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" ANY two angles of a triangle are together less than two right angles. "
The Elements of Euclid - Side 20
av Euclid - 1838 - 416 sider
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The College calendar. [Continued as] The College calendar for the United ...

Scotland free church
...sides also which subtend, or are opposite to the equal angles, shall be equal to one another. Or—Any two angles of a triangle are together less than two right angles. 3. If a straight line be divided into any two parts, the square on the whole line is equal to the squares...
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Elements of geometry, based on Euclid, book i

Edward Atkins - 1877
...side, &c. QED Proposition 17.— Theorem. Any two angles of a triangle are together less than tworigJit angles. Let ABC be any triangle. Any two of its angles together shall be less than two right angles. CONSTRUCTION. — Produce BC to D. PROOF. — Because ACD is the...
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Elementary geometry

James Maurice Wilson - 1878
...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...
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Elements of Plane Geometry, Del 1

Thomas Hunter - 1878 - 132 sider
...BC and bisecting AB, it can be demonstrated that ABG, or its equal, DEC, is greater than CAB. Cor. Any two angles of a triangle are together less than two right angles. Because the exterior angle is greater than either of the interior and opposite angles; to this inequality...
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Euclid, books i. & ii., with notes, examples, and explanations, by a late ...

Euclides - 1879
...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...
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The Elements of Plane and Solid Geometry: With Chapters on Mensuration and ...

Isaac Sharpless - 1879 - 266 sider
...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...
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A complete set of male pupil teachers' examination questions in Euclid [book ...

W J. Dickinson - 1879 - 36 sider
...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...
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Mathews' Euclid examination papers ... on Euc. i.-iv

Edward Harri Mathews - 1879
...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...
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Scientific and practical geometry for self-instruction

Rolla Rouse - 1879
...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...
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Moffatt's pupil teachers' course (ed. by T. Page). Candidates, 2nd (-4th) year

Moffatt and Paige - 1879
...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...
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