 In obtuse-angled triangles, if a perpendicular be 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...  The Element of Geometry - Page 29by John Playfair - 1836 - 114 pagesFull view - About this book
 | Euclides - 1845 - 546 pages
...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... | |
 | Great Britain. Admiralty - Geometry - 1846 - 128 pages
...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...triangle between the perpendicular and the obtuse angle. A Y str. line BD is divided into 2 parts in pt. C, BD« = BC 8 +CD 8 + 2. BC. CD, Prop. ta. add to... | |
 | Great Britain. Admiralty - Geometry - 1846 - 128 pages
...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...triangle between the perpendicular and the obtuse angle. A V str. line BD is divided into 2 parts in pt. C, BD8 = BC a +CD8+2. BC. CD, Prop.«. add to each... | |
 | Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...triangles, if a perpendicular be drawn from any of the acute angles to the opposite side produced, the square of the side subtending the obtuse angle is...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
...triangle, if a perpendicular be drawn from any 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 it, by twice the rectangle contained by the side on which when produced the perpendicular falls, and... | |
 | 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
...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 is...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
...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... | |
 | George Roberts Perkins - Geometry - 1847 - 326 pages
...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
...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... | |
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