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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 Sydney University Calendar - Página 117
de University of Sydney - 1853
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1806 - 320 páginas
...rectangle AB.BH is equal to the square of AH. Which was to be done, Book II. PROP. XII. THEOR. IN obtuse angled triangles if a perpendicular be drawn from...produced, the square of the side subtending the obtuse aigle is greater than the squares of the sides contain ng the obtuse angle, by twice the rectangle...
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A Course of Mathematics ...: Composed for the Use of the Royal Military ...

Charles Hutton - 1811 - 406 páginas
...And AC + BC . AC — BC = AB.AD + BD in the 1st figure. THEOREM XXXVI. 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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A Course of Mathematics: For the Use of Academies as Well as Private Tuition

Charles Hutton - 1812 - 620 páginas
...And AC+BC . AC — BC =AB . AD + BD in the 1st figure. THEOREM XXXVI. 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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Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Volumen 5

John Mason Good - 1813 - 714 páginas
...the other part. Prop. XII. Theor. In obtuse angled triangles, if a perpendicular be drawn from any of the acute angles to the opposite side produced,...square of the side subtending the obtuse angle is greatcf than the squares of the sides containing the obtuse angle, by twice the rectangle contained...
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Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Volumen 5

John Mason Good - 1819 - 800 páginas
...the other part. 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 of the side subtending the obtuse anule it greatt-i than the squares of the sides containing the obtuse angle, by twice the rectangle...
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A Course of Mathematics: For the Use of Academies, as Well as Private ...

Charles Hutton - 1822 - 616 páginas
...+ BC . AC — BC = AB . AB -f- BB in the 1st figure. THEOREM XXXVI. 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, transl. To which are added, algebraic ...

Euclides - 1826 - 226 páginas
...equal to the square of AH. Which was to be done. PROPOSITION XII. THEOREM. In obtuse angled triangles, the square of the side subtending the obtuse angle is greater than the squares, which are made by the sides containing the obtuse angle by twice the rectangle contained under one...
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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - 1829 - 210 páginas
...in all respects. In any obtuse-angled triangle, if a perpendicular be drawn from either of the two acute angles to the opposite side produced, the square...side subtending the obtuse angle is greater than the sum of the squares of the sides containing it by twice the rectangle under the base and the distance...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - 1832 - 358 páginas
...was to be done. B PROP. XII. THEOR. In obtuse angled triangles, if a perpendicular be drawn from any of the acute angles to the opposite side produced,...subtending the obtuse angle is greater than the squares of I he sides containing the obtuse angle, by twice Ihe reel angle contained by the side upon which, when...
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - 546 páginas
...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...
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