 | Euclides - 1848 - 52 σελίδες
...triangle be 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.... | |
 | Euclid, Thomas Tate - 1849 - 120 σελίδες
...15.), the angle ACD, is greater than the angle ABC. Therefore, if one side, &c. QED PROP. XVLL THEOR. Any two angles of a triangle are together less than two right angles. Let ABC be any triangle; any two of its angles together are less than two right angles. Produce BC to D; and because... | |
 | Great Britain. Committee on Education - 1850 - 790 σελίδες
...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 - 382 σελίδες
...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 - 48 σελίδες
...(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...its angles are together less than two right angles. Produce the side AC to D (Cor. 2.) , then the exterior angle BCD is greater than the interior angle... | |
 | Euclides - 1852 - 152 σελίδες
...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 less than two right angles. Let ABC be any triangle ; any two of its angles together are less than two right angles. Produce BC to D ; and... | |
 | Euclides - 1853 - 146 σελίδες
...that is (1. 15.) 6. The angle ACD is greater than the angle ABC. Therefore if one side, &c. QED PROP. XVII. — THEOREM. Any two angles of a triangle are together less than two right angles. Let ABC be any triangle ; any two of its angles together are less than two right angles. A Produce BC to D; and... | |
 | Euclides - 1853 - 176 σελίδες
...that is, (i. 15) the angle a С d, is greater than the angle ab С. Therefore, if one side, &c. QED PROPOSITION XVII. — THEOREM. Any two angles of a...triangle are together less than two right angles. LET ab С be any triangle ; any two of its angles together are less than two right angles. Produce b С... | |
 | Royal Military Academy, Woolwich - 1853 - 400 σελίδες
...angle ACD, is greater than the angle ABC. Therefore, if one side, etc. QED PROPOSITION XVII. THEOR. Any two angles of a triangle are together less than two right angles. Let ABC be any triangle ; any two of its angles together are less than two right angles. triangle ABC, ACD is... | |
 | William Somerville Orr - 1854 - 534 σελίδες
...actually drawn. In the next place, from the property demonstrated in Proposition XVII., namely, that any two angles of a triangle are together less than two right angles, he knows— what he could not know at an earlier stage of his progress — an important particular... | |
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Any two angles of a triangle are together less than two right angles. 
