| John Playfair - 1837 - 318 sider
...less than AB ; and it has been shewn that it is not equal to AB ; therefore AC is greater than AB. **PROP. XX. THEOR. Any two sides of a triangle are together...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... | |
| Euclid, James Thomson - 1837 - 390 sider
...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 - 1837 - 215 sider
...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 - 1837 - 215 sider
...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 - 1837 - 88 sider
...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
...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... | |
| Euclides - 1838
...' Wherefore the greater angle, &c. Q. un PROP. XX. THEOR. Any two sides of a triangle are toget/ier **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 than the side BC ; and AB, BC greater... | |
| Thomas Holliday - 1838 - 80 sider
...perpendicular to the base. A scalene triangle has all its sides and angles unequal. See fig. 7. Note 1. **Any two sides of a triangle are together greater than the third side.** 2. The greatest side of every triangle is opposite the greatest angle; and the greatest angle is also... | |
| ...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... | |
| 1839
...day passed on tolerably smoothly with one exception, that when the doctor (arguing very soundly that **any two sides of a triangle are together greater than the third side)** was taking a shorter cut across a field, his career was stopped about midway by his horse inserting... | |
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