 | James Wallace MacDonald - Geometry - 1894 - 76 pages
...right angle. 4. A line bisecting one of two vertical angles will, if continued, bisect the other. 5 . The sum of any two sides of a triangle is greater than the sum of any two lines drawn from any point in the triangle to the extremities of the third side. 6.... | |
 | James Wallace MacDonald - Geometry - 1889 - 80 pages
...right angle. 4. A line bisecting one of two vertical angles will, if continued, bisect the other. 5. The sum of any two sides of a triangle is greater than the sum of any two lines drawn from any point in the triangle to the extremities of the third side. 6.... | |
 | Seth Thayer Stewart - Geometry, Modern - 1891 - 428 pages
...preceding axioms are not inverted inequalities. * For other axioms, see p. 6. PROPOSITION XI. 145. Theorem : The sum of any two sides of a triangle is greater than the third side, and the difference between any two sides is less than the third side. 4 Statement : Let ABC be a triangle.... | |
 | 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 than the third side, and the difference between any two sides is less than the third side. PROPOSITION XII. 146. Theorem... | |
 | 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 the third side; namely,... | |
 | 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.... | |
 | 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.... | |
 | 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 - 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... | |
 | 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... | |
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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. 
