 | Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...square of AH. PROP. XII. THEOR. In obtuse angled triangles, if a perpendicular be drawn from any of the acute angles to the opposite side produced, the square...squares of the sides containing the obtuse angle, 6y twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and... | |
 | London univ - 1846 - 326 pages
...of a regular octagon ? 4. In any obtuse-angled triangle, if a perpendicular be drawn from any of the acute angles to the opposite side produced, the square...is greater than the squares of the sides containing it, by twice the rectangle contained by the side on which when produced the perpendicular falls, and... | |
 | Dennis M'Curdy - Geometry - 1846 - 166 pages
...(/) ax. 3 of b. 1. 12 Th. In any obtuse angled triangle, if a perpendicular be drawn from one of the acute angles to the opposite side produced ; the square of the side subtending the obtuse angle equals the two squares of the sides containing it, and two rectangles of the produced side and its... | |
 | Euclides - 1846 - 272 pages
...to AB. PROPOSITION XII. THEOREM. In any obtuse angled triangle (as BAC) the square of the side (AB) subtending the obtuse angle, is greater than the squares of the sides (BC and CA) which contain the obtuse angle, by twice the rectangle contained under either of these... | |
 | 1843 - 536 pages
...EK also subtends the obtuse angle EPK of the triangle EPK, and by (12 Prop. 2 Book Eu.) It is.— " The square of the side subtending the obtuse angle...obtuse angle, by twice the rectangle contained by one of the sides about the obtuse angle, and the line intercepted without by a perpendicular to it... | |
 | Charles William Hackley - Geometry - 1847 - 248 pages
...(AC + BC) . (AC - BC) = AB . (AD + BD) in the 1st fig. THEOREM XXVJU. In any obtuse-angled triangle, the square of the side subtending the obtuse angle is greater than the sum of the squares of the other two sides, by twice the rectangle of one of the sides containing the... | |
 | Euclid, Robert Potts - Euclid's Elements - 1847 - 118 pages
...the squares of the sides containing the right angle ; but in an obtuse-angled triangle (Euc. n. 12), the square of the side subtending the obtuse angle is greater than the square of the side containing the obtuse angle ; and in an acute-angled triangle (Euc. n. 13), the... | |
 | George Roberts Perkins - Geometry - 1847 - 326 pages
...the three remainders, and it will be the area. PEOPOSITION X. THEOREM. In any obtuse-angled triangle, the square of the side subtending the obtuse angle is greater than the sum of the squares of the other two sides, by twice the rectangle of the base and the distance of the... | |
 | J. Goodall, W. Hammond - 1848 - 390 pages
...of section. 3. Prove that in obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square...which, when produced, the perpendicular falls, and the straight line intercepted without the triangle between the perpendicular and the obtuse angle. Section... | |
 | Euclides - 1848 - 52 pages
...part. PROP. XII. THEOREM. In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square...which, when produced, the perpendicular falls, and the straight line intercepted without the triangle between the perpendicular and the obtuse angle. PROP.... | |
| |
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 angle, by twice the... 
