 | Euclides - 1848 - 52 pages
...triangle is subtended by the greater side, or has the greater side opposite to it. PROP. XX. THEOREM. Any two sides of a triangle are together greater than the third side. PROP. XXI. THEOREM. If from the ends of a side of a triangle, there be drawn two straight lines to... | |
 | Bengal (India) - 1848 - 520 pages
...xa~l+P xn-z+ ........ +J» = 0 J * n and in the quadratic equation »* — px + </=0 Geometry. 6. Any two sides of a triangle are together greater than the third side. 7. In a circle, the angle in a semicircle is a right angle, but the angle in a segment greater than... | |
 | Electronic journals - 1884 - 668 pages
...to Euclid, i. 5, is a modern error, and that the original asses' bridge was the proposition, " Any two sides of a triangle are together greater than the third side," the demonstration being that an ass at A will walk along the third side AB to his provender at в,... | |
 | Elias Loomis - Conic sections - 1849 - 252 pages
...each, and the angle A to the angle D. Therefore, if two triangles, &c. PROPOSITION VIII. THEOREM. Any two sides of a triangle are together greater than the third side. For the straight line AB is the shortest path between the points A and B (Def. 3); hence AB is less... | |
 | Euclid, Thomas Tate - 1849 - 120 pages
...not equal to AB; therefore AC is greater than AB. Wherefore the angle, &c. QED PROP. XX. THEOR. Any two sides of a triangle are together greater than the third side, Let ABC be a triangle; any two sides of it together are greater than the third side, viz. the sides... | |
 | Electronic journals - 1884 - 672 pages
...to Euclid, i. 6, is a modern error, and that the original asses' bridge was the proposition, " Any two sides of a triangle are together greater than the third side," the demonstration being that an ass at A will walk along the third side AB to his provender at в,... | |
 | Janet Taylor - Nautical astronomy - 1851 - 674 pages
...plane triangle, it will cut the other two sides proportionally, [Eu. vi. 2.] or Theorem D, page 26. Any two sides of a triangle are together greater than the third side [Eu. i. 20.] or Theorem IX. page 19. From this it follows also, that the difference of any two sides... | |
 | Euclides - 1852 - 48 pages
...side is greater than, equal to, or less than the angle opposite to the other. PEOP. XX. ТНЕOB. Any two sides of a triangle are together greater than the third side. In the triangle ABC, the sides л в and в c „ are greater than AC, the sides вc and CA are greater,... | |
 | Euclides - 1852 - 152 pages
...another, the side opposite that angle is greater than the side opposite the other.] PROP. XX. THEOR. Any two sides of a triangle are together greater than the third side. Let ABC be a triangle; any two sides of it together are greater than the third side, viz. the sides... | |
 | Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...therefore AC is greater than AB. "Wherefore the greater angle, etc. QED PROPOSITION XX. THEOB. Any two sides of a triangle are together greater than the third side. Produce BA to the point D, and make (3. i.) AD equal to AC, and join DC. Because DA is equal to AC,... | |
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Any two sides of a triangle are together greater than the third side. 
