 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.  Spherical trigonometry - Pàgina 186per Benjamin Martin - 1736Visualització completa - Sobre aquest llibre
 | James Atkinson - 1770 - 514 pàgines
...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... | |
 | William Mountaine - 1778 - 128 pàgines
...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... | |
 | 1801 - 658 pàgines
...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,... | |
 | Samuel Webber - 1808 - 520 pàgines
...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 side 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... | |
 | Francis Nichols - 1811 - 162 pàgines
...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... | |
 | Benjamin Peirce - 1836 - 92 pàgines
...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)... | |
 | Benjamin Peirce - 1836 - 84 pàgines
...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)... | |
 | Benjamin Peirce - 1845 - 498 pàgines
...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... | |
 | Benjamin Peirce - 1845 - 498 pàgines
...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—... | |
 | Charles William Hackley - 1851 - 536 pàgines
...spherical triangle is to the •ine 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. • Or Gauss equations. TRIANGLES IN GENERAL. The fourth may be repeated in a similar manner. These... | |
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