 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 - Pàgina 186per Benjamin Martin - 1736Visualització completa - Sobre aquest llibre
 | James Hodgson - 1723 - 724 pàgines
..."••'-• • • 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... | |
 | James Atkinson - 1770 - 514 pàgines
...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 ;... | |
 | Francis Nichols - 1811 - 162 pàgines
...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... | |
 | James Mitchell - 1823 - 666 pàgines
...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... | |
 | Benjamin Peirce - 1836 - 92 pàgines
...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... | |
 | Benjamin Peirce - 1836 - 84 pàgines
...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.... | |
 | Charles William Hackley - 1838 - 328 pàgines
...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... | |
 | Benjamin Peirce - 1845 - 498 pàgines
...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.¿... | |
 | Benjamin Peirce - 1845 - 498 pàgines
...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.%... | |
 | S. M. Saxby - 1861 - 136 pàgines
...: — 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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