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" Any side of a triangle is less than the sum of the other two sides... "
Junior High School Mathematics - Page 123
by Theodore Lindquist - 1920
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1819 - 208 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...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1825 - 224 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...
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Elements of Geometry: With Notes

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...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1841 - 235 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...
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Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ...

Nathan Scholfield - 1845 - 896 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...
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Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ...

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

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...
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Elementary Course of Geometry ...

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-...
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Elements of Geometry and Conic Sections

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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