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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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Examination Papers for Science Schools and Classes

Great Britain. Education Department. Department of Science and Art - 1894
...show that the exterior angle is greater than either of the interior opposite angles. Hence show that any two angles of a triangle are together less than two right angles. (10-) 8. Define a parallelogram. Show that opposite angles of a parallelogram are equal. Let P be any...
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The Thinker: A Review of World-wide Christian Thought, Volum 6

1894
...but, as we maintain, by a faulty method of argument, for it is as if he had attempted to prove that " any two angles of a triangle are together less than two right angles " by actually measuring a few triangles instead of proving it on more general principles. Evolutionists,...
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Report of the Secretary for Public Instruction ...

Queensland. Department of Public Instruction - 1897
...allowed.) G 1. When is one proposition said to be the conreme of another. Write out the converse of — "Any two angles of a triangle are together less than two right angles." 6 2. Show clearly by figure and explanation what is meant by (a) the parallelograms about the diagonal...
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On the Study and Difficulties of Mathematics

Augustus De Morgan - 1898 - 288 sider
...less than two right angles, is not an assumption but a consequence of his proposition which shows that any two angles of a triangle are together less than two right angles, and which is established before any mention is made of parallels. It has been found by the experience...
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Mathematics: Mechanic's bids and estimates. Mensuration for beginners. Easy ...

Seymour Eaton - 1899 - 340 sider
...that is, the angle ACD — is greater than the angle ABC (Proposition 15). PROPOSITION 17. THEOREM Any two angles of a triangle are together less than...angles. Let ABC be any triangle ; any two of its angles are together less than two right angles. Construction : Produce BC to D. Proof: Then because ACD is...
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Elementary Geometry, Plane and Solid: For Use in High Schools and Academies

Thomas Franklin Holgate - 1901 - 440 sider
...side AC. EXERCISES 1. Show that ZA is less than ZAEF, and that ZF is less than PROPOSITION XIII 60. Any two angles of a triangle are together less than two right angles. SUGGESTIONS FOR PKOOF. Produce one side of the triangle and so form an exterior angle. This exterior...
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Rekhâgaṇita

Euclid - 1901
...triangle can not be equal to two right angles. This follows from the 17th Prop. in which it is proved that any two angles of a triangle are together less than two right angles. Bil. makes the following note on this proposition : — ' Epicurus and such as followed him derided...
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Elementary Geometry: Practical and Theoretical

Charles Godfrey, Arthur Warry Siddons - 1903 - 355 sider
...produced, the exterior angle so formed is greater than either of the interior opposite angles. COR. 3. Any two angles of a triangle are together less than two right angles. COR. 4. Every triangle has at least two of its angles acute. COR. 5. If two triangles have two angles...
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A Text-book of Euclid's Elements for the Use of Schools, Bok 1

Euclid - 1904 - 456 sider
...angle ACD : I. 15. therefore also the angle ACD is greater than the angle ABC. PROPOSITION 17. THEOREM. Any two angles of a triangle are together less than two right angles. A Let ABC be a triangle. Then shall any two of the angles of the triangle ABC be together less than...
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Syllabus of Plane' Geometry: (corresponding to Euclid, Book I-VI) : Prepared ...

Cora Lenore Williams - 1905 - 42 sider
...produced, the exterior angle is greater than either of the interior angles not adjacent to it. Prop. 31. Any two angles of a triangle are together less than two right angles. Prop. 32. If a triangle has one right angle, or one obtuse angle, its remaining angles are acute. Prop....
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