| Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...therefore equal in all respects (I., D. 15) ; which was to be proved. PROPOSITION VII. THEOREM. The sum of any two sides of a triangle is greater than the...side. Let ABC be a triangle : then will the sum of any two sides, as AB, BC, be greater than the third side AC. For, the distance from A to C, measured... | |
| Charles Davies - Geometry - 1886 - 352 pages
...C. Of Triangles. THEOREM X. The sum of any two sides of a tr1angle is cheater than the third cide. Let ABC be a triangle • then will the sum of two of its sides, as AC, CB, be g1eater than the third side AB. A ft For the straight line AB is the shortest distance between the... | |
| Thomas Martin Herbert - Consciousness - 1886 - 486 pages
...continent of 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.'1 In the example of belief given by Mr. Mill, ' we believe that there is a continent of America,'... | |
| Dalhousie University - 1889 - 220 pages
............................. C. MACDONALD, MA (For Matriculation.) GEOMETRY AND ALGEBRA TIME : THREE HOURS. 1. The sum of any two sides of a triangle is greater than the third eide. 2. Either diagonal of a parallelogram divides it into two triangles equal in every respect. 3.... | |
| Seth Thayer Stewart - Geometry - 1891 - 428 pages
...: 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
...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 - 344 pages
...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
...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.... | |
| University College, Galway - 1898 - 448 pages
...— =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
...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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