| 1846
...shown, that Prop. 14. L BCG or L ACD > L ABC. Therefore, if one side, &c. PROP. XVI. THEOR. 17. IEu. **Any two angles of a triangle are together less than two right angles. Let ABC be any** ^, any two of its L s are together less than 2 rt. /_ s. B CD Produce BC to D. Prop. is. '.' ext. L... | |
| John Playfair - 1847 - 317 sider
...be demonstrated that the angle BCG, that is (15. 1.), the angle ACD; is greater than the angle ABC. **PROP. XVII. THEOR. Any two angles of a triangle are...than two right angles. Let ABC be any triangle ; any** A two of its angles together are less than two right angles. Produce BC to D ; and because ACD is the... | |
| Euclides - 1847
...QED COR. — A circle cannot cut a st. line in more pts. than two. PROP. XVII. THEOR. GEN. ENUN. — **Any two angles of a triangle are together less than two right angles.** PART. ENUN. — Let ABC be any A. Then any two of its Z s are together less than two rt. Z8. DEMONST.... | |
| Henry Pickton - 1847 - 48 sider
...sides of a triangle taken together are greater than the third side. (See EUCLID, Book I. Prop, xx.) 5. **Any two angles of a triangle are together less than two right angles.** (See EUCLID, Book I. Prop, xxii.) 6. Triangles on the same base and between the same parallels are... | |
| Euclides - 1848
...produced, the exterior angle is greater than either of the interior opposite angles. PROP. XVII. THEOREM. **Any two angles of a triangle are together less than two right angles.** PROP. XVIII. THEOREM. The greater side of every triangle is opposite to the greater angle. PROP. XIX.... | |
| Great Britain. Committee on Education - 1850
...been made to it ? 3. Distinguish between a direct and indirect demonstration. Section 2. 1. Show that **any two angles of a triangle are together less than two right angles.** •2. Draw a straight line through a given point parallel to a given straight line. 3. Show that in... | |
| 1851
...had he ? 14 1 Geometry and Mensuration. 1. Bisect a given finite straight line, _ 16 _ 2. Prove that **any two angles of a triangle are, together, less than two right angles,** . . -, J5Examination Questions — continued. Total Number of Men Examined. Number of Satisfactory... | |
| Euclides - 1852
...less than the interior angle which is adjacent to it, as may be seen in the annexed figures.] PEOP. **XVII. THEOR. Any two angles of a triangle are together...because ACD is the exterior angle of the triangle ABC,** « ""c D BOOK I. ACD is greater* than the interior and • XT ii opposite angle ABC ; to each of these... | |
| Euclides - 1852
...(Prop. 15.) ; therefore CBD is also greater than CAB. Which was to be demonstrated. PROP. ХVII. THEOB. **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 the side AC to D... | |
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