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Any side of a triangle is less than the sum of the other two sides...
Plane and Solid Geometry - Page 35
by Isaac Newton Failor - 1906 - 418 pages

## Elements of Geometry

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...

## Elements of Geometry...: Translated from the French for the Use of the ...

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...

## 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...

## Elements of Geometry

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...

## Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ...

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...

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

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...

## 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...

## 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...