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" The sine of half the sum of two angles of a spherical triangle is to the sine of half their difference as the tangent of half the interjacent side is to the tangent of half the difference of the other two sides. "
A Treatise on Trigonometry, Plane and Spherical: With Its Application to ... - Page 136
by Charles William Hackley - 1851 - 372 pages
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Spherical trigonometry

Benjamin Martin - 1736 - 414 pages
...the Tangent of half the Sum of the other two Sides. PROPOSITION V. As the Tangent of half the Bafe, . is to the Tangent of half the Sum of the other two Sides -, fo is the Tangent of half the Difference of the Sides, to the Tangent of half the Difference...
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Epitome of the Art of Navigation: Or, A Short, Easy and Methodical Way to ...

James Atkinson - 1770 - 514 pages
...Sine Complement of Half their Difference ; So is the Tangent Complement of half the contained Angle, to the Tangent of half the Sum of the other two Angles. Axiom 3. Firjt, As the Sine of half the Sum of two Angles ; is to the Sine of half their Difference...
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A Treatise of Plane and Spherical Trigonometry: In Theory and Practice ...

Francis Nichols - 1811 - 162 pages
...PROP. XVIII. . 76. In any spherical triangle the sine of half the sum of any two sides is to the sine of half their difference, as the cotangent of half the included angle is to the tangent of half the difference of the other two angles. Let the two sides AC, BC, and the included angle C be proposed;...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 354 pages
...difference of th£ angles opposite to them : ;UM! also that the cosine of half the sum of these sides, is to the cosine of half their difference, as the cotangent of half the angle contained between them, to the tangent of half the sum of the angles opposite to them. COR. 2....
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Dictionary of the Mathematical and Physical Sciences, According to the ...

James Mitchell - 1823 - 666 pages
...have let fall a perpendicular arc, and which lies within the .riangle, the tangent of the half base is to the tangent of half the sum of the other two sides, as the .angent of the half difference of .hese sides is to the tangent of half .he difference...
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Mathematical and Astronomical Tables: For the Use of Students of Mathematics ...

William Galbraith - 1827 - 412 pages
...half the difference of the angles opposite to them : And the cosine of half the sum of these sides is to the cosine of half their difference, as the cotangent of half tne angle contained between them, is to the tangent of half the sum of the angles opposite to them,t...
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Mathematical and Astronomical Tables: For the Use of Students in Mathematics ...

William Galbraith - 1834 - 454 pages
...half the difference of the angles opposite to them : And the cosine of half the sum of these sides is to the cosine of half their difference as the cotangent of half the angle contained between them is to the tangent of half the sum of the angles opposite to them, t or...
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First Part of an Elementary Treatise on Spherical Trigonometry

Benjamin Peirce - 1836 - 92 pages
...— с) ~ tang. ¿ (Л — C)' 77. Theorem. The cosine of half the sum of two sides of a triangle is to the cosine of half their difference, as the cotangent of half the included angle (852) is to the tangent of half the sum of the other two angles, or in (figs. 4. and 5.), cos. ¿ (a...
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First Part of an Elementary Treatise on Spherical Trigonometry

Benjamin Peirce - 1836 - 84 pages
...cosine of half their difference, as the tangent of half the side to (768) which they are both adjacent is to the tangent of half the sum of the other two sides ; that is, in the spherical triangle ABC (figs. 4. and 5.) cos. J (A + C) : cos. ¿ (A — C)...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - 1837 - 332 pages
...difference of the angles opposite to them : and also that the cosine of half the sum of these sides, is to the cosine of half their difference, as the cotangent of half the angle contained between them, to the tangent of half the sum of the angles opposite to them. COR. 2....
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