| 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... | |
| 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
...been shown that it is 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 - 246 pages
...to the greater angle. 13. In every triangle the greater angle is subtended by the greater side. 14. Any two sides of a triangle are together greater than the third side. 15. The difference between any two sides of a triangle is less than the third side. 16. The three sides... | |
| Charles Reiner - Geometry - 1837 - 254 pages
...of the preceding truths will guide you ? P.—" The greater side subtends the greater angle;" or, " any two sides of a triangle are together greater than the third." M.—If you adopt the former of these truths, how must you draw a line so as to find a relation between... | |
| Euclides - Euclid's Elements - 1837 - 112 pages
...AC cannot be = AB, 2. that AC cannot be < AB, 3. that :. AC must be > AB. PROPOSITION XX. Theorem. Any two sides of a triangle are together greater than the third. BC Steps of the Demonstration. 1. Prove that Z ADC = Z ACD, 2. that Z BCD > Z ACD, 3. that .'. DB >... | |
| 1837 - 860 pages
...without knowing it — both theoretical and practical. A mathematician sits down to demonstrate that the two sides of a triangle are together greater than the third side ; whereas, without any of the diagrams, anil ABC's, and f/uo(l trat demonstrandus of Euclid, a poi... | |
| 708 pages
...height of the fixed stars ? Is this what you really mean to assert to be as demonstrably true as that any two sides of a triangle are together greater than the third side ? Every mathematician would answer — it is : nay, more, that this very curve would carry a body from... | |
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