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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 - Page 29
by John Playfair - 1836 - 114 pages
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1806 - 311 pages
...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 contained...perpendicular falls, and the straight line intercepted between the perpendicular and the obtuse angle. a 12. 1. b4.! c 47. 1. Let ABC b( an obtuse angled...
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A Course of Mathematics ...: Composed for the Use of the Royal Military ...

Charles Hutton - Mathematics - 1811
...+ 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 - Mathematics - 1812
...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) cyclopędia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1813
...angles to the opposite side produced, the square of the side subtending the obtuse angle is greatcf than the squares of the sides containing the obtuse...triangle between the perpendicular and the obtuse angle. Prop. XIII. Theor. In every triangle, the square of the side subtending any of the acute angles, is...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1814
...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...produced, the perpendicular falls, and the straight line intercopted without the triangle between the perpendicular and the obtuse angle. Because the straight...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 528 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...triangle between the perpendicular and the obtuse angle. : ABC be an obtuse angled triangle, having the obtuse angle ACS, and from the .point A. let AD be drawn"...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Circle-squaring - 1819 - 333 pages
...triangles, if a perpendicular be drawn front any of i the acute angles to the opposite side produced, the square of the side subtending the obtuse angle is...perpendicular falls, and the straight line intercepted between the perpendicular and the obtuse angle. Let ABC be an obtuse angled triangle, having the obtuse...
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Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1819
...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 contained br the side upon which, when produced, the perpendicular falls, and the straight line intercepted without...
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A Course of Mathematics: For the Use of Academies, as Well as Private ...

Charles Hutton - Mathematics - 1822
...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
...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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