 | Benjamin Martin - 1736 - 414 σελίδες
...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 - 1795 - 384 σελίδες
...Angles A and C : Now IG being parallel to AC ; AH : 1H : : CH : GH. (by Cor. i. Theo. 20. Sect, i.) But the Wholes are as their Halves, ie AH : IH : :...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... | |
 | 1801 - 658 σελίδες
...and the angle included by them ; to find the rest. In a plane triangle, As the sum of any two sides : Is to their difference : : So is the tangent of half the sum of their opposite angles : • To the tangent of half their difference.* Then * DEMONSTRATION. By the... | |
 | Abel Flint - 1804 - 226 σελίδες
...this CASE 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 to half... | |
 | John Bonnycastle - 1806 - 464 σελίδες
...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 - 1807 - 476 σελίδες
...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... | |
 | Abel Flint - 1808 - 190 σελίδες
...this CASE 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 to half... | |
 | William Nicholson - 1809 - 722 σελίδες
................... 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 - 1810 - 152 σελίδες
...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... | |
 | George Adams - 1813 - 648 σελίδες
...angle ; and when an angle is wanted, it must begin with a side. As the sun, of the two given sides is to their difference ; so is the tangent of half the sum of the two 3. When two sides of a triangle and the included angle are given, to find the other angles and side.... | |
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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. 
