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" 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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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838
...angle BCG, „16 , thatis,theangle*ACD,isgreaterthantheangleABC. Therefore, if one side, &c. u. ED PROP. XVII. THEOR. Any two angles of a triangle are...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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The Elements of Euclid

Euclid - 1838 - 416 sider
...that is, (15. 1.) the angle ACD, is greater than the angle ABC. Therefore, if one side, &c. Q,. ED PROP. XVII. THEOR. ANY two angles of a triangle are...right angles. Let ABC be any triangle ; any two of A its angles together are less than two right /\ angles. / Produce BC to D ; and because ACD is / the...
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The figures of Euclid with the enunciations, as printed in Euclid's Elements ...

Euclides - 1840
...of a triangle is produced, the external angle is greater than either of the internal remote angles. PROP. XVII. THEOR. Any two angles of a triangle are together less than two right angles. cu PROP. XVIII. THEOR. If two sides of a triangle are unequal, the angle subtended by the greater side...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841 - 351 sider
...BCG, that is,* * 15. ' 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...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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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842
...BCG, that is (15. 1.), 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...angles together are less than two right angles. Produce B c to D ; and because A c D is the exterior angle of the triangle ABC, ACD is greater (16. 1.) than...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1842 - 317 sider
...be demonstrated that the angle BCG, 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 than two right angles. Let ABO be any triangle ; any two of its angles together are less than two right angles. Produce BC to...
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The British Annals of Education for ...: Being The Scholastic ..., Volum 1

1844
...their other angles shall be equal, each to each, viz. those to which the equal sides are opposite. 3. Any two angles of a triangle are together less than two right angles. 4. If a straight line falling upon two other straight lines make the alternate angles equal to one...
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1845 - 352 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 together less than two right angles. Let ABC be a triangle : any two of its angles are together less than two right angles. Produce BC to D. Then,...
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845
...than the angle ABC. Therefore, if one side of a triangle, &c. QED PROPOSITION XVII. THEOREM. Any tno angles of a triangle are together less than two right angles. Let ABC be any triangle. Then any two of its angles together shall be less than two right angles. Produce any side BC to D....
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A system of practical mathematics; being no.xvi. of a new series of school-books

Scottish school-book assoc - 1845
...= the /.ACD, (Prop. 3), is •^ the /.ABC; .-. the /.ACD is ^ either of the /.sCAB or ABC. QED Cor. Any two angles of a triangle are together less than two right angles. PROPOSITION XI. — THEOREM. The greater side of every triangle has the greater angle opposite to it....
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