| Euclides - 1847 - 128 pages
...is > AC — BC, and AC > BC — AB. Wherefore any side Sec.— QED PROP. XX. THEOR. GEN. ENUN. — **Any two sides of a triangle are together greater than the third side.** PART. ENUN. — Let ABC be any A. Then the sum of any two of its sides is > the third side, viz., BA... | |
| 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... | |
| Euclid, Thomas Tate - 1849 - 120 pages
...is 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 - 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,... | |
| 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 - 672 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 - 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 - 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... | |
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