 | Thomas Simpson - 1748 - 84 sider
...AC ; AB+ BC :: AB— BC: E THEOREM V. In any flam 'Triangle, it will be, as the Sum of any two Sides is to their Difference, fo is the Tangent of Half the Sum of the two oppojite Angles, to the Tangent cf Half their Difference. For, let ABC be the Triangle, and ABand... | |
 | 1751 - 420 sider
...that as the Tangent of half the Sum of the unknown Angles in one Triangle, is to the Tangent of half their Difference, fo is the Tangent of half the Sum of the unknown Angles in the other Triangle, to the Tangent of half their Difference. But if the included Angle of one Triangle... | |
 | Henry Wilson - 1761 - 580 sider
...required. £3 AXIOM in Trigonometry. Chap. I, AXIOM III. In all Triangles, as tlie Sum of the Leg"; of any Angle is to their Difference, fo is the Tangent of half the Sum of the other two Angles, to the Tangent of half their Difle^ rencc; and therefore, When there are given two... | |
 | James Atkinson - 1765 - 504 sider
...is. 7**' 3°™Their DifF. 33 " 6 ( f Sum is 394. ijm. Then, As the Sum of the Sides BC and BD, is te their Difference ; fo is the Tangent of half the Sum of the Angles BDC and BCD, to the Tangent of half their Difference. Or thus, Sum BC&BD-- Diff. BC & BD : :... | |
 | James Atkinson - 1770 - 514 sider
...• f Sum is The twooppofite Angles [iSum.s Their- Diff. 33, Then, As the Sum of the Sides BC and BD, is to their Difference ; fo is the Tangent of half the Sum of the Angles BDC and BCD, to the Tangent of half their Difference. Or thus, SumBC&BD..Diff.BC&BD::T.|SumAngle.1T_4Di<r.... | |
 | Archibald Patoun - 1770 - 578 sider
...AB: BC, öfr. 'Tbeor. 2. In any plane Triangle ABC, icwill be as the Sum of any two Sides AC and BC, is to their Difference, fo is the Tangent of half the Sum of the Angles ВАС, ABC, at the Bafe AB, to the Tangent of half the Difference of the fame . Artgles. Î... | |
 | John Hamilton Moore - 1791 - 578 sider
...on the Line of Numbers.' AXIOM III. In every Plane Triangle it will be, as the Sum of any two Side» is to their Difference,, fo is the Tangent of half the Sum of the Angles oppofite theft- Sides to the Tangent of half their Difference. ' Which half Difference, being... | |
 | Robert Gibson - 1795 - 384 sider
...Wholes are as their Halves, ie AH : IH : : CE : ED, that is, as the Sum of the two Sides AB and BC, is to their Difference ; fo is the Tangent of half the Sum of the two unknown Angles A and C, • to the Tangent of half their Difference. QED THEO. Plate V. <THE 0.... | |
 | Alexander Ingram - 1830 - 458 sider
...to get half the sum of the unknown angles. Then as the sura of the sides is to their difference, so is the tangent of half the sum of the unknown angles to the tangent of half their difference. Having thus found the half difference, add it to the half sum to get the angle opposite... | |
 | Thomas Holliday - 1838 - 404 sider
...are given, to find the rest. u2 Rule.—As the sum of the two given sides is to their difference, so is the tangent of half the sum of the unknown angles to the tangent of half their difference: this half difference being added to half the sum of the unknown angles will give... | |
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Then as the sum of the sides is to their difference, so is the tangent of half the sum of the unknown angles to the tangent of half their difference (Theor. 
