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Llibres Llibres 31 - 40 de 194 sobre In the same way it may be proved that a : b : : sin. A : sin. B, and these two proportions....
" In the same way it may be proved that a : b : : sin. A : sin. B, and these two proportions may be written a : 6 : c : : sin. A : sin. B : sin. C. THEOREM III. t8. In any plane triangle, the sum of any two sides is to their difference as the tangent of... "
Elements of Trigonometry: Plane and Spherical - Pągina 45
per Lefébure de Fourcy (M., Louis Etienne) - 1868 - 288 pągines
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The Second [-fifth and Sixth] Part of A Course of Mathematics: Adapted to ...

Jeremiah Day - 1824
...equal to the sum, and FH to the di/erencc of AC and AB. And by theorem II, [Art. 144.] the sum of the sides is to their difference ; as the tangent of half the sum of the opposite angles, to the tangent of half their difference. Therefore, R : Tan(ACH-45°)::Tan^(ACB-fB)...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - 1825 - 372 pągines
...proportion AC + CB : AC— CB:: tangķ (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. Let...
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The New American Practical Navigator: Being an Epitome of Navigation ...

Nathaniel Bowditch - 1826 - 617 pągines
...any 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 ABC,...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - 1826 - 320 pągines
...'.'. BE : BG, (2. 6.) that is, the sum of the two sides of the triangle ABC is to their differenee as the tangent of half the sum of the angles opposite to those sides to the tangent of half their differenee. QED PROP. V. THEOR. If a perpendieular be drawn from any angle...
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An Introduction to the Theory and Practice of Plain and Spherical ...

Thomas Keith - 1826 - 442 pągines
...chords of 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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An Elementary Treatise on Plane and Spherical Trigonometry and on the ...

Silvestre Franēois Lacroix - 1826 - 165 pągines
...^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 - 617 pągines
...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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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - 1827 - 513 pągines
...three 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 of any two...
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An Analytical Treatise on Plane and Spherical Trigonometry, and the Analysis ...

Dionysius Lardner - 1828 - 317 pągines
...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, Volum 3

1829
...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 sum,...
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