 | 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... | |
 | 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,... | |
 | 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.... | |
 | 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.... | |
 | 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... | |
 | 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,... | |
 | 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... | |
 | Adrien Marie Legendre - Geometry - 1874 - 500 pages
...i« - c, and, - . - = i« - J. Substitutmg in ( 5 ), and reducing, \re have, hence, 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, into the half sum minus the other adjacent side, divided by the rectangle... | |
 | Benjamin Greenleaf - Trigonometry - 1876 - 204 pages
...V 6 с Similarly, 1 — ; 7T (107)(108) у аи That is, TAe cosine of half of any angle of aplane 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.... | |
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... sides, into half the sum less the side opposite the angle, divided by the rectangle of the two adjacent sides, 117. Dividing (102) by (106), (103) by (107), and (104) by (108), we have, by (13... 
