| Adrien Marie Legendre - Geometry - 1819 - 574 pages
...infer that the other three are also equal, namely, *4fi = DE, AC — DF, and A = D. THEOREM. 40. One **side of a triangle is less than the sum of the other two.** Fig. 23. Demonstration. The straight line BC (Jig. 23), for example* is the shortest way from B to... | |
| Adrien Marie Legendre, John Farrar - Geometry - 1825 - 294 pages
...= F, we may thence infer that the other three are also equal, namely, AB = DE, THEOREM. f % 40. One **side of a triangle is less than the sum of the other two.** Fig. 23. Demonstration. The straight line BC (Jig. 23), for example, is the shortest way from B to... | |
| John Radford Young - Euclid's Elements - 1827 - 246 pages
...X., this angle can neither be acute nor right. Scholium. unrestricted form, thus: If the square of **any side of a triangle is less than the sum of the** squares of the other two sides, the angle opposite the former side is acute, but if it is greater than... | |
| Adrien Marie Legendre - Geometry - 1841 - 288 pages
...infer, that the other three are also equal, namely, AB = DE, AC zr DF, and A = D. THEOREM. 40. One **side of a triangle is less than the sum of the other two.** Fig. 23. Demonstration. The straight line BC (fig. 23), for example, is the shortest way from B to... | |
| Nathan Scholfield - 1845 - 894 pages
...JSrholiiim. The last corollary may obviously be expressed in a more unrestricted form, thus: if the square of **any side of a triangle is less than the sum of the** squares of the other two sides, the angle opposite the former side is acute, but if it is greater than... | |
| Leicester Ambrose Sawyer - Philosophy - 1846 - 640 pages
...proved, and problems, operations to be performed. The following are examples of propositions : Any one **side of a triangle is less than the sum of the other two** ; a diameter divides a circle and its circumference into two equal parts. The following are examples... | |
| Dennis M'Curdy - Geometry - 1846 - 168 pages
...each of the triangles BEF, CEF, GEF, a radius, and the side EF common, which are equal to AF: but one **side of a triangle is less than the sum of the other two** (a) ; therefore FG, FC, or FB is less than FA, which passes through the centre. 3. Also, since the... | |
| Alpheus Crosby - Geometry - 1847 - 190 pages
...aACD ? ni ADC yx BCD? .-. InfDBC, BCawBD? •». But, as AD = AC, BD sw BA + AC ? § 78. THE OR. X- **Any side of a triangle is less than the sum of the other two.** [Proved by the aid of Theor. IX] $79. a.) AsBC<BA + AC, BC — ACswBA? 30.3-. And BC — BA «y AC... | |
| Charles William Hackley - Geometry - 1847 - 248 pages
...arcs, are equal. 13. A straight line is the shortest distance between two points. Corollary. — One **side of a triangle is less than the sum of the other two.** 14. But one straight line can be drawn between two points.* EXERCISE WITH RULE AND DIVIDERS UPON THE-... | |
| Elias Loomis - Conic sections - 1857 - 242 pages
...the other two sides of the triangle. Produce BD until it meets the side AC BC in E ; and, because one **side of a triangle is less than the sum of the other two** (Prop. VIII.), the side CD of the triangle CDE is less than the sum of CE and ED. To each of these... | |
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