 | John Martin Frederick Wright - Euclid's Elements - 1829 - 206 pages
...right angles; .-. angles A, ABC are together < than two right angles. PROP. XX. 56. To prove that ' any two sides of a triangle are together greater than the third side,' what is the general construction ? From the point where they meet, produce either of the two sides... | |
 | John Playfair - Geometry - 1829 - 210 pages
...therefore AC is greater than AB. Wherefore, the greater angle &c. QED PROPOSITION XX. THEOREM. Any two sides of a triangle are together greater than the third side. Let ABC be a triangle; any two sides of it are together greater than the third side, namely, the sides... | |
 | Pierce Morton - Geometry - 1830 - 584 pages
...the case. Therefore AB cannot but be greater than A C. Therefore, &c. PROP. 1 0. (Eue. i. 20.) Any two sides of a triangle are together greater than the third side : and any side of a triangle is greater than the difference of the other two. Let А В С be a triangle... | |
 | Thomas Perronet Thompson - Euclid's Elements - 1833 - 168 pages
...angle is the greatest. tI.I7.Cor.2. For the angle ist the greatest. PROPOSITION XX. THEOREM. — Any two sides of a triangle are together greater than the third side. Let ABC be a triangle. Any two sides of D it are together greater than the third side ; viz. the sides... | |
 | Mathematics - 1835 - 684 pages
...not the case. Therefore AB cannot but be greater than A C. Therefore, &c. PROP. 10. (Eue. L 20.) Any two sides of a triangle are together greater than the third side : and any side of a triangle is greater than the difference of the other two. Let А В С be a triangle... | |
 | Mathematics - 1836 - 488 pages
...of every triangle is subtended by the greater side, or has the greater side opposite to it. XX. Any two sides of a triangle are together greater than the third side. XXI. If from the ends of one side of a triangle, there be drawn two straight lines to a point within... | |
 | George Darley - Euclid's Elements - 1836 - 172 pages
...side opposite to that greater side is greater than the side opposite to the lesser, ibid. ART. 43. Any two sides of a triangle are together greater than the third side, 31. ART. 44. If two triangles have two sides of the one equal respectively to two sides of the other,... | |
 | Eugenius Nulty - Geometry - 1836 - 242 pages
...be less than С ; wherefore the side A С must be greater than the side A B. THEOREM IV. 35. Aпу two sides of a triangle are together greater than the third side. А с Any two sides AB, B С of the triangle ABС, are together greater than the third side A С. In... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...not equal toAB: therefore AC is greater than A B. Wherefore, if two angles, &c. PROP. XX. THEOR. ANY two sides of a triangle are together greater than the third side. 8 Let ABC be a triangle ; any two sides of it are together greater than the third side. Produce (I.... | |
 | Charles Reiner - Geometry - 1837 - 254 pages
...chord with a diameter. P.—A chord is always less than a diameter. For, join cd and ce ; then V any two sides of a triangle are together greater than the third side, .*. cd + ce > de. But cd + ce = ab, the diameter of the circle; .'. a6> de. M.—From the centre erect... | |
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Any two sides of a triangle are together greater than the third side. 
