 | Jeremiah Day - 1815 - 172 pàgines
...equal to the sum,, and FH to the difference of AC and AB. And by theorem II, [Art. 144.] the sum of the sides is to their difference ; as the tangent of half the sum of the opposite angles, to the tangent of half their difference. Therefore, R:Tan (ACH-45°,)::Tan >(ACB+B;... | |
 | Olinthus Gregory - 1816 - 278 pàgines
...cosines being the sines of the complements, it follows from the proposition that the sum of the cosines, is to their difference, as the tangent of half the sum of the complements, is to the tangent of half their difference. But half the sum of the complements of two... | |
 | Olinthus Gregory - 1816 - 276 pàgines
...cosines being the sines of the complements, it follows from the proposition that the sum of the cosines, is to their difference, as the tangent of half the sum of the complements, is to the tangent of half their difference. But half the sum of the complements of two... | |
 | Sir John Leslie - 1817 - 450 pàgines
...= cos 7a + 7 cosSa + 21 cosSa + 3Sc. &c. &c. &c. PROP. IV. THEOR. The sum of the sines of two arcs is to their difference, as the tangent of half the sum of those arcs to the tangent of half the difference. If A and B denote two arcs; s/nA+«»B : sinA—sinB... | |
 | Robert Gibson - 1818 - 502 pàgines
...In any plane triangle »4BC, the sfymofthe two given sides AB and BC, including a given angle ABC, is to their difference, as the tangent of half the sum of the two unknown angles A and C is to the tangent of half their difference. Fig. fi. Produce AB and make... | |
 | Charles Hutton - 1818 - 652 pàgines
...is readily converted into a very useful proportion, viz. The sum of the sines of two ara or angles, is to their difference, as the tangent of half the sum of those arcs or angles, is to the tangent of half their difference. 26. Operating with the third and... | |
 | John Playfair - 1819 - 354 pàgines
...parallel to FG, CE : CF : : BE : BG, (2. 6.) that is, the sum of the two sides of the triangle ABC is to their difference as the tangent of half the sum of the angles opposite to those sides to the tangent of half their difference. QED PROP. V. If a perpendicular be dramnfrojn any angle of... | |
 | John Playfair - 1819 - 350 pàgines
...difference between either of them and 45">. • PROP. IV. The sum tif any two sides of a triangle it to their difference, as the tangent of half the sum of the angles opposite to those sides, to the of half their differenee. Let ABC be any plane triangle ; CA+AB : CA—AB : : tan. £ (B+C)... | |
 | 1819 - 408 pàgines
...of the circumscribing hexagon. 8. Prove, geometrically, that in any plane triangle, the sum of the sides is to their difference as the tangent of half the sum of the angles at the base to the tangent of half their difference. 7. In an ellipse, if the line Ioi be drawn parallel... | |
 | Thomas Leybourn - 1819 - 430 pàgines
...of the circumscribing hexagon. 8. Prove, geometrically, that in any plane triangle, the surrt of the sides is to their difference as the tangent of half the sum of the angles at the base to the tangent of half their difference. 7. In an ellipse, if the line / oi be drawn parallel... | |
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in any triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite to those sides is to the tangent of half their difference. 
