 | Euclides - 1848 - 52 pages
...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 - School buildings - 1850 - 790 pages
...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 pages
...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 - 152 pages
...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 - 48 pages
...(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... | |
 | Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...(15. i.), the 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...its angles together are less than two right angles. triangle ABC, ACD is greater (16. i.) than the interior and opposite angle ABC ; to each of these add... | |
 | Euclides - 1853 - 146 pages
...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...its angles together are less than two right angles. A Produce BC to D; and because ACD is the exterior angle of the triangle ABC, (1. 16.) 1. ACD is greater... | |
 | Euclides - Geometry - 1853 - 176 pages
...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... | |
 | William Somerville Orr - Science - 1854 - 534 pages
...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... | |
 | Euclides - 1855 - 270 pages
...From a point without a straight line, only one perpendicular can be drawn to it. PROP. XVII. THEOREM. Any two angles of a triangle are together less than two right angles. Let ABС be any triangle ; any two of its angles are together less than two right angles. Produce B С... | |
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ANY two angles of a triangle are together less than two right angles. 
