 | Education - 1868 - 516 pages
...that triangles upon equal bases and between the same parallels are equal to one another, and that any two sides of a triangle are together greater than the third side ; and so on with all the propositions. But though your teacher have thus truly educated you, he has... | |
 | 1868 - 876 pages
...upon one side of it are either two right angles or are together equal to two right angels 20 3. Any two sides of a triangle are together greater than the third side 20 4. In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the... | |
 | James Maurice Wilson - Geometry - 1868 - 132 pages
...be on the other side of the perpendicular and equally inclined to it . . . . . . .23 THEOREM 14. Any two sides of a triangle are together greater than the third side . . . . . . . . ^^ THEOREM 15. If two angles of one triangle are equal respectively to two angles of... | |
 | Cambridge univ, exam. papers - 1870 - 272 pages
...with the dead body of his brother. GROUP C FRIDAY, June 21, 1872. 11£ to 1. SEucIto 1. PROVE that any two sides of a triangle are together greater than the third side. Find the point in a given straight line such that the sum of its distances from two given points is... | |
 | Henry William Watson - Geometry - 1871 - 320 pages
...sum of the two non-intersecting sides AB and DC. R ' Let DB and AC intersect in the point E. Because two sides of a triangle are together greater than the third side, therefore AE + EB is greater than AB. Similarly CE + ED is greater than CD, therefore AE + EB+ CE+ED... | |
 | John Addington Symonds - 1871 - 470 pages
...opposites ; such, for instance, as the statements, "that two lines cannot inclose a sp.-i ii;" and "that two sides of a triangle are together greater than the third side ;" while the declaration that " all birds are oviparous," is a contingent truth ; that is, it is true... | |
 | Francis Campin - Bridges - 1871 - 260 pages
...produced by the weight W will be represented by the two sides ad, rf/of the triangle dfa, but, because any two sides of a triangle are, together, greater than the third side (Euc. Bk. 1, prop. 20), ad, df are, together, greatei than a f. But af is equal to W, hence the sum... | |
 | Elias Loomis - Geometry - 1871 - 302 pages
...difference. Let two circumferences cut each other in the point A. Draw the radii CA, DA ; then, because any two sides of a triangle are together greater than the third side (Prop. VIII., B. I.), CD must be less than the sum of AD and AC. Also, DA must be less than the sum... | |
 | Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...that which is nearer to the perpendicular is less than the more remote. PROPOSITION XX. THEOREM. Any two sides of a triangle are together greater than the third side. Let ABC be a A. Then any two of its sides must be together greater than the third side. Produce BA... | |
 | George Grote - 1872 - 508 pages
...шгтваччтвш ус àvayxa'iov TÓOf TI »caí тгоО кп\ ñv. * Ibid. b. .45: 8f;Xoi/ ¿TI /tai «í r¡v two sides of a triangle are together greater than the third side. According to Proklue, the Epikureans derided the demonstration of such a point as absurd; and it seems... | |
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Any two sides of a triangle are together greater than the third side. 
