| Great Britain. Admiralty - Geometry - 1846 - 130 pages
...PROP. XLVII. THEOR. 12. 2 Eu. In obtuse angled triangles, if a perpendicular be drawn from either of **the acute angles to the opposite side produced, the...perpendicular falls, and the straight line intercepted** without the triangle between the perpendicular and the obtuse angle. A V str. line BD is divided into... | |
| John Playfair - Euclid's Elements - 1846 - 332 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...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
...angle 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...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 - 138 pages
...47; (/) 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... | |
| George Roberts Perkins - Geometry - 1847 - 308 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... | |
| 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... | |
| 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... | |
| Euclides - 1848 - 52 pages
...other 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...perpendicular falls, and the straight line intercepted** without the triangle between the perpendicular and the obtuse angle. PROP. XIII. THEOREM. In every... | |
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