 | Adrien Marie Legendre - Geometry - 1819 - 574 pages
...thence 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 - Geometry - 1825 - 276 pages
...thence infer that the other three are also equal, namely, AB = DE, AC = DF, and .#=!>. 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... | |
 | Adrien Marie Legendre - Geometry - 1841 - 288 pages
...thence 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... | |
 | Dennis M'Curdy - Geometry - 1846 - 166 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. 2. And, because EG,... | |
 | 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... | |
 | Charles William Hackley - Geometry - 1847 - 248 pages
...or 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-... | |
 | Alpheus Crosby - Geometry - 1847 - 192 pages
...aADCswaACD? 73.1. ADC tx, BCD? .-. In*DBC, BCswBD? 73. But, as AD = AC, BD xx BA + AC ? § 78. THEOR. X. Any side of a triangle is less than the sum of the other two. [Proved by the aid of Theor. IXl COR. I. The difference between any two sides of a triangle is less... | |
 | William Dexter Wilson - Logic - 1856 - 456 pages
...of truth, represented by the Conception, and not by any means or necessarily of any diagram ? " Any one side of a triangle is less than the sum of the two other sides." which we may draw, or of any piece of matter which may be brought into the form of... | |
 | William Dexter Wilson - Logic - 1856 - 464 pages
...of truth, represented by the Conception, and not by any means or necessarily of any diagram * " Any one side of a triangle is less than the sum of the two other sides." which we may draw, or of any piece of matter which may be brought into the form of... | |
 | Elias Loomis - Conic sections - 1857 - 242 pages
...AC, 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... 
