 | Great Britain. Admiralty - 1846 - 128 sider
...2a (a + b) + b>. Or(« + bf + 6 8 = 2b (a + b} + a'. 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... | |
 | Euclides - 1848 - 52 sider
...the whole and one of the parts, shall be equal to the square of the other part. PROP. 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... | |
 | J. Goodall, W. Hammond - 1848 - 390 sider
...square of half the line, and of the square of the line between the points of section. 3. Prove that 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... | |
 | 1850 - 488 sider
...contained by the whole and each of the parts, are together equal to the square of the whole line. 3. 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 - 1852 - 152 sider
...equals 48, which is less than 64, or the square of 8.] OF EUCLID. 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 sides subtending the obtuse angle is greater than the squares of the sides containing the obtuse... | |
 | Euclides - 1853 - 146 sider
...that the rectangle AB, BH, is equal to the square of AH. Which was to be done. PROP. 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... | |
 | University of Sydney - 1853 - 134 sider
...remaining side, shew that the angle opposite to this latter side is a right angle. 7. In obstuse 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... | |
 | Euclid - 1853 - 176 sider
...and the segment between the perpendicular and the base is equal in area to the square on the base. ( The square on the side subtending the obtuse angle is greater than the sum of the squares on the two sides which contain the obtuse angle, by double the rectangle under the... | |
 | William Somerville Orr - 1854 - 534 sider
...to be done. PROPOSITION XII.— THEOEEM. In an obtuse-angled triangle (ABC), if a perpendicular (AD) be drawn from either of the acute angles to the opposite side prolonged, the square of the side (AB) subtending thf ebtuse angle is greater than the squares of the... | |
 | Euclides - 1855 - 270 sider
...by catting off from it a part equal to their difference, and so on continually. PROP. XIL THEOREM. In obtuse-angled triangles, if a perpendicular be...acute angles to the opposite side produced, the square of the side tubtending the obtuse angle, ii greater than the squares of the sides containing the obtuse... | |
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... 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... 
