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" 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 - Side 29
av John Playfair - 1836 - 114 sider
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845
...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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The Elements of Geometry, Symbolically Arranged

Great Britain. Admiralty - 1846
...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...
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The Elements of Geometry, Symbolically Arranged

Great Britain. Admiralty - 1846
...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...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - 1846 - 317 sider
...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...
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The London University Calendar

London univ - 1846
...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...
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Euclid's Elements of geometry, the first three books (the fourth, fifth, and ...

Euclides - 1846
...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...
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The Mechanic's Magazine, Museum, Register, Journal and Gazette, Volum 38

1843
...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...
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Elementary Course of Geometry ...

Charles William Hackley - 1847 - 103 sider
...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...
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Elements of Geometry: With Practical Applications ...

George Roberts Perkins - 1847 - 308 sider
...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...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson with ...

Euclid, Robert Potts - 1847 - 478 sider
...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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