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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 included side is to the tangent of half the difference of the other two sides. "
The Projection and Calculation of the Sphere for Young Sea Officers Being a ... - Page 78
by S. M. Saxby - 1861 - 112 pages
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Spherical trigonometry

Benjamin Martin - Plane trigonometry - 1736 - 414 pages
...PROPOSITION III. As the Sine of half the Sum of the two Angles, is to the Sine of half the Difference ; ío is the Tangent of half the contained Side, to the...Tangent of half the Difference of the other two Sides. PROPOSITION IV. As the Co-fine of half the Sum of the Angles, is to the Co-fine 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
...two Angles ; is to the Sine of half their Difference j So So is the Tangent of half their interjacent Side, to the Tangent of half the Difference of the other two Sides : Again, Secondly^ As the Sine Complement of half the Sum of two Angles, is to the Sine Complement...
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A Description of the Lines Drawn on Gunter's Scale, as Improved by Mr. John ...

William Mountaine - Astronomical instruments - 1778 - 128 pages
...Angles given,-' • is to the Sine of half their Difference ; fo is the Tangent of half the interjacent Side, to the Tangent of half the Difference of the other two Sides. ' Secondly, As the Sine Complement of half the Surn of the two given- Angles, is to the Sine Complement...
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Mathematics: Compiled from the Best Authors and Intended to be the ..., Volume 2

Mathematics - 1801 - 658 pages
...difference of the other side?. THEOREM VII. As the cosine of half the sum of two angles Is to the cosine of half the difference, So is the tangent of half the contained side To the tangent of half the sum of the other sides; These four Theorems may be applied not only to the second and fourth cases,...
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Mathematics: Compiled from the Best Authors, and Intended to be ..., Volume 2

Samuel Webber - Mathematics - 1808 - 520 pages
...the other angles. THEOREM VI. As the sine of half the sum of two angles Is to the sine of half their difference, So is the tangent of half the contained...To the tangent of half the difference of the other sides. •f THEOREM vii. • *••t. % ' As the cosine of half the sum of two angles Is to the cosine...
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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 sine of half their difference, as the tangent of half the included side is to the tangent of half the difference of the other two sides: also, the cosine of half the sum of any two angles is to the cosine of half their difference, as 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 (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. J (A + C) : siiu b(A—C) (750)...
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First Part of an Elementary Treatise on Spherical Trigonometry

Benjamin Peirce - Spherical trigonometry - 1836 - 84 pages
...to the sine of half their difference, as the tangent of half the side to 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.), sin. J (A + C) : sin. i (A — C) (760)...
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An Elementary Treatise on Plane & Spherical Trigonometry: With Their ...

Benjamin Peirce - Plane trigonometry - 1845 - 498 pages
...difference, as the tangent of half the side to which Napier's Analogies. they are both adjacent is to the tangent of half the difference of the other two sides ; that is, ill the spherical triangle ABC (figs. 32 and 33), ua.%(A-{-C) : sm.$(A— C)=tang.J6 : tang...
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An Elementary Treatise on Plane & Spherical Trigonometry: With Their ...

Benjamin Peirce - Plane trigonometry - 1845 - 498 pages
...difference, as the tangent of half the side to which Napier's Analogies. 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. 32 and 33), : sin. £(A— C)=tang.£& : tang £ (a—...
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