 | Euclides - 1842 - 316 pages
...equal to BE; join also F, C, and produce AC to G. Because AE is equal to EC, and BE to EF; AE, EB arc equal to CE, EF, each to each ; and the angle AEB...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... | |
 | John Playfair - Euclid's Elements - 1842 - 332 pages
...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... | |
 | Education - 1844 - 688 pages
...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... | |
 | Euclid, James Thomson - Geometry - 1845 - 382 pages
...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,... | |
 | Euclides - 1845 - 546 pages
...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.... | |
 | Scottish school-book assoc - 1845 - 444 pages
...= 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.... | |
 | Great Britain. Admiralty - Geometry - 1846 - 128 pages
...shown, that Prop. 14. L BCG or L ACD > L ABC. Therefore, if one side, &c. PROP. XVI. THEOR. 17. IEu. Any two angles of a triangle are together less than two right angles. Let ABC be any ^, any two of its L s are together less than 2 rt. /_ s. B CD Produce BC to D. Prop. is. '.' ext. L... | |
 | John Playfair - Euclid's Elements - 1847 - 340 pages
...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...than two right angles. Let ABC be any triangle ; any A two of its angles together are less than two right angles. Produce BC to D ; and because ACD is the... | |
 | Henry Pickton - Geometrical drawing - 1847 - 84 pages
...sides of a triangle taken together are greater than the third side. (See EUCLID, Book I. Prop, xx.) 5. Any two angles of a triangle are together less than two right angles. (See EUCLID, Book I. Prop, xxii.) 6. Triangles on the same base and between the same parallels are... | |
 | Euclides - 1847 - 128 pages
...QED COR. — A circle cannot cut a st. line in more pts. than two. PROP. XVII. THEOR. GEN. ENUN. — Any two angles of a triangle are together less than two right angles. PART. ENUN. — Let ABC be any A. Then any two of its Z s are together less than two rt. Z8. DEMONST.... | |
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ANY two angles of a triangle are together less than two right angles. 
