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" Any two sides of a triangle are together greater than the third side. "
Euclid's Elements of Geometry - Page 59
edited by - 1893 - 504 pages
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Space, Time and Gravitation: An Outline of the General Relativity Theory

Sir Arthur Stanley Eddington - Gravitation - 1923 - 242 pages
...true geometry? Phys. Yes. Our experimental work proves it true. Rel. How, for example, do you prove that any two sides of a triangle are together greater than the third side? Phys. I can, of course, only prove it by taking a very large number of typical cases, and I am limited...
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Plane Geometry

Walter Burton Ford, Charles Ammermann - Geometry, Modern - 1923 - 406 pages
...meet at the point D within the triangle, and if AB > AC, prove that DB > DC. 40. Prove that the sum of any two sides of a triangle are together greater than the third side. [HiNT. Given the A ABC. To prove AB + AC > BC. Proof. Prolong BA to D making AD = AC. Join D to C....
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Plane and Solid Geometry

Walter Burton Ford, Charles Ammerman - Geometry, Plane - 1923 - 414 pages
...meet at the point D within the triangle, and if AB > AC, prove that DB > DC. 40. Prove that the sum of any two sides of a triangle are together greater than the third side. [HINT. Given the A ABC. To prove AB + AC > BC. Proof. Prolong BA to D making AD = AC. Join D to C....
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Theoretical Geometry: Based on the Various Geometry Books by Godfrey and Siddons

Arthur Warry Siddons, Reginald Thomas Hughes - Geometry - 1926 - 202 pages
...angles of a triangle are unequal, the greater angle has the greater side opposite to it 36 ^THEOREM 18. Any two sides of a triangle are together greater than the third side 37 THEOREM 19. Of all the straight lines that can be drawn to a given straight line from a given point...
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The Analysis of Matter

Bertrand Russell - Matter - 1927 - 444 pages
...between B and C is zero, but that between A and C may have any time-like magnitude. Euclid proved that two sides of a triangle are together greater than the third side, and was criticized on the ground that this proposition was evident even to asses. But in relativity...
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Studies and Exercises in Formal Logic: Including a Generalisation of Logical ...

John Neville Keynes - Logic - 1928 - 580 pages
...ordinary formal logic, the two propositions, Every angle in a semi-circle is equal to a right angle, Any two sides of a triangle are together greater than the third side, may be considered to be identical in form. Each is universal, and each is affirmative ; they differ...
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Educational Review, Volume 6

Nicholas Murray Butler, Frank Pierrepont Graves, William McAndrew - Education - 1893 - 554 pages
...already proved. Euclid demonstrates things more axiomatic by far. He demonstrates what every dog knows, that any two sides of a triangle are together greater than the third. Yet after he has finished his demonstration, that straight lines making with a transversal equal alternate...
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Educational Review, Volume 6

Education - 1893 - 562 pages
...already proved. Euclid demonstrates things more axiomatic by far. He demonstrates what every dog knows, that any two sides of a triangle are together greater than the third. Yet after he has finished his demonstration, that straight lines making with a transversal equal alternate...
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Non-Euclidean Geometry: A Critical and Historical Study of Its Development

Roberto Bonola - Mathematics - 1955 - 452 pages
...Euclid without it. Euclid demonstrated things more axiomatic hy far. He proves what every dog knows, that any two sides of a triangle are together greater than the third. Yet after he has finished his demonstration, that straight lines making with a transversal equal alternate...
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Texas State Journal of Medicine, Volume 9

Medicine - 1914 - 422 pages
...who are distrustful of scientific methods. They will grudgingly admit that while, as a general thing, two sides of a triangle are together greater than the third side, yet after all we must be careful, as it is easy to carry mathematical reasoning too far.— Journal...
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