| Gilbert Murray, William Ralph Inge, John Burnet - Greece - 1921 - 508 pages
...quadratic equation xz=ab. The Pythagoreans knew the properties of parallels and proved the theorem that the sum of the three angles of any triangle is equal to two right angles. As we have seen, the Pythagorean theory of proportion, being numerical, was inadequate in that it did... | |
| College Entrance Examination Board - Universities and colleges - 1922 - 124 pages
...credits will not be given on this paper for plane geometry and solid geometry. Take ir=3} 1. Prove: The sum of the three angles of any triangle is equal to two right angles. 2. Prove: If two triangles have their sides respectively proportional, the triangles are similar. 3.... | |
| Charles William Weick - Geometrical drawing - 1925 - 276 pages
...between 90° and 180°. TRIANGLES 320. A triangle is any plane figure bounded by three straight lines. The sum of the three angles of any triangle is equal to 180°. If one of the angles is 90°, or a right angle, the sum of the other two is 90°. In radian... | |
| John Charles Stone - Mathematics - 1926 - 344 pages
...formed by all three angles of the triangle? By trying this experiment with any triangle, you will find that The sum of the three angles of any triangle is equal to 180 degrees. 12. How many degrees in each angle of an equilateral triangle ? (The angles are all equal.)... | |
| Education - 1893 - 650 pages
...hypothesis. 2. Write two postulates and two axioms. 3. Define chord, segment, sector, polygon. 4. Demonstrate that the sum of the three angles of any triangle is equal to two right angles. 5. Demonstrate that any angle formed by a tangent and a chord is measured by one-half the intercepted... | |
| Kenneth Sylvan Guthrie, David R. Fideler - Philosophy - 1987 - 374 pages
...parallel lines, which they used for the purpose of establishing by a general proof the proposition that the sum of the three angles of any triangle is equal to two right angles. This latter proposition they again used to establish the well-known theorems about the sums of the exterior... | |
| Ranan Banerji Ph.D. - Science - 2006 - 145 pages
...this and some other initial axioms he could deduce many facts about geometrical figures (for example, "the sum of the three angles of any triangle is equal to the sum of two right angles"). Now one of his axioms (about parallel lines) did not seem very obvious... | |
| Euclid - Euclid's Elements - 1920 - 304 pages
...and the other two angles must in either case be acute. This follows from the fact (proved in i, 32) that the sum of the three angles of any triangle is equal to two right angles. Euclid introduces them as 'parallelogrammic areas or, more exactly, 'parallelogram areas' (ĦrapaXXrjXo-fjuLifji,!... | |
| Engineering - 1883 - 562 pages
...opposite ; and the sum of the lesser angles of each, being each equal to a right angle, it follows that the sum of the three angles of any triangle is equal to two right angles. Thus are all of the fundamental propositions of geometry rigorously demon; strated without the aid... | |
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