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" ... the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle between the perpendicular and the obtuse... "
Euclid's Elements of geometry, books i. ii. iii. iv - Side 66
av Euclides - 1862
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A complete practical guide to her majesty's Civil service, by a certificated ...

Civil service - 366 sider
...the square of the straight line which is made up of the half and the part produced. PEOP. XII. — In obtuse-angled triangles, if a perpendicular be...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...
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Examination papers used at the examinations for direct commissions [&c.].

War office - 1861 - 714 sider
...given rectilineal figure and have an angle equal to a given rectilineal angle. 3. In obtuse angled triangles, if a perpendicular be drawn from either...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...
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Responsions

University of Oxford - 1863 - 328 sider
...half the line bisected and of the square of the line made up of the half and the part produced. 10. In obtuse-angled triangles, if a perpendicular be...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...
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The school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864 - 448 sider
...divided in H, so that the rectangle AB, BH is equal to the square on AH. QEF PROPOSITION XII. THEOREM. 2n obtuse-angled triangles, if a perpendicular be drawn...from either of the acute angles to the opposite side produved, the square on the side subtending the obtuse angle, is greater than the squares on the sides...
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Papers Read at the Royal Institute of British Architects

1865 - 276 sider
...5. What is the definition of the gnomon of a parallelogram ? 6. Prop. 12. Theorem. In obtuse angled triangles, if a perpendicular be drawn from either...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...
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The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865 - 402 sider
...II. 1. D. On the Relations between the Sides of a Triangle and the Perpendicular from the Vertet. 1. In obtuse-angled triangles, if a perpendicular be...from either of the acute angles to the opposite side prodnced, the square on the side subtending the obtuse angle is greater than the squares on the sides...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1867 - 426 sider
...to the 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 - 1867 - 424 sider
...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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Elementary Geometry, Volum 1

James Maurice Wilson - 1868 - 132 sider
...-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, Volum 4

1868 - 344 sider
...the whole and that part, together with the square of the other part. 3. In an obtuse angled 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...
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