| Mathematics - 1836 - 472 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... | |
| 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... | |
| 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... | |
| John Playfair - Geometry - 1837 - 332 pages
...the angle ABC would be less (18 l.)than the angle ACB ; but it is not ; therefore the side AC is nof **less than AB ; and it has been shewn that it is not...Let ABC be a triangle ; any two sides of it together** arc greater than the third side, viz. the sides BA, AC greater than the side BC ; and AB, BC greater... | |
| Andrew Bell - Euclid's Elements - 1837 - 240 pages
...has been shown that it is not equal to AB ; therefore AC is greater than AB. PROPOSITION XX. THEOREM. **Any two sides of a triangle are together greater than...sides of it together are greater than the third side;** namely, the sides BA, AC, greater than the side BC ; and AB, BC, greater than AC; and BC, CA, greater... | |
| Euclid - 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... | |
| 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... | |
| 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... | |
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