 | John Playfair - 1806 - 320 pagine
...AB.BH is equal to the square of AH. Which was to be done, Book II. PROP. XII. THEOR. 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 aigle is greater than the squares of the sides contain ng the obtuse... | |
 | Robert Simson - 1827 - 546 pagine
...rectangle AB, BH is equal to the square of AH. Which was to be done. PROP. XII. THEOR. 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 - 1834 - 518 pagine
...the rectangle AB, BH is equal to the square of AH. Which was to be done. PROPOSITION XII. THEOR. — 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 - 1837 - 112 pagine
...ie, fig FK = AB% ie, fig. AD, 4. that FH = HD, 3. that .'. AS x BH = AH*. PROPOSITION XII. Theorem. 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... | |
 | Charles Reiner - 1837 - 254 pagine
...subtending the right angle is equal to the sum of the squares of the sides containing the right angle. 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 - 1838 - 264 pagine
...Which was to be done. PROP. XII. THEOR. In an obtuseangledtriangle, if a perpendicular be drawnfrom 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 - 1841 - 378 pagine
...AH. Which was to be done. PROP. XII. THEOR. In obtuse-angled Mangles, if a perpendicular be dratcn 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... | |
 | 1844 - 688 pagine
...between the points of section, is equal to the square of half the line. 7. 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 - 1845 - 546 pagine
...divided in H, so that the rectangle AB, BH is equal to the square of AH. QE r. PROPOSITION XII. THEOREM. 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... | |
 | Great Britain. Admiralty - 1846 - 128 pagine
...2a(a+ &) + £". Or(rt -|- b)" + b t =2b(a + b+ a 8 . PROP. XLVII. THEOR. 12. 2 Eu . 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... | |
| |
... 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 the triangle between the perpendicular and the obtuse... 
