 | Henry William Watson - Geometry - 1872 - 326 pages
...any one side of a triangle, is greater than either of the interior and non-adjacent angles, and any two angles of a triangle are together less than two right angles. Let ABC be a triangle, and let the side BC be produced to D, then ist. The exterior angle ACD shall be greater than either... | |
 | Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...given line; the perpendicular will fall on the side of the acute angle. PROPOSITION XVII. THEOREM. Any two angles of a triangle are together less than two right angles. 3 CU Let ABC be any A . ' Then must any two of its is be together less than two rt, L s. Produce BC... | |
 | Henry Major - Student teachers - 1873 - 588 pages
...it may be demonstrated that the angle BOG, that is the angle ACD, is greater than ABC. XVII. — Any two angles of a triangle are together less than two right angles. Let ABC be any triangle; any two of its angles are together less than two right angles. Produce BC to D ; and... | |
 | Euclid, James Bryce, David Munn (F.R.S.E.) - Geometry - 1874 - 236 pages
...this is impossible. PROP. XIII.— THEOREM. (Euc. I. 17). Any two angles of a triangle are tor/ether less than two right angles. ^ Let ABC be a triangle; any two of its angles, B and C, are together less than two right angles. K Produce BC to K. Then because the exterior angle... | |
 | Edward Atkins - 1874 - 426 pages
...ACD), is greater than the angle ABC. Therefore, if one side, &c. QED Proposition 17. — Theorem. Any two angles of a triangle are together less than two right angles. Let ABC be any triangle. CONSTRUCTION. — Produce BC to D. PROOF. — Because ACD is the ex- A ^ ABC terior angle... | |
 | Euclides - 1874 - 342 pages
...greater than the angle ABC. Therefore, if one side of a triangle, &c. QED PROPOSITION 17.— Theorem. Any two 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. B c D Construction.... | |
 | Francis Cuthbertson - Euclid's Elements - 1874 - 400 pages
...AC be produced to G, that L BCG is > the L ABC. But /^CZ?is= LBCG; (1.6) Hence it follows that Any two angles of a triangle are together less than two right angles. Let ^.5C be a A. Then shall any two of its angles, as ABC »nd ACB, be together < two right angles. Produce... | |
 | William Alexander Myers - Circle-squaring - 1874 - 207 pages
...theorem, as for example : To describe an equilateral triangle on a given finite straight line, or any two angles of a triangle are together less than two right angles. After the general enunciation follows the discussion of the proposition. First, the enunciation is... | |
 | Euclides - 1874 - 120 pages
...mentioned at the end of the proposition, and show that ACD is greater than ABCPROPOSITION 17. THEOREM. Any two angles of a triangle are together less than two right angles. i Let ABC be any triangle : any two of its angles ' • are together loss than two right angles. 0... | |
 | Robert Potts - Geometry - 1876 - 446 pages
...than the angle ABC. Therefore, if one side of a triangle, &c. QED PROPOSITION XVIL THEOREM. Any tieo angles of a triangle are together less than two right angles, Let ABCbe any triangle. Then any two of its angles together shall be less than two right angles. Produce... | |
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Any two angles of a triangle are together less than two right angles. 
