 | 1827 - 600 ページ
...right linr." Again, the first problem which he introduces has, for its object, to establish " that any two sides of a triangle are, together, greater than the third side." He might, \ve think, have taken this for ¡minted with as much safety as that, " when equals are added... | |
 | George Darley - 1828 - 190 ページ
...the side which the sparrow has to fly in proportion to that which it has to fly itself. ART. 43. " Any two sides of a triangle are together greater than the third sidr." As I have observed before, we often, without knowing an angle from a triangle, give an involuntary... | |
 | Ferdinand Rudolph Hassler - 1828 - 180 ページ
...neither equal nor less than AB, it must be greater than it; as was to be demonstrated. § 19. THEOREM. Two sides of a triangle are together greater than the third side. APPLIC. Let ABC, (fig. 26.) be a triangle, the two sides AC, and CB, taken together, are greater than... | |
 | John Playfair - 1829 - 210 ページ
...AB; 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 BA, AC are greater... | |
 | John Martin Frederick Wright - 1829 - 206 ページ
...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... | |
 | Pierce Morton - 1830 - 584 ページ
...not 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 - 1833 - 168 ページ
...BE, EC. But AE, EC are equal to AC; therefore BA, AC are together greater than BE, EC. Again, because two sides of a triangle are together greater than the third side, EC and ED are together greater than CD. To each of these add DB; therefore EC, ED, DB are together... | |
 | Euclides - 1834 - 518 ページ
...is greater than AB. Wherefore, the greater angle, &c. QED PROPOSITION XX. See N. THEOR — Any Iwo sides of a triangle are together greater than the third side. Let ABC be a triangle : any two sides of it together shall be greater than the third side ; viz. the sides BA, AC greater... | |
 | 1835 - 684 ページ
...is 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... | |
 | 1836 - 488 ページ
...angle 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... | |
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Any two sides of a triangle are together greater than the third side. 
