 | Moffatt and Paige - 1879 - 428 pages
...necessary to stipulate that the given straight line must be of unlimited length. (5) Prove that any two angles of a triangle are together less than two right angles. (6) If one side of a triangle be produced, the exterior angle is greater than either of the interior... | |
 | Edward Harri Mathews - 1879 - 94 pages
...by those sides equal to one another, they shall also have their bases or -third sides equal. 2. Any two angles of a triangle are together less than two right angles. 3. The opposite sides and angles of a parallelogram are equal to one another. 4. If two isosceles triangles... | |
 | W J. Dickinson - Geometry - 1879 - 44 pages
...and bisect the angle CBD. Show that the two bisecting lines are at right angles. 17. Prove that any two angles of a triangle are together less than two right angles. 18. Give Euclid's definition of a plane rectilineal angle and of a triangle. Prove that the greater... | |
 | Euclides, Frederick Burn Harvey - Geometry - 1880 - 178 pages
...adjacent angle ACB bisected by CG ; prove that the angle GCF = a right angle. PROP. XVII. THKOREM. Any two angles of a triangle are together less than two right angles. Let ABC be a triangle. Then it is to he proved thai The angles ABO and ACB are together less than two right angles. Similarly,... | |
 | 1880 - 160 pages
...Draw a straight line at right angles to a given straight line from a given point in the same. 3. Any two angles of a triangle are together less than two right angles. 4. If two triangles have two sides of the one equal to two sides of the other, each to each, but the... | |
 | Isaac Todhunter - Euclid's Elements - 1880 - 426 pages
...theorem; as for example, To describe an equilateral triangle on a given finite straight line, or Any two angles of a triangle are together less than two right angles. After the general enunciation follows the discussion of the proposition. First, the enunciation is... | |
 | Science - 1880 - 922 pages
...somewhat complicated so-called axiom is only the converse or inverse of proposition seventeen, that " any two angles of a triangle are together less than two right angles," a theorem readily demonstrated from the preceding postulates and axioms. An inverse is usually exceedingly... | |
 | T S. Taylor - 1880 - 152 pages
...Repeat. — The enunciation of Euc. I. 13, and ot Euc. I. 1 6, and Axiom 4«. General Enunciation. Any two angles of a triangle are together less than two right angles. .Particular Enunciation. Given. — The triangle ABC. Required. — To prove that any two of its angles... | |
 | Science - 1880 - 900 pages
...somewhat complicated so-called axiom is only the converse or inverse of proposition seventeen, that " any two angles of a triangle are together less than two right angles," a theorem readily demonstrated from the preceding postulates and axioms. An inverse is usually exceedingly... | |
 | Euclides - Euclid's Elements - 1881 - 236 pages
...XVII. THEOREM. Any two anglet of a triangle are together leu than two right angle* Let A BC be any triangle; any two of its angles are together less than two right angles. Produce BC to D. Because ACD is the exterior angle of the triangle ABC, the angle ACD is greater (I. 16) than the interior... | |
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Any two angles of a triangle are together less than two right angles. 
