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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. The sine of half the sum of two sides of a... "
A Treatise of Plane and Spherical Trigonometry: In Theory and Practice ... - Page 87
by Francis Nichols - 1811 - 128 pages
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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1861 - 638 pages
...the other two angles. The sine of half the sum of two sides of a spherical triangle 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. BOOK V. cos 4 (A -+- 13) : cos £ (4 — 5) : : tan £ c : tan...
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Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 518 pages
...the other two angles. The sine of half the sum of two sides of a spherical triangle 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. cos £ (A -f- B) : cos £ (A — B) : : tan £ c : tan £ (a +...
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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 532 pages
...the other two angles. The sine of half the sum of two sides of a spherical triangle is to the sine of half their difference as the cotangent of half the included angle is to the tangent of haJf the difference of the other two angles. By applying (186) and (187) to the polar triangle, Art....
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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1863 - 504 pages
...the other two angles. The sine of half the sum of two sides of a spherical triangle 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. BOOK V. cos £ (A + B) : cos £ (A — B) : : tan £ c : tan £...
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Elements of Plane and Solid Geometry: And of Plane and Spherical ...

Gerardus Beekman Docharty - Geometry - 1867 - 474 pages
...two sides is to the cosine of half their difference, so is the cotangent of half the included angle to the tangent of half the sum of the other two angles. And As the sine of half the sum of two sides is to the sine of half their difference, so is the cotangent...
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Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - 1869 - 516 pages
...the other two angles. The sine of half the sum of two sides of a spherical triangle 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. cos £ (A + B) :cos$(A — 5) : : tan $ e : tan 4(a -f- 6), (188)...
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Elements of Trigonometry: Plane and Spherical

Edward Olney - Trigonometry - 1885 - 222 pages
...upon the opposite side or side produced, the tangent of half the sum of the segments* of that side is to the tangent of half the sum of the other two sides, as the tangent of half the difference of those sides is to the tangent of half the difference...
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A Treatise on Special Or Elementary Geometry, Volumes 1-2

Edward Olney - Geometry - 1872 - 562 pages
...upon the opposite side or side produced, the tangent of half the sum of the segments* of that side is to the tangent of half the sum of the other two sides, as the tangent of half the difference of those sides is to the tangent of half the difference...
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A Treatise on Special Or Elementary Geometry

Edward Olney - Geometry - 1872 - 472 pages
...upon the opposite side or side produced, the tangent of half the sum of the segments* of that side is to the tangent of half the sum of the other two sides, as the tangent of half the difference of those sides is to the tangent of half the difference...
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Elements of Trigonometry, Plane and Spherical

Edward Olney - Trigonometry - 1872 - 216 pages
...upon the opposite side or side produced, the tangent of half the sum of the segments* of that side is to the tangent of half the sum of the other two sides, as the tangent of half the difference of those sides is to the tangent of half the difference...
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