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Any side of a triangle is less than the sum of the other two sides...
Elements of Geometry - Page 8
by Adrien Marie Legendre - 1841 - 235 pages

## Elements of Geometry

Adrien Marie Legendre - Geometry - 1819 - 208 pages
...= E, and C = F, we may thence infer that the other three are also equal, namely, *4fi = DE, AC — DF, and A = D. THEOREM. 40. One side of a triangle...two. Fig. 23. Demonstration. The straight line BC (Jig. 23), for example* is the shortest way from B to C (3) ; BC therefore is less than BA+AC. THEOREM....

## Elements of Geometry

Adrien Marie Legendre - 1825 - 224 pages
...C = F, we may 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...C (3) ; BC therefore is less than BA+AC. THEOREM. Fig.84. 41. Jf from a point O (fig. 24), vilhin a triangle ABC, there be drawn straight lines OB, OC,...

## Elements of Geometry

Adrien Marie Legendre - Geometry - 1825 - 224 pages
...the other three are also equal, namely, AB = DE, THEOREM. 9 40. One side of a triangle is less titan the sum of the other two. Fig. 23. Demonstration....shortest way from -B to C (3) ; BC therefore is less than BA + AC. THEOREM. Fig. 24. 41. If from a point O (fig. 24), within a triangle ABC, there be drawn straight...

## Elements of Geometry

Adrien Marie Legendre - Geometry - 1825 - 224 pages
...E, and C = 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...two. Fig. 23. Demonstration. The straight line BC (Jig. 23), for example, is the shortest way from B to C (3) ; BC therefore is less than BA+AC. THEOREM....

## Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ...

Dennis M'Curdy - Geometry - 1846 - 138 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,...

## Elements of Mental Philosophy: Containing a Critical Exposition of the ...

Leicester Ambrose Sawyer - Psychology - 1846 - 432 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...

## Elementary Course of Geometry ...

Charles William Hackley - Geometry - 1847 - 103 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-...

## First Lessons in Geometry: Upon the Model of Colburn's First Lessons in ...

Alpheus Crosby - Geometry - 1847 - 164 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...