 | James Maurice Wilson - 1878 - 450 pages
...perpendicular, OQ an oblique ; it is required to prove first that OP is less than OQ. Proof. Since any two angles of a triangle are together less than two right angles; (Th. 18.) therefore OPQ and OQP are together less than two right angles : but OPQ is a right angle... | |
 | Euclides - 1879 - 146 pages
...exterior angles of a triangle are together greater than two right angles. PROPOSITION XVII. THEOREM. Any two angles of a triangle are together less than two right angles. Let ABC be A. Then any two of its Z. s together shall be less than two rt. Z. s. ° CD Constr. Produce any side... | |
 | Isaac Sharpless - Geometry - 1879 - 282 pages
...greater than ABC. ANALYSIS. (By Const.), " BE= EF—f (I. 7), BA E= ECF Proposition 19. Theorem.—Any two angles of a triangle are together less than two right angles. Let ABC be a triangle; any two of its angles are together less than two right angles. Produce BC to D. Then, because... | |
 | Edward Harri Mathews - 1879 - 94 pages
...contained 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... | |
 | Moffatt and Paige - 1879 - 428 pages
...is 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... | |
 | Rolla Rouse - 1879 - 400 pages
...triangle be extended, the exterior angle is greater than either of the interior and opposed angles, 3 108 Any two angles of a triangle are together less than two right angles, 4 ... ... ... ... ... „ If one side of a triangle be greater than the second, the angle opposed to... | |
 | W J. Dickinson - Geometry - 1879 - 44 pages
...D, 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.... | |
 | 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... | |
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ANY two angles of a triangle are together less than two right angles. 
