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Bøker Bok 2130 av 168ANY 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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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1835 - 316 sider
...that the angle BCG, that is (8. 1.) the angle ACD, is greater than the angle ABC. PROP. X. THEOR. Aw) two angles of a triangle are together less than two...Produce BC to D ; and because ACD is the exterior ano-le of the triangle ABC, ACD is greater (9. 1.) than the interior and opposite angle ABC ; to each...
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The Elements of Euclid: viz. the first six books, together with the eleventh ...

Euclid, Robert Simson - 1835 - 513 sider
...d 15. 1. greater than the angle ABC. Therefore, " if one side" &c. QED PROP. XVII. THEOR. Any tico angles of a triangle are together less than two right...right angles. Produce BC to D ; and because ACD is the exteriorangle of the triangle ABC, ACD is greater3 than the interior and , opposite angle ABC; to each...
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Library of Useful Knowledge: Geometry, plane, solid, and spherical [by ...

1835
...Therefore, Sic. Cor. The two triangles are equal in every respect. (4. & 4 Cor.) PROP. 8. (Eue. i. 17.) Any two angles of a triangle are together less than two right angles. Let А В С be any triangle : any two of its angles, ABC and ACB, shall be together less than two right...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1836 - 471 sider
...angle BCG, that is1', the angle ACD, is greater than the angle ABC. Therefore, if one side, &c. QED PROP. XVII. THEOR. Any two angles of a triangle are together less than two right angles. Book I. Let ABC be any triangle ; any two of its angles together are less than two right angles. Produce...
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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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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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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid - 1837 - 390 sider
...angle would 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...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, Introduction to geometry as given in a Pestalozzian ...

Charles Reiner - 1837
...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
...= 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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