 | Adrien Marie Legendre - 1819 - 574 σελίδες
...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 - 1825 - 294 σελίδες
...= 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 - 1827 - 246 σελίδες
...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 - 1841 - 288 σελίδες
...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 σελίδες
...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 - 1846 - 640 σελίδες
...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 - 1846 - 168 σελίδες
...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 - 1847 - 190 σελίδες
...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 - 1847 - 248 σελίδες
...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 - 1857 - 242 σελίδες
...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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Any side of a triangle is less than the sum of the other two sides... 
