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" In any plane triangle, the sum of any two sides is to their difference, as the tangent of half the sum of the opposite angles is to the tangent of half their difference. "
A Course of Mathematics: In Three Volumes : Composed for the Use of the ... - Page 63
by Charles Hutton - 1811
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The Second [-fifth and Sixth] Part of A Course of Mathematics: Adapted to ...

Jeremiah Day - 1824 - 440 pages
...—sin b tan $(a — b) ' sin a+sin b : sin a— sin b::tan±(a+b) : tan ^(a—b.) Jt \.\ That is, The sum of the sines of two arcs or angles, is to the "ference of those sines j as th? tangent of half the sum of the or angle, to the tangent of half...
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A Course of Mathematics for the Use of Academies: As Well as ..., Volume 2

Charles Hutton - 1826 - 682 pages
...i+ein. B' . . . (XXII.) The equation is readily converted into a very useful proportion, viz. Ttie sum of the sines of two arcs or angles, is to their...tangent of half the sum of those arcs or angles, is to Hie tangent of half thtir difference. 26. Operating with the third and fourth formulae of the preceding...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - 1825 - 1046 pages
...: AC— CB:: tangí (B+C) : tang-i (B—C) it follows that in any triangle the sum of any two sides is to their difference, as the tangent of half the sum of the two angles opposite these sides, is to the tangent of half the difference of these same angles....
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The New American Practical Navigator: Being an Epitome of Navigation ...

Nathaniel Bowditch - 1826 - 764 pages
...triangle (supposing any aide to be the base, and calling the other two the tide*) the sum of the sida is to their difference, as the tangent of half the sum of tht ongfcs at the base is to the tangent of half the difference of the tame angla. Thus, in the triangle...
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An Elementary Treatise on Plane and Spherical Trigonometry and on the ...

Silvestre François Lacroix - 1826 - 190 pages
...^r;» ^'otn which tang i (a' -f- 6') sin a' + sin 6' we infer, that the sum of the sines of two arcs is to their difference, as the tangent of half the sum of these arcs is to the tangent of half their difference, is obtained immediately by a very elegant geometrical...
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The New American Practical Navigator: Being an Epitome of Navigation ...

Nathaniel Bowditch - 1826 - 732 pages
...triangle (supposing any side to be the basr, and calling the other two the sides) the sum of the sides is to their difference, as the tangent of half the sum of the angles at the base is to the tangent of half the difference of the tame angles. Thus, in the triangle...
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An Introduction to the Theory and Practice of Plain and Spherical ...

Thomas Keith - 1826 - 504 pages
...double their opposite angles. PROPOSITION IV. (E) 1. In any plane triangle, the sum of any two sides is to their difference, as the tangent of half the sum of their ^opposite angles, is to the tangent of half their difference. Let ABC be any triangle; make BE...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - 1827 - 546 pages
...being given, the fourth is also given. PROP. III. FIG. 8. In a plane triangle, the sum of any two 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. Let ABC be a plane triangle, the sum...
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An Analytical Treatise on Plane and Spherical Trigonometry, and the Analysis ...

Dionysius Lardner - 1828 - 434 pages
...plane triangle are as the sines of the opposite angles. (73.) The sum of two sides of a plane triangle is to their difference as the tangent of half the sum of the opposite angles to the tangent of half their difference. •* ^74.) Formulae for the sine, cosine,...
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The Southern Review, Volume 3

1829 - 536 pages
...first of these cases is shewn to depend on the theorem, that, " the sum of two sidi\s of a triangle is to their difference, as the tangent of half the sum of the opposite angles to the tangent of half their difference." This half difference added to half the...
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