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" Any side of a triangle is less than the sum of the other two sides... "
Elements of Geometry - Page 8
by Adrien Marie Legendre - 1841 - 235 pages
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The Elements of Solid Geometry

William C. Bartol - Geometry, Solid - 1893 - 112 pages
...351. Two parallel lines cannot meet. 352. Two lines perpendicular to the same straight line 353. Any side of a triangle is less than the sum of the other two sides. 354. The sum of the three angles of a triangle is equal to two right angles. 355. Two triangles...
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Plane and Solid Geometry: Suggestive Method

George Clinton Shutts - Geometry - 1894 - 412 pages
...the vertical angle of an isosceles triangle bisects the triangle. PROPOSITION XI. 87. Theorem. Any side of a triangle is less than the sum of the other two. A Let ABC represent any triangle. To prove that any side, as AB, is less than the sum o] the other...
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Elements of Geometry: Plane and Solid

John Macnie - Geometry - 1895 - 390 pages
...acute ; (2) without the triangle if one of those angles is obtuse. PROPOSITION XIX. THEOEEM. 88. Any side of a triangle is less than the sum of the other two. Given : Any side BC of a triangle ABC ; To Prove : BC is less than AB + AC. Produce BA to D, so that...
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Concrete Geometry for Beginners

Adelia Roberts Hornbrook - Geometry - 1895 - 222 pages
...the longer, AB or A C+ CB ? 73. Show the truth of the following proposition : PRINCIPLE 3. — Any side of a triangle is less than the sum of the other two sides. 74. Cut three narrow strips of paper, one 10 inches long, the others each 5 inches long, and...
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Number and Its Algebra: Syllabus of Lectures on the Theory of Number and Its ...

Arthur Lefevre - Algebra - 1896 - 242 pages
...empiricism, — never to clip the growing tree at the top. Now every man (and every dog) knows that one side of a triangle is less than the sum of the other two sides ; but no one would suppose that this circumstance entitled every man to opinions concerning the...
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Essentials of Geometry (plane).

Webster Wells - Geometry - 1898 - 264 pages
...angle. BD 61. Since a straight line is the shortest line between two points (Ax. 4), it follows that Any side of a triangle is less than the sum of the other two sides. PROP. XIV. THEOREM. 62. Any side of a triangle is greater than the difference of the other two...
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Plane and Solid Geometry

James Howard Gore - Geometry - 1898 - 232 pages
...77. Since a straight line is the shortest distance between two points (by 6), it follows that either side of a triangle is less than the sum of the other two. 78. By (77) BC < AB + AC. Transpose AB, then BC-AB<AC; that is, any side of a triangle is greater than...
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The Essentials of Geometry

Webster Wells - Geometry - 1899 - 424 pages
...BD C 61. Since a straight line is the shortest line between two points (Ax. 4), it follows that Any side of a triangle is less than the sum of the other two sides. PROP. XIV. THEOREM. 62. Any side of a triangle is greater than the difference of the other two...
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Plane Geometry

William James Milne - Geometry, Modern - 1899 - 258 pages
...the other two sides? 2. How does the sum of any two sides compare with the third side? Theorem. .Any side of a triangle is less than the sum, of the other two sides. c Data : Any triangle, as ABC, and any side, as AC. To prove AC less than AB + BC. AB Proof....
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Plane and Solid Geometry

William James Milne - Geometry - 1899 - 396 pages
...the other two sides ? 2. How does the sum of any two sides compare with the third side? Theorem. Any side of a triangle is less than the sum of the other two sides. c Data : Any triangle, as ABC, and any side, as AC. To prove AC less than AB + BC. AB Proof....
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