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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... "
Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ... - Page 96
by Robert Potts - 1860 - 361 pages
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 400 pages
...square on AH. QEF PKOPOSITION 12. THEOREM. In obtuse-angled triangles, if a perpendicular lie 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...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 400 pages
...sides containing the acute angle. 127. The square on the side subtending an obtuse angle of a triangle is greater than the squares on the sides containing the obtuse angle. 128. If the square on one side of a triangle bo less than the squares on the other two sides, the angle...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 410 pages
...obtuse-angled triangles, if a perpendicular be drawn from either of the mute angles to the opposite tide produced, the square on the side subtending the obtuse...which, when produced, the perpendicular falls, and t/ie straight line intercepted without the triangle between the perpendicular and the obtuse angle....
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Elementary Geometry, Volume 1

James Maurice Wilson - Geometry - 1868
...-2CBxBD (by Theorem 26). Therefore A C" = AB* + BC* - 2 CB x BD. THEOREM 31. In an obtuse-angled triangle the square on the side subtending the obtuse angle...is greater than the squares on the sides containing that angle by twice the rectangle contained by either of these sides and the projection on it of the...
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Papers for the schoolmaster, Volume 4

1868
...triangle, if a perpendicular be drawn from either of the acute angles to the opposite side prsrtuced, the square on the side subtending the obtuse angle is greater than the sqnares on the sides containing the obtuse angle, by twice the rectangle contained by the side upon...
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Elements of geometry, containing the first two (third and fourth ..., Part 1

Euclides - 1871
...XIIL of Book II. Thus the enunciation of Prop. xn. might be : — • " In oblique-angled triangles, the square on the side subtending the obtuse angle...is greater than the squares on the sides containing that angle, by twice the rectangle contained by one of these sides and the projection of the other...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - Geometry - 1872 - 349 pages
...and XIH. of Book II. Thus the enunciation of Prop. xn. might be : — " In oblique.angled triangles, the square on the side subtending the obtuse angle...is greater than the squares on the sides containing that angle, by twice the rectangle contained by one of these sides and the projection of the other...
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The first and second books of Euclid explained to beginners, by C.P. Mason

Euclid, Charles Peter Mason - Geometry - 1872
...In an obtuse-angled triangle the square on the side subtending the obtuse angle exceeds the sum of the squares on the sides containing the obtuse angle by twice the rectangle contained by either of them and the distance between a perpendicular drawn to that side produced from the opposite...
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The Acting Teacher's and Student's in Training Guide and Text Book for ...

Henry Major - Student teachers - 1873
...AB, BH is equal to the square of AIL XII. — 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 sub' tending the obtuse angle, is greater than the squares of the sides containing the...
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A school Euclid, being books i. & ii. of Euclid's Elements, with notes by C ...

Euclides - 1874
...in section.' medial PROPOSITION 12. THEOREM. In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side...angle, by twice the rectangle contained by the side on which, when produced, the perpendicular falls, and the staight line intercepted without the triangle,...
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