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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... "
Elements of Geometry: Containing the First Six Books of Euclid, with a ... - Page 62
by John Playfair - 1819 - 333 pages
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1806 - 518 pages
...was to be done. PROP. XII. THEOR. IN obtuse angled triangles, if a perpendicular be drawn from any of the acute angles to the opposite side produced, the...perpendicular falls, and the straight line intercepted without the triangle between the perpendicular and the obtuse angle. Let ABC be an obtuse angkd triangle,...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1806 - 311 pages
...done, Book II. PROP. XII. THEOR. 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 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 - Mathematics - 1811
...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 - Mathematics - 1812
...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) cyclopędia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1813
...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 angle is greatcf than the squares of the sides containing the obtuse angle, by twice the rectangle contained...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1814
...done. <r HB D PROP. XII. THEOR. IN obtuse angled triangles, if a perpendicular be drawn from any of the acute angles to the opposite side produced, the...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
...to be done. D PROP. XII. THEOtt. IN obtuse angled triangles, if a perpendicular be drawn from any of the acute angles to the opposite side produced, the...perpendicular falls, and the straight line intercepted without the triangle between the perpendicular and the obtuse angle. : ABC be an obtuse angled triangle,...
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Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1819
...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 - 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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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 372 pages
...done. Proposition XII. Theorem. In obtuse angled triangles, if a perpendicular be drawn from any of the acute angles to the opposite side produced, the...perpendicular falls, and the straight line intercepted without the triangle between the perpendicular and the obtuse angle. Let ABC be an obtuse-angled triangle,...
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