallelogram ? 6. Prop. 12. Theorem. In obtuse angled triangles, if a perpendicular be drawn from either...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
...II. 1. D. On the Relations between the Sides of a Triangle and the Perpendicular from the Vertet. 1. In obtuse-angled triangles, if a perpendicular be...from either of the acute angles to the opposite side prodnced, the square on the side subtending the obtuse angle is greater than the squares on the sides... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...to the 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... | |
 | 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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