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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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A Treatise on Special Or Elementary Geometry: An advanced course in geometry

Edward Olney - Geometry - 1872 - 102 pages
...of the other sides. The figure will suggest the demonstration, which is based on the fact that any side of a triangle is less than the sum of the other two. FIG. 474. 923. Tlieo.—The difference between the distances from two points on opposite sides of a fixed...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1872 - 382 pages
...vertex upon the base is then called the altitude of the triangle. PROPOSITION XVII—THEOREM. 66. Any side of a triangle is less than the sum of the other two. Let BC be any side of a triangle whose other two Bides are AB and AC; then BC < AB + AC. For, the straight...
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A Treatise on Special Or Elementary Geometry, Volumes 1-2

Edward Olney - Geometry - 1872 - 562 pages
...of the other sides. The figure will suggest the demonstration, which is based on the fact that any side of a triangle is less than the sum of the other two. Fio. 923. TJieo. — The difference between the distances from two points on opposite sides of a fixed...
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New Elementary Geometry: With Practical Applications ; a Shorter Course Upon ...

Benjamin Greenleaf - Geometry - 1873 - 202 pages
...triangle bisects the base at right angles. 4. Every equilateral triangle is also equiangular. 5. Any side of a triangle is less than the sum of the other Y. two. 6. The difference between any two sides of a triangle is less than the other side. T. The side...
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New Elementary Geometry: With Practical Applications : a Shorter Course Upon ...

Benjamin Greenleaf - Geometry - 1874 - 206 pages
...and A C. Let the straight line BO be produced till it meets the side AC in the point D ; and because one side of a triangle is less than the sum of the other two sides (26, Ax. 10), the side OC in the triangle CD O is less than the sum of OD and D C. To each of...
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The Methodist Quarterly Review, Volume 57

Methodist Church - 1875 - 714 pages
...in some one of these special forms, to the exclusion of the others. But the mind which affirms that one side of a triangle is less than the sum of the other two, takes no account of these details of form, but dwells simply upon that general concept of a triangle...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1875 - 390 pages
...upon the base is then called the altitude of the triangle. PROPOSITION XVII.— THEOREM. 66. Any aide of a triangle is less than the sum of the other two. Let BC be any side of a triangle whose other two Bides are AB and AC; then BC < AB + AC. For, the straight...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Conic sections - 1877 - 458 pages
...•Let two circumferences cut each other in the point A. Draw the radii CA, DA ; then, because any side of a triangle is less than the sum of the other two (BI, Pr. 8), CD must be less than the sum of AD and AC. Also, DA must be less than the sum of CD and...
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Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 416 pages
...are opposite the exterior angle, are called the two opposite interior angles, as AA and С. 96. Any side of a triangle is less than the sum of the other two sides. Since a straight line is the shortest distance between two points, AC<AB + BC. 97. Any side...
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Elements of Geometry: And the First Principles of Modern Geometry

William Henry Harrison Phillips - Geometry - 1878 - 236 pages
...Any side may be taken as the base. The sign A is often used for the word triangle. XVT. Theorem. Any side of a triangle is less than the sum of the other two sides, and greater than their difference. HYPOTH. Let AB be any side of the triangle, ABC. To BE PROVED....
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