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Any side of a triangle is less than the sum of the other two sides.
Elements of Plane and Solid Geometry - Σελίδα 38
των George Albert Wentworth - 1877 - 398 σελίδες
Πλήρης προβολή - Σχετικά με αυτό το βιβλίο

Elements of Geometry and Conic Sections

Elias Loomis - 1858 - 234 σελίδες
...the other two sides of the triangle. Produce BD until it meets the side AC BC in E ; and, because one side of a triangle is less than the sum of the other two (Prop. VIII.). the side CD of the triangle CDE is less than the sum of CE and ED. To each of these...

Elements of Geometry and Conic Sections

Elias Loomis - 1860 - 234 σελίδες
...each, and the angle A to the angle D. Therefoxe, if two triangles, &c. PROPOSITION VIII. THEOREM. v Any side of a triangle is less than the sum of the other-two Let ABC be a triangle; any one of its aides is less than the sum of the other two, viz.:...

Elements of Geometry and Conic Sections

Elias Loomis - 1861 - 234 σελίδες
...each, and the angle A to the angle D. Therefore, if two triangles, dsc. PROPOSITION VIII. THEOREM. Any side of a triangle is less than the sum of the other two For the straight line AB is the shortest path between the points A and B (Def. 3) ; hence AB is less...

Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - 1861 - 490 σελίδες
...ABC is 61. Cor. Therefore every equiangular triangle is equilateral. PROPOSITION IX. — THEOREM. 62. Any side of a triangle is less than the sum of the other two. In the triangle ABC, any one side, as AB, is less than the sum of the other two sides, AC and C B....

Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - 1862 - 490 σελίδες
...BOOK I. 61. Cor. Therefore every equiangular triangle is equilateral. PROPOSITION IX. — THEOREM. 62. Any side of a triangle is less than the sum of the other two. In the triangle ABC, any one side, C as AB,is less than the sum of the other two sides, AC and C B....

Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - 1863 - 320 σελίδες
...isosceles. 61. Cor. Therefore every equiangular triangle is equilateral. PROPOSITION IX. — THEOREM. 62. Any side of a triangle is less than the sum of the other two. In the triangle ABC, any one side, as AB,is less than the sum of the other two sides, AC and C B. For...

Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - 1868 - 320 σελίδες
...isosceles. 61. Cor. Therefore every equiangular triangle is equilateral. PROPOSITION IX. — THEOREM. 62. Any side of a triangle is less than the sum of the other two. In the triangle ABC, any one side, as AB, is less than the sum of the other two sides, AC and C B....

The Normal Elementary Geometry: Embracing a Brief Treatise on Mensuration ...

Edward Brooks - 1868 - 275 σελίδες
...straight line can be drawn parallel to a given line. Corollary. Prom axiom 10, it is evident that either side of a triangle is less than the sum of the other two sides. POSTULATES. 32. The following postulates are self-evident problems resulting from the preceding definitions:—...

A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - 1871 - 368 σελίδες
...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 sides are AB and AC; then BC < AB + AC. For, the straight...

Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - 1871 - 58 σελίδες
...the other two sides of the triangle. Produce BD until it meets the side AC BC in E ; and, because one side of a triangle is less than the sum of the other two (Prop. VIII.), the side CD of the triangle CDE is less than the sum of CE and ED. To each of these...