 If, from a point within a triangle, two straight lines are drawn to the extremities of either side, their sum will be less than the sum of the other two sides of the triangle.  Elements of Geometry - Page 45by Andrew Wheeler Phillips, Irving Fisher - 1897 - 354 pagesFull view - About this book
 | William Chauvenet - Geometry - 1875 - 390 pages
...triangle two arcs of great circles are drawn to a point within the triangle, the sum of these arcs is less than the sum of the other two sides of the triangle. BOOK viii. 263 In the spherical triangle ABC, let the arcs BD and CD be drawn to any point D within... | |
 | Elias Loomis - Conic sections - 1877 - 458 pages
...AC, and AC less than the sum of AB and BC. Therefore, any two sides etc. * PROPOSITION IX. THEOREM. If, from a point within a triangle, two straight lines are drawn to the extremities of either side, their sum will be less than the sum of the other two sides of the triangle. Let the two... | |
 | George Albert Wentworth - Geometry - 1877 - 416 pages
...triangle, two arcs of great circles be drawn to a point within the triangle, the sum of these arcs is less than the sum of the other two sides of the triangle. 2. On the same sphere, or on equal spheres, if two spherical triangles have two sides of the one equal... | |
 | Universities and colleges - 1879 - 88 pages
...drawn from each of the angular points to the opposite side ? Illustrate. 2. Prove this proposition : 14 from a point within a triangle two straight lines are drawn to the extremities of either side, their sum will be less than the sum of the other two sides of the triangle. 3. (a) What... | |
 | George Albert Wentworth - 1879 - 196 pages
...height of the second. Ans. 10 in. PAGE 383. to a point within the triangle, the sum of these arcs is less than the sum of the other two sides of the triangle. In the spherical A ABC, let the arcs BD and CD be drawn to any point D within the A. Produce BD to... | |
 | Simon Newcomb - Geometry - 1881 - 418 pages
...If from any point within a triangle lines be drawn to the ends of the base, the sum of these lines will be less than the sum of the other two sides of the triangle, but they will contain a greater angle. Hypothesis. ABC, any triangle; P, any point within it. Conclusions.... | |
 | Edward Olney - Geometry - 1883 - 352 pages
...triangle arcs of great circles be drawn to the extremities of any side, the sum of these two arcs is less than the sum of the other two sides of the triangle. PROPOSITION XVII. 697. Theorem.— The trirectangular triangle is oneeighth of the surf aee of the... | |
 | Delaware. General Assembly. House of Representatives - Delaware - 1885 - 1060 pages
...Demonstrate : If from any point within a triangle, two straight lines be drawn to the extremities of any side, their sum will be less than the sum of the other two sides of the triangle. 4. — Prove that the diagonals of a rectangle are equal to each other. 5. — In a triangle the two... | |
 | Trinity College (Hartford, Conn.) - 1888 - 978 pages
...is^. What are the numbers? PLANK GEOMETRY. Demonstrate the following propositions : 1. If from any point within a triangle two straight lines are drawn to the extremities of any side, their sum is less than that of the two remaining sides of the triangle. 2. If two circumferences... | |
 | Euclid - Geometry - 1890 - 442 pages
...side of a triangle two straight lines are drawn to a point within the triangle, the sum of them is less than the sum of the other two sides of the triangle ; but they contain a greater angle. Let P be a pt., within the A ABC, to which BP, CP are drawn. Produce... | |
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