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" The cosine of half of any angle of a plane triangle is equal to the square root of half the sum of the three sides, into half the sum less the side opposite the angle, divided by the rectangle of the two adjacent sides. "
Elements of Plane and Spherical Trigonometry: With Practical Applications - Page 46
by Benjamin Greenleaf - 1876 - 170 pages
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The Mathematical Miscellany, Volumes 1-2

Mathematics - 1836 - 798 pages
...It is obvious that the sides of the triangle will be r, + r3, r, -fr,, гз + r\ i but the area of a triangle is equal to the square root of half the sum of the sides multiplied by the several differences between this half sum and the sides. Now the half sum is...
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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 532 pages
...preceding equation, we have cos ¿ A = 4lifZ^L) . (106) V be Similarly, (107) (108) ° That is, The cosine of half of any angle of a plane triangle is equal...the square root of half the sum of the three sides, into half the sum less the side opposite the angle, divided by the rectangle of the two adjacent sides....
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Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 518 pages
...ts(sa) . (106) V ft c Similarly, / — rr (107) cos (7 = . A(s— iQ . (108) V ab That is, ?%e cosine of half of any angle of a plane triangle is equal...the square root of half the sum of the three sides, into half the sum less the side opposite the angle, divided by the rectangle of the two adjacent sides,...
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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1861 - 638 pages
...4/li?^?) . (106) V bc Similarly, i : rr (107) ms j. <7— ./-"fr — c). (108) V aft That is, The cosine of half of any angle of a plane triangle is equal to the square root of half the mm of the three sides, into half the sum less the side opposite the angle, divided by the rectangle...
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Elements of Geometry and Trigonometry;: With Practical Applications

Benjamin Greenleaf - Geometry - 1863 - 502 pages
...preceding equation, we have be Similarly, (106) ' (107) cos* tf= 4 *iz£. (108) That is, V ab The cosine of half of any angle of a plane triangle is equal...the square root of half the sum of the three sides, into half the sum less the side opposite the angle, divided by the rectangle of the two adjacent sides....
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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1863 - 504 pages
...— J?> . (106) V bc Similarly, cos j5=1/l('JzAJ, (107) cos A (7 = = V/^' (108) That is, The cosine of half of any angle of a plane triangle is equal...the square root of half the sum of the three sides, into half the sum less the side opposite the angle, divided by the rectangle of the two adjacent sides....
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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - 1867 - 188 pages
...obtain sin tJS = JV— >*-">, (103) sin JC/ = -==. (104) That is, The sine of half of any angle in a plane triangle is equal to the square root of half...half the sum less the other adjacent side, divided by the rectangle of the two adjacent sides. 116. If 1 be added to both sides of (99), then, substituting...
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Elements of Trigonometry, Plane and Spherical

Lefébure de Fourcy (M., Louis Etienne) - Trigonometry - 1868 - 350 pages
...hence, sin í A = ч A V , be From which we form the following important rule, that the sine of half an angle of a plane triangle is equal to the square root of half the sum of the three sides minus one of the adjacent sides, multiplied by the half sum of the three sides minus the other adjacent...
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Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - 1869 - 516 pages
...equation, we have (106) 6 c Similarly, (107) cos j. C = . /'~(,-0 . (108) V at That is, 7'As cosine of half of any angle of a plane triangle is equal to <Ae square root of half the sum of the three sides, into half the sum less the side opposite the angle,...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1872 - 464 pages
...e - 2 - = i» - c, and, - 3 - Substituting in ( 5 ), and reducing, we have, hence, sine cf half an angle of a plane triangle, is equal to the square root of half the sum of the three sides, minus one of the adjacent sides, into the half sum minus tht other adjacent side, divided by the rectangle...
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