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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 of the side subtending the obtuse angle, is greater than the squares of the sides containing the obtuse angle, by twice the... "
Elementary Course of Geometry ... - Pągina 33
per Charles William Hackley - 1847 - 103 pągines
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Short, But Yet Plain Elements of Geometry: Shewing how by a Brief and Easie ...

Ignace Gaston Pardies - 1734 - 164 pągines
...PROP. II. In an Acute-angled Triangle, the Square of the Side (h) fubtending an Acute Angle, " is lefs than the Sum of the Squares of the other two Sides, by double the Rettangle under the whole Safe, (b + a) and the Segment of the Bafe (a) which is next to...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1806 - 518 pągines
...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 greater than the squares of the sides containing the obtuse angle, by twice the rectangle contained by the side upon...
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A Course of Mathematics ...: Composed for the Use of the Royal Military ...

Charles Hutton - 1811
...AD — BD in the 2d figure. And AC + BC . AC — BC = AB.AD + BD in the 1st figure. THEOREM XXXVI. IN any Obtuse-angled Triangle, the Square of the Side...of the other two Sides, by Twice the Rectangle of the Base and the Distance of the Perpendicular from the Obtuse Angle. ( Let ABC be a triangle, obtuse...
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A Course of Mathematics: For the Use of Academies as Well as Private Tuition

Charles Hutton - 1812
...AB . AD - BD in the 2d figure. And AC+BC . AC — BC =AB . AD + BD in the 1st figure. THEOREM XXXVI. IN any Obtuse-angled Triangle, the Square of the Side...of the other two Sides, by Twice the Rectangle of the Base and the Distance of the Perpendicular from the Obtuse Angle. Let ABC be a triangle, obtuse...
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An Easy Introduction to the Mathematics: In which the Theory and ..., Volum 2

Charles Butler - 1814
...from the former,) -- Therefore AB>* —~Ub\* + ~*Tl1= ...... 2 bx * * That is, the square of ^B/the side subtending the obtuse angle,, is greater than the sum of the squares of CB and AC, the sides containing the obtuse angle, by (2 bx) twice the rectangle BC, CD. QED 175. Prop....
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A Course of Mathematics: In Two Volumes : for the Use of Academies ..., Volum 1

Charles Hutton - 1816
...in the 1st figure. THEOREM XXXVI. IN any Obtuse-angled Triangle, the Square of the Side subren .ing the Obtuse Angle, is Greater than the Sum of the Squares of the other two Sides, by Twice the Rrctungle of the Base and the Distance of the Perpendicular from the Obtuse Angle. Let ABC be a triangle,...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 528 pągines
...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 greater than the squares of the sides containing the obtuse angle, by twice the, rectangle contained by the side upon...
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A Course of Mathematics: For the Use of Academies, as Well as Private Tuition

Charles Hutton - 1818
...in the 1st figure. THEOREM XXXVI. IN any Obtuse-angled Triangle, the Square of the Side subtenHing 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 (he Perpendicular from the Obtuse Angle. Let ABC be a triangle, obtuse...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 317 pągines
...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 greater than the squares of the sides containing the obtuse angle, by twice the rectangle contained by the side upon...
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A Course of Mathematics: For the Use of Academies, as Well as Private ...

Charles Hutton - 1822
...— BD in the 2d figure. And AC + BC . AC — BC = AB . AB -f- BB in the 1st figure. THEOREM XXXVI. IN any Obtuse-angled Triangle, the Square of the Side...of the other two Sides, by Twice the Rectangle of the Base and the Distance of the Perpendicular from the Obtuse Angle. Let ABC be a triangle, obtuse...
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