 | Her MAjesty' Inspectors of schools - 1850 - 912 σελίδες
...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 - 1851 - 674 σελίδες
...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 σελίδες
...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...third side. Let ABC be a triangle; any two sides of it together are greater than the third side, viz. the sides BA, AC greater than the side BC ; and AB,... | |
 | Euclides - 1852 - 48 σελίδες
...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 σελίδες
...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 σελίδες
...that it is not equal to ab ; 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... | |
 | sir George Ramsay (9th bart.) - 1853 - 282 σελίδες
...14. Alexander conquered Darius. 15. The three angles of a triangle are equal to two right lines. 16. Any two sides of a triangle are together greater than the third side. 17. The French Convention treated Louis XVI. cruelly. 18. The Chamber of Peers condemned Ney to death... | |
 | Royal Military Academy, Woolwich - 1853 - 400 σελίδες
...AB ; 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,... | |
 | Euclides - 1853 - 146 σελίδες
...the point A. B For, if not, let it fall otherwise, if possible, as FGDH, and join AF, AG. And because two sides of a triangle are together greater than the third side, (1. 20.) 1. AG, 6F, are greater than FA; but FA is equal (I. Def. 15.) to FH, both being from the same... | |
 | Popular educator - 1852 - 1272 σελίδες
...of the least straight line A D. Therefore, if from a point without a given straight line, &c. QE.D. PROPOSITION XX.— THEOREM. Any two sides of a triangle are together greater than the third side. In fig. 20, let ABO be a triangle; MI. SO. any two of its sides are together greater than the third... | |
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Any two sides of a triangle are together greater than the third side. 
