 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 - Σελίδα 186των Benjamin Martin - 1736Πλήρης προβολή - Σχετικά με αυτό το βιβλίο
 | James Atkinson - 1770 - 514 σελίδες
...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 σελίδες
...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 σελίδες
...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 σελίδες
...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 σελίδες
...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 σελίδες
...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 σελίδες
...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 σελίδες
...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 σελίδες
...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 σελίδες
...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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