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" The cosine of half the sum of two sides of a spherical triangle is to the cosine of half their difference as the cotangent of half the included angle is to the tangent of half the sum of the other two angles. "
First Part of an Elementary Treatise on Spherical Trigonometry - Page 51
by Benjamin Peirce - 1836 - 71 pages
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A System of the Mathematics: Containing the Euclidean Geometry ..., Volume 2

James Hodgson - Astronomy - 1723
..."••'-• • • In every Oblique-angled Spherical Triangle it will be, As the Tangent of half the Bafc, To the Tangent of half the Sum of the other two Sides ; So is the Tangent of half the Difference of the two Sides, To the Tangent of half the Difference...
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Spherical trigonometry

Benjamin Martin - Plane trigonometry - 1736
...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 of...
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Epitome of the Art of Navigation: Or, A Short, Easy and Methodical Way to ...

James Atkinson - Navigation - 1770 - 447 pages
...to the Sine Complement of half their Difference ; So is the Tangent of half their interjacent Side, to the Tangent of half the Sum of the other two Sides. Axiom 4. As the Re&angle of the Sines of the two containing Sides, is to the Square of the Radius ;...
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A Treatise of Plane and Spherical Trigonometry: In Theory and Practice ...

Francis Nichols - Plane trigonometry - 1811 - 128 pages
...any two sides is to the cosine of half their difference, as the cotangent of half the included angle is to the tangent of half the sum of the other two angles. 78. Remark. From this proposition and cor. we obtain half the sum S, and half the difference...
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Dictionary of the Mathematical and Physical Sciences, According to the ...

James Mitchell - Mathematics - 1823 - 576 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 of the...
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First Part of an Elementary Treatise on Spherical Trigonometry

Benjamin Peirce - Spherical trigonometry - 1836 - 92 pages
...spherical triangle is to the sine of half their difference, as the tangent of half the side to (749) which they are both adjacent is to the tangent of half the difference of the other two sides ; that is, in the spherical triangle ABC (figs. 4. and 5.), 33 sin....
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Elements of Trigonometry, Plane and Spherical: Adapted to the Present State ...

Charles William Hackley - Trigonometry - 1838 - 307 pages
...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 sum of the other two sides. The other may be repeated in a similar manner. These two proportions, and the two from which they were...
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Elements of Trigonometry, Plane and Spherical: Adapted to the Present State ...

Charles William Hackley - Trigonometry - 1838 - 307 pages
...spherical triangle is to the cosine of half their difference, as the cotangent of half the included angle is to the tangent of half the sum of the other two angles. The second may be repeated in a similar manner, changing cosine into sine and tangent of the...
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An Elementary Treatise on Plane & Spherical Trigonometry: With Their ...

Benjamin Peirce - Plane trigonometry - 1845 - 449 pages
...of a triangle is to the cosine of half their difference, as the cotangent of half the included angle is to the tangent of half the sum of the other two angles, or in (figs. 32 and 33), cos.(a— c) : cos.|(a— c)=cotan.J5 : tang. \ (A-\-C). (370)...
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An Elementary Treatise on Plane & Spherical Trigonometry: With Their ...

Benjamin Peirce - Plane trigonometry - 1845 - 498 pages
...of a triangle is to the cosine of half their difference, as the cotangent of half the included angle is to the tangent of half the sum of the other two angles, or in (figs. 32 and 33), соз4(а^с) : cos?4(a— c)=:cotan. \B : tang. ( Л+С). (370)...
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