 America, but know that we are alive, that two and two make four, and that the sum of any two sides of a triangle is greater than the third side.  Plane and Solid Geometry - Page 54by George Albert Wentworth, David Eugene Smith - 1913 - 470 pagesFull view - About this book
 | Seth Thayer Stewart - Geometry - 1891 - 428 pages
...Conclusion : ABC being any triangle, and AB and AC being any two sides, it follows, in general, that : The sum of any two sides of a triangle is greater...between any two sides is less than the third side. PROPOSITION XII. 146. Theorem : The greater side in any triangle has the greater angle opposite to... | |
 | Seth Thayer Stewart - Geometry, Modern - 1891 - 422 pages
...being any triangle, and AB and AC being any two sides, it follows, in general, that : The sum of any TO sides of a triangle is greater than the third side, and the .rence between any two sides is less than the third side. PROPOSITION XII. 146. Theorem : The greater... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 344 pages
...without the assump- y<_ tion. Now reverse the process ; v Z b > Z a, OBA .'. PA>PBbyth. 7. Theorem 8. The sum of any two sides of a triangle is greater than the third side. Given the A ABC. To prove that a + b > c. Proof. 1. Suppose ZC bisected by CD. 2. ThenZCDA>Z DCB. Th.... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 346 pages
...assuming the theorem untrue, and endeavor to show the absurdity. (Reductio ad absurdum.} Theorem 8. The sum of any two sides of a triangle is greater than the third side. Given the A ABC. To prove that a + b> c. Proof. 1. Suppose /_ C bisected by CD. 2. ThenZCDA>ZDCB. Th.... | |
 | Henry Martyn Taylor - Euclid's Elements - 1895 - 708 pages
...bisecting the vertical angle : prove that the greater part is adjacent to the greater side. PROPOSITION 20. The sum of any two sides of a triangle is greater than the third side. Let ABC be a triangle : it is required to prove that the sum of any two sides of it is greater than... | |
 | George Albert Wentworth - Mathematics - 1896 - 68 pages
...from the extremities of a straight line is the perpendicular bisector of that line. 137. The sum of two sides of a triangle is greater than the third side, and their difference is less than the third side. 138. The sum of the three angles of a triangle is equal... | |
 | University College, Galway - 1898 - 448 pages
...5 — + — =9' 5. Find the HCF of 27s3 - 39zs + 23* - 7 and 135z3 - 114*" - 2* + 7. 7. Prove that the sum of any two sides of a triangle is greater than the third side. 8. Divide a straight line so that the rectangle contained by the whole and one part may be equal to... | |
 | George Chrystal - Algebra - 1898 - 476 pages
...the hypotenuse, that side is £ of the other side. 6. Deduce from the theorem <? = a? + 62 + 2bx that the sum of any two sides of a triangle is greater than the third, and their difference less. * See Henrici, Art. "Geometry," Encyclopaedia Britannica, 9th ed. vol. xp... | |
 | George Chrystal - Algebra - 1898 - 480 pages
...the hypotenuse, that side is | of the other side. 6. Deduce from the theorem c3= a2 + 62 + Zlix that the sum of any two sides of a triangle is greater than the third, and their difference less. * See Henrici, Art. "Geometry," Encydopaxlia Britannica, 9th ed. vol. xp... | |
 | William James Milne - Geometry - 1899 - 404 pages
...ABC which joins the points A and C. That is, AC is less than AB + BC. Therefore, etc. QED 125. Cor. The sum of any two sides of a triangle is greater than the third side. Ex. 65. May a triangle be formed with lines 4, 2, and 3 inches long ? With lines 6, 1, and 2 inches... | |
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