 | Howard Whitley Eves - 1997 - 370 sider
...lines are equaL 16. An exterior angle of a triangle is greater than either remote interior angle. 17. Any two angles of a triangle are together less than two right angles. 18. In a triangle the greater side is opposite the greater angle. 19. In a triangle the greater angle... | |
 | Victor J. Katz - 2000 - 284 sider
...geometry without the parallel postulate. 21 In particular, Saccheri used Elements 1-17 which states that any two angles of a triangle are together less than two right angles, a result which depends on the ability to extend a straight line to any given length. Euclid explicitly... | |
 | Cambridge Philosophical Society - 1927 - 1058 sider
...a certain group of propositions, viz. i. 16, 18, 19, 20. Euclid, after proving I. 16, deduces I. 17 (any two angles of a triangle are together less than two right angles). Then from i. 16 he deduces I. 18 (the greater side of any triangle is opposite to the greater angle),... | |
 | 1908 - 608 sider
...to the Committee. GEOMETRY AND ALGEBRA. Monday, 23rd March, 1908. 9.30 am to 12.30 pm J. Prove that "Any two angles of a triangle are together less than two right angles"; and show that only one perpendicular can be drawn to a straight line from a given point without it.... | |
 | Euclid - 1845 - 336 sider
...produced to D ; hence, show that each of the angles A, B of the triangle is an acute angle. 4. Prove that any two angles of a triangle are together less than two right angles by joining the vertex to any point in the base. 5. If two angles of a triangle be equal, prove that... | |
 | Euclid - 454 sider
...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... | |
 | 130 sider
...BCG > L ABC; but L. BCG = vert. opp. L. ACD ; 16. It follows, from the preceding proposition, that any two angles of a triangle are together less than two right angles. For, if BC be produced to D, ext. L. ACD > int. opp. L ABC, .'. L ACD + ^ACB>^ABC + ^ACB; but L ACD... | |
 | James McMahon - 2018 - 244 sider
...angle so formed is equal to the sum of the two interior opposite angles. (Proof as above.) COB. 3. Any two angles of a triangle are together less than two right angles. COB. 4. Every triangle has at least two of its angles acute. COB. 5. If two triangles have two angles... | |
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ANY two angles of a triangle are together less than two right angles. 
