 | Benjamin Martin - Plane trigonometry - 1736 - 414 pages
...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... | |
 | Abel Flint - Surveying - 1804 - 226 pages
...depends on the following PROPOSITION. In every Plane Triangle, As the Sum of any two Sides ; Is to their Difference ; So is the Tangent of half the Sum...the Angles and you will have the greater Angle ; and subtract the half Difference from the half Sum and you will have the lesser Angle. In the Triangle... | |
 | Robert Gibson - Surveying - 1806 - 486 pages
...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... | |
 | Isaac Dalby - Mathematics - 1807 - 476 pages
...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... | |
 | Abel Flint - Surveying - 1808 - 190 pages
...depends on the following PROPOSITION. In every Plane Triangle, As the Sum of any two Sides ; Is to their Difference ; So is the Tangent of half the Sum...the Angles and you will have the greater Angle ; and subtract the half Difference from the half Sum and you Will have the lesser Angle V * In the Triangle... | |
 | Nicolas Pike - Algebra - 1808 - 470 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... | |
 | Robert Gibson - 1808 - 482 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... | |
 | William Nicholson - 1809 - 722 pages
................... 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 - 168 pages
...(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, and AB, AC the two proposed sides ; and from... | |
 | Thomas Simpson - Trigonometry - 1810 - 152 pages
...- J -- : tang -- - - ; that is, As the sine of the sum of the tivo perpendiculars is to the sine of their difference, so is the tangent of half the sum of the two bases to the tangent of half their difference. PROP. XXVI. The product of the square of radius and... | |
| |
Plane Triangle, 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 the Difference between them. 
