| Ferdinand Rudolph Hassler - Geometry - 1828 - 180 pages
...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... | |
| George Darley - Geometry - 1828 - 190 pages
...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... | |
| John Playfair - Geometry - 1829 - 210 pages
...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...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 than the side BC ; and... | |
| 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... | |
| Pierce Morton - Geometry - 1830 - 584 pages
...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... | |
| John Playfair - Euclid's Elements - 1832 - 358 pages
...equal to AB; therefore AC is greater than AB. Wherefore the greater angle, &c. QE D PROP. XX. THEOR. I **Any two sides of a triangle are together greater than...side, viz. the sides BA, AC greater than the side BC** j and AB, BC greater than AC; andBC, CA greater than AB. Produce BA to the point D, and make (3. 1.)... | |
| Thomas Perronet Thompson - Euclid's Elements - 1833 - 168 pages
...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... | |
| Mathematics - 1835 - 684 pages
...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... | |
| Mathematics - 1836 - 488 pages
...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... | |
| George Darley - Euclid's Elements - 1836 - 172 pages
...than BAC, by preceding ART. ; which it is not. Hence BA must be greater than BC. This, &c. ART. 43. **Any two sides of a triangle are together greater than the third** tide. In the triangle ABC, any two of its sides, as AB, BC, are together greater than the third side... | |
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