 | Eugene Randolph Smith - Geometry, Plane - 1909 - 424 pages
...respectively greater than, equal to, or less than, the angle opposite the second side, and conversely. (b) The sum of two sides of a triangle is greater than the third side; their difference is less than that side. (c) The perpendicular bisectors of the sides of... | |
 | Robert Louis Short, William Harris Elson - Mathematics - 1910 - 202 pages
...89. Any side of a triangle is greater than the difference of the other two sides 62 THEOREM VI 90. The sum of two sides of a triangle is greater than the sum of two lines drawn from any point within the triangle to the extremities of the third side of the triangle 63 THEOREM... | |
 | Norman Colman Riggs - Geometry, Analytic - 1910 - 318 pages
...on the locus of this equation, then ±FP± F'P=±2a. The same sign cannot be used throughout, since the sum of two sides of a triangle is greater than the third side, and 2a<2c. The same signs for the terms on the left and the opposite sign on the right... | |
 | David Eugene Smith - Geometry - 1911 - 360 pages
...sides of a base angle of the triangle. Then TP = TS. By measuring TB, BS can then be found. THEOREM. The, sum of two sides of a triangle is greater than the third side, and their difference is less than the third side. If the postulate is assumed that a straight... | |
 | Clara Avis Hart, Daniel D. Feldman - Geometry, Modern - 1911 - 328 pages
...circumscribed polygon of twice as many sides. The proof is left as an exercise for the student. HINT. The sum of two sides of a triangle is greater than the third side. Ex. 1000. A square and a regular octagon are inscribed in a circle whose radius is 10 inches... | |
 | Clara Avis Hart, Daniel D. Feldman - Geometry - 1912 - 504 pages
...circumscribed polygon of twice as many sides. The proof is left as an exercise for the student. HINT. The sum of two sides of a triangle is greater than the third side. Ex. 1000. A square and a regular octagon are inscribed in a circle whose radius is 10 inches... | |
 | Michael Angelo McGinnis - Equations, Theory of - 1913 - 47 pages
...sum of the squares of two numbers or quantities is greater than the greater number.) (9) a + /3 > 7. (The sum of two sides of a triangle is greater than the third side.) (See any geometry for proof.) (10) Assume that 7-/3=A£. Then A/3+ ^8 = 7. Let A/3 = x.... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry, Plane - 1913 - 328 pages
...equidistant from three given lines. UNEQUAL LINES AND UNEQUAL ANGLES , PROPOSITION XXVIII. THEOREM 127. The sum of two sides of a triangle is greater than the third side. Given A A CB. B A To prove AB + AC>So. HINT. See Axioms. Ex. 302. Is it possible to draw... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 486 pages
...to trihedral or polyhedral angles that correspond to the following theorems of plane geometry : (a) The sum of two sides of a triangle is greater than the third side. (6) If two angles of a triangle are equal, the opposite sides are equal. (c) If two sides... | |
 | American Mathematical Society - Mathematics - 1913 - 876 pages
...the primary merit of being always true. Take the theorem which scandalized the sophists of old : " The sum of two sides of a triangle is greater than the third side." We take an isosceles triangle ABC, where AB = AC; A, remaining always on the perpendicular... | |
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The sum of two sides of a triangle is greater than the third side, and their difference is less than the third side. 
