 | 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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Any two sides of a triangle are together greater than the third side. 
