| 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,... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| Euclid, H. S. Hall, F. H. Stevens - 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... | |
| 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.... | |
| Euclid, Sir Thomas Little Heath, Johan Ludvig Heiberg - 1908
...perpendiculars would form a triangle in which two angles would be right angles : which is impossible, since **any two angles of a triangle are together less than two right angles.** PROPOSITION 18. In any triangle the greater side subtends the greater angle. For let ABC be a triangle... | |
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