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" The cosine of half the sum of two angles of a spherical triangle is to the cosine of half their difference as the tangent of half the included side is to the tangent of half the sum of the other two sides. "
Spherical trigonometry - Page 186
by Benjamin Martin - 1736
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A System of the Mathematics: Containing the Euclidean Geometry ..., Volume 2

James Hodgson - Astronomy - 1723 - 724 pages
..."••'-• • • 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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Epitome of the Art of Navigation: Or, A Short, Easy and Methodical Way to ...

James Atkinson - Navigation - 1770 - 514 pages
...Angles, is 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 - 162 pages
...any two angles is to the cosine of half their difference, as the tangent of half the included side is to the tangent of half the sum of the other two sides. Fig. page 80. Let the angles C; CAB, and the included side AC, be proposed; then in the supplemental...
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Dictionary of the Mathematical and Physical Sciences, According to the ...

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

Benjamin Peirce - Spherical trigonometry - 1836 - 92 pages
...of half their difference, as the tangent of half the side to (758) 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.) Demonstration. The product of (702) and...
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First Part of an Elementary Treatise on Spherical Trigonometry

Benjamin Peirce - Spherical trigonometry - 1836 - 84 pages
...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) : : tang....
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Elements of Trigonometry, Plane and Spherical: Adapted to the Present State ...

Charles William Hackley - Trigonometry - 1838 - 328 pages
...spherical triangle is to the sine of half their difference as tfc.e 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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An Elementary Treatise on Plane & Spherical Trigonometry: With Their ...

Benjamin Peirce - Plane trigonometry - 1845 - 498 pages
...Napier's Analogies. their difference, as the tangent of half the side to which they are both adjacent is to the tangent of half the sum of the other two sides ; that is, in the spherical triangle ЛВС (figs. 32 and 33), cos. ¿ (Л+С) : cos.2(¿— C)=tang.¿...
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An Elementary Treatise on Plane & Spherical Trigonometry: With Their ...

Benjamin Peirce - Plane trigonometry - 1845 - 498 pages
...Napier's Analogies. their difference, as the tangent of half the side to 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. 32 and 33), cos. % (A-\-C) : cos.i(4 — C)=iang.%...
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The Projection and Calculation of the Sphere for Young Sea Officers Being a ...

S. M. Saxby - Nautical astronomy - 1861 - 136 pages
...: — As the cosine of half the sum of the two angles is to the cosine of half their difference, go is the tangent of half the included side to the tangent of half the sum of the other sides ; and half the difference added to half the sum will give the greater side, and half the difference...
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