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Bøker Bok 141150 av 150ANY two angles of a triangle are together less than two right angles.
" ANY two angles of a triangle are together less than two right angles. "
The Elements of Euclid - Side 20
av Euclid - 1838 - 416 sider
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The practice of navigation and nautical astronomy

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...
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Plane and Solid Geometry

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...
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A School Geometry, Deler 1-4

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...
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The Irish Law Times and Solicitors' Journal, Volum 38

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...
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Foundations and Fundamental Concepts of Mathematics

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...
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Using History to Teach Mathematics: An International Perspective

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...
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The Surveyor, Volumer 21-22

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....
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The Elements of Plane Geometry

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...
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The Thirteen Books of Euclid's Elements: Tr. from the Text of Heiberg

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...
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A First Course of Geometry

...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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