| H. Raper - 1908 - 934 sider
...and bisecting AB, it would be proved that the angle ABG, or its equal CBD, is greater than A. 122. **Any two angles of a triangle are together less than two right angles.** Produce the side BC of the triangle ABC, to D. Then the exterior angle AC D of the triangle is greater... | |
| Elmer Adelbert Lyman - 1908 - 340 sider
...If in the figure to Theorem VII CF is drawn, prove CF = AB. 5. Prove by Theorem VII that the sum of **any two angles of a triangle are together less than two right angles.** 6. It is required to find the distance of A from B, two points on the opposite shores of a lake. What... | |
| Henry Sinclair Hall - 1908 - 138 sider
...opposite L ACD. .-. the L ACD is greater than the L ABC. EXTERIOR AND INTERIOR ANGLES. COROLLARY 1 . **Any two angles of a triangle are together less than two right angles.** For the /.ABC ia less than the /.ACD : Proved. to each add the /.ACB. Then the Lf ABC, ACB are less... | |
| 1904
...another, makes with it are either both right angles, or their sum is equal to two right angles. 2. **Any two angles of a triangle are together less than two right angles.** 3. Through a given point draw a right line parallel to a given right line. 4. Construct a parallelogram... | |
| Howard Whitley Eves - 1997 - 344 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 - 261 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... | |
| 1908
...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.... | |
| 1840
...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 - 1926
...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... | |
| ...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... | |
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