| Benjamin Martin - Plane trigonometry - 1736
...Sides, Is to the Sine of their Difference, ( So is the Sine of the Sum of the Angles, to the Sine of **their Difference ; ) So is the Tangent of half the Sum of the** Angles, To the Tangent of halt their Différence. 14. That is, IK : IH: : AP :AO. Therefore IK+IH m... | |
| Robert Gibson - Surveying - 1806 - 452 pages
...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 ; so is the tangent of half the sum of the two** unknown angles A and C, to the tangent of half their difference. QED 104 PLANE TRIGONOMETRY. Plate... | |
| John Bonnycastle - Trigonometry - 1806 - 419 pages
...included angle are given, to find the rest. SR.ULE. As the sum of any two sides of a plane triangle, **is to their difference, so is the tangent of half the sum of** their opposite angles, to the tangent of half their difference. Then the half difference of these angles,... | |
| Isaac Dalby - Mathematics - 1807
...triangles DRA, DGB will be similar; whence we have, DG : DR :: GB : RA; That is, as the sum of the **sides, is to their difference, so is the tangent of half the sum of the** unknown or opposite angles, to the tangent of half the difference of those angles. Examp. 1. Let CD... | |
| Robert Gibson - 1808 - 440 pages
...wholes areas their halves, ie 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 C, to the tangent of half their difference. QED Plate V. THEO. III. In any right-lined... | |
| Samuel Webber - Mathematics - 1808
...and the angle include^ by them; to fmd the rest. In a plane triangle, As the sum of any two sifts : **Is to their difference " : : So is the tangent of half the sum of** their opposite angles : To the tangent of half their difference.* * DEM0NSTRATI0N. By the first problem,... | |
| Nicolas Pike - Algebra - 1808 - 480 pages
...given. RULE 2. — As the sum of any two sides is to their difference ; so 5s the tangent of the half **sum of the two opposite angles, to the tangent of half the difference** of those two opposite angle* ; which hah" difference being added to the half sum, gives the greater... | |
| William Nicholson - 1809
...9.74198 To the sine DC .56.88 ................ l .75486 Axiom III. In every plane triangle it will bn **as the sum of any two sides is to their difference; so is the tangent of half the sum of the** angles opposite there, to the tangent of half their difference. Which lialf difference, being added... | |
| Thomas Simpson - Trigonometry - 1810 - 125 pages
...(AC + BC) : : BH (AC — 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,...of the two opposite angles, to the tangent of half** their difference, For, let ABC (fig. 5.) be the triangle, and AB, AC the two proposed sides ; and from... | |
| Thomas Simpson - Trigonometry - 1810 - 125 pages
...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... | |
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