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" The sum of the three straight lines drawn from any point within a triangle to the three vertices, is less than the sum and greater than the half sum of the three sides of the triangle (I . 33, 66). "
Elements of Geometry - Page 90
by Simon Newcomb - 1881 - 399 pages
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Elements of Geometry: Including Plane, Solid, and Spherical Geometry

George Washington Hull - Geometry - 1807 - 408 pages
...has the greatest vertical angle. 361. The sum of the lines drawn from the centre of an equilateral triangle to the three vertices is less than the sum of the lines drawn from any other point to these vertices. PROPOSITION VIII. THEOREM. 364. Of all polygons...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1871 - 380 pages
...exercises, and the student is finally left wholly to his own resources. GEOMETRY.— BOOK I. THEOREMS. 1. The sum of the three straight lines drawn from any...triangle to the three vertices, is less than the sum and greater than the half sum of the three sides of the triangle (I. 33, 66). 2. The medial line to...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1872 - 382 pages
...exercises, and the student is finally left wholly to his own resources. GEOMETRY.—BOOK I. THEOREMS. 1. The sum of the three straight lines drawn from any...triangle to the three vertices, is less than the sum and greater than the half sum of the three sides of the triangle (I . 33, 66). 2. The medial line to...
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A Treatise on Special Or Elementary Geometry: In Four Parts ..., Part 3

Edward Olney - Geometry - 1872 - 96 pages
...construction is needed. The demonstration is based upon the doctrine of parallels. 627. The sum of three straight lines drawn from any point within a triangle to the vertices is less than the sum, and greater than the half sum of the three sides of the triangle. SUG'S.—...
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A Treatise on Special Or Elementary Geometry, Volumes 1-2

Edward Olney - Geometry - 1872 - 562 pages
...construction is needed. The demonstration is based upon the doctrine of parallels. 627- The sum of three straight lines drawn from any point within a triangle to the vertices is less than the sum, and greater than the half sum of the three sides of the triangle. Suo's....
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A Treatise on Special Or Elementary Geometry: An advanced course in geometry

Edward Olney - Geometry - 1872 - 102 pages
...construction is needed. The demonstration is based upon the doctrine of parallels. 027- The sum of three straight lines drawn from any point within a triangle to the vertices is less than the sum, and greater than the half sum of the three sides of the triangle. Sue's.—The...
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Elements of Geometry with Exercises for Students: An an Introduction to ...

Aaron Schuyler - Geometry - 1876 - 384 pages
...point within a triangle to the vertices is greater than one-half the sum of the three sides (65). 3. The sum of the three straight lines drawn from any point within a triangle to the vertices is less than the sum of the three sides (68). 4. In a right triangle, the middle point of...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Conic sections - 1877 - 458 pages
...sides is bisected in that point, and also bisects- the parallelogram. See Props. 7 and 29. Prop. 10, The sum of the three straight lines drawn from any...triangle to the three vertices is less than the sum and greater than the half sum of the three sides of the triangle. See Props. 8 and 9. PROBI.EMS. *...
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A Treatise on Elementary Geometry, with Appendices Containing a Collection ...

William Chauvenet - Geometry - 1879 - 380 pages
...exercises, and the student is finally left wholly to his own resources. GEOMETRY.—BOOK L THEOREMS. 1. The sum of the three straight lines drawn from any...within a triangle to the three vertices, is less than tne.sum and greater than the half sum of the three sides of the triangle (I . 33, 66). 2. The medial...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - 1880 - 456 pages
...sides is bisected in that point, and also bisects the parallelogram. See Props. 7 and 29. Prop. 10. The sum of the three straight lines drawn from any...a triangle to the three vertices is less than the sura and greater than the half sum of the three sides of the triangle. See Props. 8 and 9. PROBI.EMS....
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