 | George Clinton Shutts - 1905 - 260 pages
...bisects the vert'cal angle of an isosceles triangle bisects the triangle. PROPOSITION XL 87. Theorem. Any side of a triangle is less than the sum of the other two. B A Let ABC represent any triangle. To prove that any s'de, as AB, is less than the sum o] the other... | |
 | Education - 1913 - 914 pages
...so as to discern the relation of any side to the sum of the other two. II. Fundamental theorems. Any side of a triangle is less than the sum of the other two. III. Dependent theorems. a. If two sides of a triangle are unequal the angles opposite them are unequal,... | |
 | Education - 1918 - 922 pages
...is the line segment joining the points; (4) Two distinct points determine a straight line; (5) Any side of a triangle is less than the sum of the other two sides; (6) A diameter bisects a circle; (7) A straight line intersects a circle at most in two points;... | |
 | Education - 1911 - 946 pages
...angles are equal. [N3.] 12. The bisectors of vertical angles lie in a straight line. [J4-] 13. Any side of a. triangle is less than the sum of the other two and greater than their difference. [*] 1-4. A diameter bisects a circle. [A5.1 15. A straight line... | |
 | Alva Walker Stamper - Geometry - 1906 - 188 pages
...straight line is the shortest path between two points. Boys cross lots without first learning that one side of a triangle is less than the sum of the other two. These facts of nature are used because they are serviceable. The Indian fastened his pony to a stake,... | |
 | Edward Rutledge Robbins - Geometry, Plane - 1906 - 268 pages
...drawn to each of two parallels they will be in the same line. [Draw a third II through the point.] 86. One side of a triangle is less than the sum of the other two sides. 87. The sum of the sides of any polygon ABODE is greater than the sum of the sides of triangle... | |
 | Isaac Newton Failor - Geometry - 1906 - 440 pages
...a triangle are 65° and 84° respectively, find the third angle. PROPOSITION XIII. THEOREM 160 Any side of a triangle is less than the sum of the other two sides. HYPOTHESIS. Let AC be the longest side of the triangle ABC. CONCLUSION. AC < AB + BC. PROOF... | |
 | Isaac Newton Failor - Geometry - 1906 - 431 pages
...a triangle are 65° and 84° respectively, find the third angle. PROPOSITION XIII. THEOREM 160 Any side of a triangle is less than the sum of the other two sides. HYPOTHESIS. Let AC be the longest side of the triangle ABC. CONCLUSION. AC < AB + BC. PROOF... | |
 | Edward Rutledge Robbins - Geometry - 1907 - 428 pages
...drawn to each of two parallels they will be in the same line. [Draw a third II through the point.] 86. One side of a triangle is less than the sum of the other two sides. 87. The sum of the sides of any polygon ABCDE is greater than the sum of the sides of triangle... | |
 | Euclid - Mathematics, Greek - 1908 - 550 pages
...Consider the point Jlf, one of those which follow M, such that AfAf is equal to tr. Then, because any side of a triangle is less than the sum of the other two, OM' <OM + MM'. But OM+ MM1 = OM + a- < R, whence OM' < R, which is absurd. A similar absurdity would... | |
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Any side of a triangle is less than the sum of the other two sides... 
