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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. "
The first three books of Euclid's Elements of geometry, with theorems and ... - Side 17
av Euclid, Thomas Tate - 1849 - 108 sider
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Library of Useful Knowledge: Mathematics I.

1836
...than two right angles, is not an assumption but a consequence of his proposition, which shews that any two angles of a triangle are together less than two right angles, and which is established before any mention is made of parallels. It has been found by the experience...
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

1836 - 472 sider
...be produced, the exterior angle is greater than either of the interior, and opposite angles. XVII. Any two angles of a triangle are together less than two right angles. XVIII. The greater side of every triangle has the greater angle opposite to it. XIX. The greater angle...
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A System of Popular Geometry: Containing in a Few Lessons So Much of the ...

George Darley - 1836 - 128 sider
...together. Hence the angles BCA, ABC, BAC together are equal to -^ \* v two right angles. This, &c. ART. 38. Any two angles of a triangle are together less than two right angles ; and if any angle of a triangle be obtuse or right, the other two are acute ; also, if two angles...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - 1837 - 318 sider
...demonstrated that the angle BUG, that is (15. 1.), the angle ACD, is greater than the angle ABC. PROP. XVII. THEOR. Any two angles of a triangle are together less...exterior angle of the triangle ABC, ACD is greater (16. 1.) than the interior and opposite angle ABC ; to each of these add the angle ACB; therefore the...
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Elements of Plane Geometry According to Euclid

Andrew Bell - 1837 - 240 sider
...angle BCG, that is (1. 15), the angle ACD, is greater than the angle ABC. PROPOSITION XVII. THEOREM. Any two angles of a triangle are together less than...exterior angle of the triangle ABC, ACD is greater than the interior and opposite angle ABC (1. 16) ; to each of these add the angle ACB ; therefore the...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1837 - 390 sider
...be greater than the interior and remote right angle, which (I. def. 10.) is impossible. PROP. XVII. THEOR.* ANY two angles of a triangle are together...angles. Let ABC be any triangle ; any two of its angles are together less than two right angles. ing the equality of CEB and AED, either AEC or BED may be...
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Lessons on Form: Or, An Introduction to Geometry, as Given in a Pestalozzian ...

Charles Reiner - 1837 - 215 sider
...12 \ a / rt. £s; and .'. the sum of the 9 ext. /.s = 10 rt. /.s. SUBSTANCE OF SECTION III. / \ 1. Any two angles of a triangle are together less than two right angles. 2. The interior angles of every triangle are together equal to two right angles. 3. A right-angled...
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A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - 1837 - 88 sider
...= Z ACF, 2 3. that Z ACD > Z BAC, that similarly Z BCG or ACD > Z ,IBC. PROPOSITION XVII. Theorem. Any two angles of a triangle are together less than two right angles. Steps of the Demonstration. 1. Prove that Zs DCA + ACB > Zs ACB + CBA, 2. that Zs ACB + CBA < 2 right...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Euclid, Robert Simson - 1838 - 416 sider
...(15. 1.) the angle ACD, is greater than the angle ABC. Therefore, if one side, &c. QED B PROP. XVII. THEOR. ANY two angles of a triangle are together less...exterior angle of the triangle ABC, ACD is greater (16. 1.) than the interior and opposite angle ABC ; to each of these add the angle ACB; therefore the...
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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838
...„16 , thatis,theangle*ACD,isgreaterthantheangleABC. Therefore, if one side, &c. u. ED PROP. XVII. THEOR. Any two angles of a triangle are together less...ABC be any triangle ; any two of its angles together shall be less than two right angles. Produce BC to D ; and because ACD is the exterior angle of the...
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