| 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
...+P 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... | |
| Elias Loomis - Conic sections - 1849 - 252 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... | |
| Electronic journals - 1884 - 668 pages
...appellation 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,... | |
| Electronic journals - 1884 - 674 pages
...appellation 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,... | |
| Her MAjesty' Inspectors of schools - 1850 - 912 pages
...sides of a triangle be unequal, the greater side has the greater angle opposite. 8. Prove Euc. 1. '.iO. **Any two sides of a triangle are together greater than the third** tide. 9. Prove Kuc. I. 48. If the square described upon one side of a triangle be equal to the squares... | |
| Janet Taylor - Nautical astronomy - 1851 - 702 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
...the 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,... | |
| 1858 - 422 pages
...an assertion relating to the mind is proved by an induction as wide as that on which we believe that **any two sides of a triangle are together greater than the third,** we have a right to suppose it true for us ; we feel it to be true by our intuition, our experience... | |
| Euclides - 1853 - 176 pages
...therefore a С is greater than a b. Wherefore the greater angle, &c. QED PROPOSITION XX. — THEOREM. **Any two sides of a triangle are together greater than the third side. LET** ab С be a triangle ; any two sides of it together are greater than the third side, viz. the sides... | |
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