 | George Chrystal - Algebra - 1898 - 480 pages
...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... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1899 - 400 pages
...triangle ABC " (see figure on p. 28), it is often better to say: PROPOSITION VIII. 75. Theorem. 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 Z. C bisected by CD. Then Z CD A > Z.DCB.... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry, Modern - 1899 - 265 pages
...p. 28), it is often better to say : PLANE GEOMETRY. [BK. I. PROPOSITION VIII. 75. Theorem. The sum of any two sides of a triangle is greater than the third side. Given the A AB C. To prove that Proof. 1. Suppose Then 2. And a-\-b > c. ZC bisected by CD. Z CD A... | |
 | William James Milne - Geometry, Modern - 1899 - 258 pages
...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... | |
 | Eldred John Brooksmith - Mathematics - 1901 - 368 pages
...violate Euclid's sequence of propositions. Great importance will be attached to accuracy.] 1. The sum of any two sides of a triangle is greater than the third side, and their difference is less than the third side. 2. If two quadrilaterals ABCD, EFGH have the four... | |
 | Edward Brooks - Geometry, Modern - 1901 - 278 pages
...sides are called the medial lines or medians of the triangle. PROPOSITION XVI. — THEOREM. The sum of any two sides of a triangle is greater than the third side, and their difference is less than the third side. Given. — Let ABC be a triangle. To Prove. — We... | |
 | Euclid - Geometry - 1901 - 672 pages
...together greater than the third, we have to remark that it has already been demonstrated that the sum of any two sides of a triangle is greater than the third side. It is therefore that the two circles cut each other. If the sum of A and В be not greater than J,... | |
 | 1903 - 898 pages
...opposite angles. Hence show that every triangle must have at least two acute angles. 5. Prove that the sum of any two sides of a triangle is greater than the third side. Prove also that the sum of the three sides of a. triangle is greater than twice the straight line drawn... | |
 | Fletcher Durell - Geometry, Plane - 1904 - 382 pages
...as possible, then those of two triangles. 92. Property of a triangle immediately inferred. The sum of any two sides of a triangle is greater than the third side. For a straight line is the shortest line between two points (Art. 15.) Ex. 1. Point out the hypothesis... | |
 | Fletcher Durell - Geometry - 1911 - 553 pages
...Given AB any side of the A ABC, and AOBC. To prove AB>AC—BC. Proof. AB + BO AC, Art. 92. (the sum of any two sides of a triangle is greater than the third side), Subtracting BC from each member of the inequality, AB>AC—BC, Ax. 9. yf equals l)e subtracted from... | |
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The sum of any two sides of a triangle, is greater than the third side. 
