| Thomas Simpson - 1810 - 125 páginas
...— BC) : BG (2ED), by 4. 6. ^ ED THEOREM V. In any plane triangle, it will be, as the sum of any two **sides is to their difference, so is the tangent of half the sum of the** two opposite angles, to the tangent of half their difference, For, let ABC (fig. 5.) be the triangle,... | |
| Thomas Simpson - 1810 - 125 páginas
...co-sine AC : : tang. C : co-tang. A. £>. E, D. LEMMA. As the sum of the sines of two unequal arches **is to their difference, so is the tangent of half the sum of** those arches to the tangent of half their difference : and, as the sum of* the co-sines is to their... | |
| John Dougall - 1810 - 580 páginas
...containing the given angle, AD — 840 + DB = 640 = 980, to the difference between the sane sides = 300, **so is the tangent of half the sum of the remaining angles** (found by subtracting ADB = 65°, 37' from 180°) =.57", 11' j, to the tangent of half the difference... | |
| Robert Gibson - 1811 - 508 páginas
...wholes are as their halves, that is, AH: Iff : : CE : ED, that ia as the sum of the two sides AB and BC, **is to their difference ; so is the tangent of half the sum of the** two unknown angles A and C, to the tangent of half their difference. 2. E. DK THEO. III. fig. 12. In... | |
| George Adams - 1813 - 534 páginas
...triangle and the included angle are given, to find the other angles and side. As the sum of the two **given sides is to their difference ; so is the tangent of half the sum of the** two unknown angles, to the tangent of half their difference. Half the difference thus found, added... | |
| George Adams - 1813 - 534 páginas
...the angle CDB, and the side CD: to find CDB we use this proportion; as the sum of the two given aides **is to their difference, so is the tangent of half the sum of the** two unknown angles to the tangent of half their difference; the angle C'DB being found; the following... | |
| John Gummere - 1814 - 346 páginas
...remain' der will be the sum of the two unknown angles. Then ; • * * * * • * As the sum of the two **given sides, „• Is to their difference ; ,. % So is the tangent -of half the sum of the** two uuknown angles, To the tangent of half their difference.* This half difference of the two unknown... | |
| Robert Gibson - 1814 - 508 páginas
...wholes are as their halves, that is, AH : IH: : CE : ED, that is as the sum of the two sides AB and BC, **is to their difference ; so is the tangent of half the sum of the** two unknown angles A and G, to the tangent of half their difference. QED THEO. III. Fig. 12. In any... | |
| Jeremiah Day - 1815 - 96 páginas
...other radius. (Art. 1 19.) THEOREM II. 144. In a plane triangle, As the sum of any two of the sides, **To their difference; • • So is the tangent of half the sum of the** opposite angles, !£o the tangent of half their difference. Thus the sum of AB and AC (Fig. 25.) is... | |
| Jeremiah Day - 1815 - 126 páginas
...radius. (Art. 11 9.) THEOREM II. ..* 144. In a plane triangle, Jl 3 the sum of any two of the sides, **To their difference; So is the tangent of half the sum of the** opposite angles, To the tangent of half their difference. Thus the sum of AB and AC (Fig. 25.) is to... | |
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