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" The sum of any two sides of a triangle is to their difference, as the tangent of half the sum of the angles opposite to those sides, to the tangent of half their difference. "
Geometry: Plane Trigonometry. Chain Surveying. Compass Surveying. Transit ... - Página 18
por International Correspondence Schools - 1906
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An Analytical Treatise on Plane and Spherical Trigonometry, and the Analysis ...

Dionysius Lardner - 1828 - 317 páginas
...of a 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, tangent, and cotangent...
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Southern Review, Volumen3

1829
...given. The solution of the first of these cases is shewn to depend on the theorem, that, " the sum of two sides 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, gives the greater,...
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The Southern Review, Volumen3

1829
...solution of the 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, gives the greater,...
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The Southern Review, Volumen3

1829
...given. The solution of the first of these cases is shewn to depend on the theorem, that, " the sum of two sides of a triangle is to their difference, as the tangent of half the mm of the opposite angles to the tangent of half their difference." This half difference^added to half...
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A concise system of mathematics

Alexander Ingram - 1830 - 120 páginas
...sura. PROP. XXXIX. In any triangle ABC, of which the sides are unequal, the sum of the sides AC + AB is to their difference as the tangent of half the sum of the opposite angles B and C, to the tangent of half their difference. CA + AB : CA — AB : : tan. £ (B + C) : tan. £...
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Elements of Surveying

Charles Davies - 1830 - 300 páginas
...should obtain, THEOREM. 44. In any plane triangle, the sum of tfte two sides containing either angle, is to their difference, as the tangent of half the sum of the other two angles, to the tangent of half their difference. Let ABC (PI. I. Fig. 3) be a triangle ;...
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The Principles of Plane Trigonometry, Mensuration, Navigation and Surveying

Jeremiah Day - 1831 - 370 páginas
...sines of their opposite angles. It follows, therefore, from the preceding proposition, (Alg. 389.) that the sum of any two sides of a triangle, is to their...the tangent of half the sum of the opposite angles, to the tangent of half their difference. This is the second theorem applied to the solution of oblique...
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The Principles of Plane Trigonometry, Mensuration, Navigation and Surveying

Jeremiah Day - 1831 - 370 páginas
...THE OPPOSITE ANGLES; To THE TANGENT OF HALF THEIR DIFFERENCE. Thus the sum of AB and AC (Fig. 25.) is to their difference ; as the tangent of half the sum of the angles ACB and ABC, to the tangent of half their difference. Demonstration. Extend CA to G, making...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - 1832 - 333 páginas
...difference as the radius to the tangent of the difference between either of them and 45°. PROP. IV. The sum of any two sides of a triangle is to their difference, at the tangent of half the sum of the angles opposite to those sides, to the tangent of half their...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1833 - 333 páginas
...difference as the radius to the tangent of the difference between either of them and 45°. PROP. IV.. The sum of any two sides of a triangle is to their difference, as the tangent of half the sum of the angles opposite to those sides, to the tangent of half their difference. Let ABC be any plane triangle...
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