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" AB>AC-BC: that is, the difference of any two sides of a triangle is less than the third side. "
A Course of Mathematics: In Two Volumes. For the Use of Academies, as Well ... - Page 257
by Charles Hutton - 1818
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New Plane and Solid Geometry

Wooster Woodruff Beman, David Eugene Smith - Geometry - 1899 - 416 pages
...v Z.ACD = Z.DCB, Step 1 .'. b > AD. Prop. VII. State it Similarly, a > DB. 3. ,'.a+b>c. COROLLARY. The difference of any two sides of a triangle is less than the third side. For if a + b > c, and c > b. then a > c - 6, by ax. 5. Exercises. 37. Two equal lines, AC and AD, are...
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New Plane Geometry

Wooster Woodruff Beman, David Eugene Smith - Geometry, Modern - 1899 - 265 pages
...it Step 1 Similarly, 3. Z CD A > .'. b > AD. a > DB. .'. a -f- b > c. Prop. VII. State it COROLLARY. The difference of any two sides of a triangle is less than the third side. For if a -f 6 > c, and c > b, then a > c — b, by ax. 5. Exercises. 37. Two equal lines, AC and AD,...
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Calendar, for the Year ...

1900 - 164 pages
...by one side and the produced part of another is greater than either of the interior opposite angles. The difference of any two sides of a triangle is less than the third side. 2. In the same or in equal circles, angles at the circumference which stand on equal arcs are equal....
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A Text-book of Euclid's Elements for the Use of Schools, Books I.-IV., Book 1

Henry Sinclair Hall, Frederick Haller Stevens - Euclid's Elements - 1900 - 304 pages
...respectively : shew that, if AB is greater than AC, then OB is greater than OC. ON PROPOSITION 20. 7. The difference of any two sides of a triangle is less than the third side. 8. In a quadrilateral, if two opposite sides which are not parallel are produced to meet one another...
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Elements of Plane Geometry

Alan Sanders - Geometry, Modern - 1901 - 260 pages
...THEOREM 168. The sum of two sides of a triangle is greater than, the third side, but the difference of two sides of a triangle is less than the third side. Let ABC be any A. To Prove . AR + BOAC. Proof. Apply axiom 14. Let DEF be any A. To Prove DE — EF < D F. Proof....
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Elementary Geometry, Plane and Solid: For Use in High Schools and Academies

Thomas Franklin Holgate - Geometry - 1901 - 460 pages
...What is the limitation on the construction in Proposition III. 3. Prove that the difference between any two sides of a triangle is less than the third side. PROPOSITION XVII 71. From a given point in a straight line to draw a perpendicular to the line. Let...
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Elementary Geometry

John Elliott (M.A.) - Geometry - 1902
...any two sides of a triangle are greater than the third side. This is often put more conveniently as " The difference of any two sides of a triangle is less than the third side." Statements about differences can be put as follows:— If AB is equal to the difference of CD and EF...
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Elementary Geometry: Practical and Theoretical

Charles Godfrey, Arthur Warry Siddons - Geometry - 1903 - 355 pages
...bisector of /.A, and applying I. 17 to the two triangles thus formed. Ex. 643. The difference between any two sides of a triangle is less than the third side. Prove this (i) by means of the same construction as in fig. 136. (ii) by means of the result of I....
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Rational Geometry: A Text-book for the Science of Space; Based on Hilbert's ...

George Bruce Halsted - Geometry - 1904 - 324 pages
...A perpendicular side-bisector which contains a vertex . 8. Two congruent angle-bisectors. Ex. 165. The difference of any two sides of a triangle is less than the third side. Ex. 1 66. From the ends of a side of a triangle the two sects to a point within the triangle are together...
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A Text-book of Euclid's Elements for the Use of Schools, Book 1

Euclid - Euclid's Elements - 1904 - 484 pages
...respectively : shew that, if AB is greater than AC, then OB is greater than OC. ON PROPOSITION 20. 7. The difference of any two sides of a triangle is less than the third side. 8. In a quadrilateral, if two opposite sides which are not parallel are produced to meet one another...
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