| Andrew Bell - 1837 - 240 páginas
...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 the third** side. Let ABC be a triangle ; any two sides of it together are greater than the third side; namely,... | |
| Euclides - 1837 - 88 páginas
...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 >... | |
| ...the 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... | |
| Thomas Holliday - 1838 - 80 páginas
...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... | |
| Euclid, Robert Simson - 1838 - 416 páginas
...equal to AB ; therefore AC is greater than AB. Wherefore the greater angle, &c. QED PROP. XX. THEOR. **ANY two sides of a triangle are together greater than the third** side. * Let ABC be a triangle ; any two sides of it together are greater than the third side, viz.... | |
| 1839
...The 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... | |
| Euclides - 1840
...or subtending the greater angle is greater than the side opposite the less angle. PROP. XX. THEOR. **Any two sides of a triangle are together greater than the third** side. COR..—Hence the difference between any two sides of a triangle is less than the third side.... | |
| Euclides - 1841 - 351 páginas
...equal to AB; therefore AC is greater than AB. Wherefore the greater angle, &c. QED PROP. XX. THEOR. **Any two 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.... | |
| Chambers W. and R., ltd - 1842
...A proposition is first stated in general terms : take, for instance, the 20th proposition — '• **Any two sides of a triangle are together greater than the third** side." This is but bare assertion : to advance a step farther, Euclid places the figure referred to,... | |
| John Playfair - 1842 - 317 páginas
...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 greater than the third** side. Let ABC be a triangle ; any two sides of it together arc greater than the third side, viz. the... | |
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