 | Royal Military Academy, Woolwich - 1853 - 400 σελίδες
...(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 σελίδες
...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 - 1853 - 176 σελίδες
...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 - 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... | |
 | Euclides - 1855 - 270 σελίδες
...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... | |
 | 1858 - 642 σελίδες
...truths — its general principles — unchangeable and unchanged. When we enunciate the proposition that any two angles of a triangle are together less than two right angles, we enunciate an absolute truth in mathematics. When we enunciate the proposition that heat is always... | |
 | W. Davis Haskoll - 1858 - 422 σελίδες
...two straight lines cut one another, the vertical or opposite angles shall be equal. The 17th, Book I. Any two angles of a triangle are together less than two right angles. The 18th, Book I. The greater side of every triangle is opposite to the greater angle. The 32nd, Book... | |
 | Euclides - 1858 - 248 σελίδες
...reducing them to rectangular figures, these and similar conclusions are of great PROP. 17.— TMEOR. Any two angles of a triangle are together less than two right angles. CONSTRUCTION. — Pst. 2. A st. line may be produced to any length in a st. line. DEMONSTRATION. —... | |
 | Robert Potts - 1860 - 380 σελίδες
...greater than the angle ABC. Therefore, if one side of a triangle, &c. QED PKOPOSITION XVII. THEOREM. Any two angles of a triangle are together less than two right angles. Let ABC be any triangle. Then any two of its angles together shall be less than two right angles. Produce any side BC to D.... | |
 | Euclides - 1860 - 288 σελίδες
...therefore the exterior angle ACD is greater than either the angle CAB or ABC. PHOPOSmON XVII. THEOREM. Any two angles of a triangle are together less than two right angles. Given any triangle ABC ; to prove that any two of its angles together are less than two right angles.... | |
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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. 
