 | William Leybourn - Geometry - 1704 - 432 pages
...Therefore, As the Sine of the Sum of the Angles^ * Is to tbeSiae of the Difference of the Angles $ So is the Tangent of half the Sum of the Angles, To ihsTangent of half the Difference of the Angles. But, The Sine of the Sum of the Sides, Is to the Sine... | |
 | 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 of the two opposite Angles ; To the Tangent of half the Difference between them. Add this half difference... | |
 | 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 of the two opposite Angles ; To the Tangent of half the Difference between them. Add this half difference... | |
 | 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... | |
 | 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 to half... | |
 | Thomas Simpson - Trigonometry - 1810 - 152 pages
...AD — AB , . - 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... | |
 | Thomas Simpson - Trigonometry - 1810 - 168 pages
...£ f* : that is, As the tangent of half the sum of the two perpendiculars is to the tangent of half their difference, so is the tangent of half the sum of the two hypothenuses to the tangent of half their difference. PROP. XXV. Since tang. DE : tang. BC : :... | |
 | Robert Gibson - Surveying - 1811 - 580 pages
...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... | |
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TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE. 
