 | 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 - Geometry - 1853 - 176 pages
...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 pages
...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 - Mathematics - 1853 - 400 pages
...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 pages
...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 pages
...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... | |
 | John Cumming - Bible - 1854 - 496 pages
...are not equally important. Two and two are four, is a truth ; the sun rises and sets, is a truth ; any two sides of a triangle are together greater than the third side, is a truth ; the square of the hypothenuse of a right-angled triangle is equal to the sum of the squares... | |
 | Euclides - 1855 - 270 pages
...lines can be drawn to the given straight line, one upon , each side of the shortest line. : PROP. XX. THEOREM. Any two sides of a triangle are together greater than the third side. Let ABC be a triangle : any two of its sides are together greater than the third side ; viz., the sides BA, AC,... | |
 | John Hind - Trigonometry - 1855 - 540 pages
...excluded. The circumstances here pointed out, are nothing more than what have all along been assumed, that any two sides of a triangle are together greater than the third : but it thus appears that the Algebraical Formulae are sufficient of themselves to determine the consistency... | |
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Any two sides of a triangle are together greater than the third side. 
