 | Henry William Watson - Geometry - 1871 - 320 pages
...producing 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. p. , Let ABC be a triangle, and let the side BC be produced to D, then i st. The exterior angle ACD... | |
 | Henry William Watson - Geometry - 1872 - 326 pages
...producing 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 1 st. The exterior angle AC D shall be greater... | |
 | 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
...bisected, 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...angles. Let ABC be any triangle; any two of its angles are together less than two right angles. Produce BC to D ; and because ACD is the exterior angle of... | |
 | 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. Produce... | |
 | Edward Atkins - 1874 - 426 pages
...equal 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 of the triangle... | |
 | Francis Cuthbertson - Euclid's Elements - 1874 - 400 pages
...shewn, if 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... | |
 | 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... | |
 | William Alexander Myers - Circle-squaring - 1874 - 207 pages
...or 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... | |
 | 1876 - 710 pages
...Define the terms , an equilateral triangle, an isosceles triangle, a scalene triangle. 4. Prove that any two angles of a triangle are, together, less than two right angles. Л. PYoru a given point draw a straight line equal to a given straight line. FIRST AND SECOND DIVISION.... | |
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ANY two angles of a triangle are together less than two right angles. 
