| 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... | |
| 1839 - 92 pages
...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 - 82 pages
...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 - Geometry - 1841 - 378 pages
...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...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... | |
| Euclides - 1842 - 320 pages
...equal to AB ; therefore AC is greater than лB. Wherefore the greater angle, &c. QED PROP. XX. THEOR. **Let ABC be a triangle; any two sides of it together,...side, viz. the sides BA, AC greater than the side** вc ; and AB, вc greater than AC ; and вc, c A greater than AB. Produce BA indefinitely, and make(3.... | |
| John Playfair - Euclid's Elements - 1842 - 332 pages
...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...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... | |
| Chambers W. and R., ltd - 1842 - 744 pages
...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, namely,... | |
| William Chambers, Robert Chambers - Encyclopedias and dictionaries - 1842 - 938 pages
...to, namely, a triangle, before the student, and tells him that, in the annexed triangle, namely, ABC, **any two sides of it together are greater than the third side** ; that is to say, the sides ВЛ, AC, are together greater than the one side BC ; the sides AB,BC,aregreaterthanAC;and... | |
| Philip Kelland - Algebra - 1843 - 168 pages
...theorems of Euclid's first Element. I can compel your assent to the truth of the proposition, that " **any two sides of a triangle are together greater than the third side** ;" and this without requiring from you any notion of a straight line at all. But I must stop here.... | |
| Charles Hutton - Mathematics - 1843 - 570 pages
...Prove by means of the equations that connect the sides and angles of a spherical triangle, that (1.) **Any two sides of a triangle are together greater than the third.** (2.) The difference of two sides is less than the third. (3.) If three sides of a triangle be equal... | |
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