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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 - 1825 - 224 pages
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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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The Teaching of Elementary Mathematics

David Eugene Smith (mathematics) - Mathematics - 1900 - 342 pages
...example, that equals result from adding equals to equals. But when Euclid was criticised for proving that one side of a triangle is less than the sum of the other two, as having proved what even the beasts know, his disciples were entirely right in saying that they were...
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College Algebra

James Harrington Boyd - Algebra - 1901 - 812 pages
...side of the octagon would be longer than the side of the square, which is not possible. * Since any side of a triangle is less than the sum of the other two sides, 2 а > b, and 4 аг > Ь2; hence v 4 ns — 6г is always real. PROBLKM V. — The median lines...
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Elementary Geometry, Plane and Solid: For Use in High Schools and Academies

Thomas Franklin Holgate - Geometry - 1901 - 460 pages
...rectangle contained by either of the equal sides and the projection on it of the base. 13. If the square on one side of a triangle is less than the sum of the squares on the other two sides, how does the angle contained by these two sides compare with a right...
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Euclid, His Life and System

Thomas Smith (D.D.) - Euclid's Elements - 1902 - 244 pages
...some geometric truth, as, for example, of that truth which now takes rank as a proposition, that any one side of a triangle is less than the sum of the two others. We might go further, and say that 1 " Dublin University Press" Series, Greek Geometry from...
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The New International Encyclopędia, Volume 6

Daniel Coit Gilman, Harry Thurston Peck, Frank Moore Colby - Encyclopedias and dictionaries - 1903 - 1072 pages
...the other in solid geometry, as when the terms triangle and trihedral anale дге interchanged : eg one side of a triangle is less than the sum of the other two ; one face angle of я trihedral angle is less than the sum of the other two. The term duality appears...
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Plane Geometry by the Suggestive Method

John Alton Avery - Geometry, Modern - 1903 - 136 pages
...CRB. Auth. SUG. 2. Compare CM and (7/£, using Scholiums under Theo. VI. Conclusion. 38. Scho. Any side of a triangle is less than the sum of the other two sides. EXERCISES 13. The bisector of the vertical angle of an isosceles triangle is perpendicular to...
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Mathematics, mechanics, heat

American School (Chicago, Ill.) - Engineering - 1903 - 392 pages
...base. 68. Since a straight line is the shortest distance between two points, it follows that either side of a triangle is less than the sum of the other two. THEOREM XV. 69. Either side of a triangle is greater than the difference of the other two. Let ABC...
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Elementary Geometry: Plane

James McMahon - Geometry, Plane - 1903 - 380 pages
...to any point in the base extended is greater than either side. Sum of two sides. 87. THEOREM 17. Any side of a triangle is less than the sum of the other two. Let ABC be a triangle. To prove that any side AB is less than X/ the sum of the other two sides AC...
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School Science and Mathematics, Volume 6

Education - 1906 - 958 pages
...which begin with the triangle it is an easy matter to avoid the use of this axiom by assuming that "one .side of a triangle is less than the sum of the other two sides," but if they begin with the simple relations of lines and angles it seems necessary that some...
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