 | Fletcher Durell - Geometry, Solid - 1904 - 232 pages
...with the perpendicular. 81. A triangle is a portion of a plane bounded by three straight lines. 92. The sum of any two sides of a triangle is greater than the third side. 94. The perpendicular is the shortest line that can be drawn from a given point to a given line. other... | |
 | Fletcher Durell - Geometry, Plane - 1904 - 382 pages
...Given AB any side of the A ABC, and AOBC. To prove AB > A C— BC. Proof. AB + BOAC, Art. 92. (tht 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. (</ equals be subtracted from... | |
 | Cora Lenore Williams - Geometry - 1905 - 50 pages
...more than two equal oblique lines can be drawn from a given point to a given straight line. Prop. 38. The sum of any two sides of a triangle is greater than the third side. Prop. 39. The difference of any two sides of a triangle is less than the third side. Prop. 40. If from... | |
 | Trinity College (Dublin, Ireland) - 1907 - 536 pages
...half-inches in length, internally and externally in the ratio of 5 to 3. Theoretical. 4. Prove that the sum of any two sides of a triangle is greater than the third aide. 5. Prove geometrically that the rectangle under the sum and difference of two lines is equal... | |
 | Webster Wells - Geometry, Plane - 1908 - 206 pages
...points.] (Ax. 7) 2. Subtracting AC from both members of the inequality, AB>BC—AC. PROP. XI. THEOREM 63. The sum of any two sides of a triangle is greater than the sum of the lines drawn from any point within the triangle to the extremities of the remaining side.... | |
 | Webster Wells - Geometry - 1908 - 336 pages
...(Ax. 7) 2. Subtracting AC from both members of the inequality, AB > BC- AC. \ PROP. XI. THEOREM 63. The sum of any two sides of a triangle is greater than the sum of the lines drawn from any point within the triangle to the extremities of the remaining side.... | |
 | Webster Wells - Geometry - 1908 - 329 pages
...points.] (Ax. 7) 2. Subtracting AC from both members of the inequality, AB>BC-AO. PROP. XI. THEOREM 63. The sum of any two sides of a triangle is greater than the sum of the lines drawn from any point within the triangle to the extremities of the remaining side.... | |
 | Webster Wells - Geometry, Plane - 1908 - 208 pages
...Subtracting AC from both members of the inequality, AB>BC-AC. ~ V •-A\^ PROP. -XL THEOREM <&&: Tlie sum of any two sides of a triangle is greater than the su-ttvof the lines drawn from any point within the triangle to the extremities of the remaining side.... | |
 | Eugene Randolph Smith - Geometry, Plane - 1909 - 424 pages
...and the base of one double the altitude of the other, the triangles are equivalent. 107. Theorem IX. The sum of any two sides of a triangle is greater than the third side. Draw the sum of the two sides in the simplest position possible ; then classify. 108. COR. I. The difference... | |
 | George William Myers - Mathematics - 1910 - 304 pages
...Problems 1-4 will now be shown to be immediate consequences of Axioms 8 and 10. PROPOSITION I 196. 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 any triangle ABC. To prove: a+b>c; b+c>a; a—b<.c;... | |
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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. 
