| Benjamin Martin - Plane trigonometry - 1736 - 414 pages
...the Tangent of half the Sum of the other two Sides. PROPOSITION V. As the Tangent of half the Bafe, . is to the Tangent of half the Sum of the other two Sides -, fo is the Tangent of half the Difference of the Sides, to the Tangent of half the Difference... | |
| James Atkinson - Navigation - 1770 - 514 pages
...Sine Complement of Half their Difference ; So is the Tangent Complement of half the contained Angle, to the Tangent of half the Sum of the other two Angles. Axiom 3. Firjt, As the Sine of half the Sum of two Angles ; is to the Sine of half their Difference... | |
| Francis Nichols - Plane trigonometry - 1811 - 162 pages
...PROP. XVIII. . 76. In any spherical triangle the sine of half the sum of any two sides is to the sine of half their difference, as the cotangent of half the included angle is to the tangent of half the difference of the other two angles. Let the two sides AC, BC, and the included angle C be proposed;... | |
| John Playfair - 1819 - 354 pages
...difference of th£ angles opposite to them : ;UM! also that the cosine of half the sum of these sides, is to the cosine of half their difference, as the cotangent of half the angle contained between them, to the tangent of half the sum of the angles opposite to them. COR. 2.... | |
| 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... | |
| William Galbraith - Astronomy - 1827 - 412 pages
...half the difference of the angles opposite to them : And the cosine of half the sum of these sides is to the cosine of half their difference, as the cotangent of half tne angle contained between them, is to the tangent of half the sum of the angles opposite to them,t... | |
| William Galbraith - Astronomy - 1834 - 454 pages
...half the difference of the angles opposite to them : And the cosine of half the sum of these sides is to the cosine of half their difference as the cotangent of half the angle contained between them is to the tangent of half the sum of the angles opposite to them, t or... | |
| Benjamin Peirce - Spherical trigonometry - 1836 - 92 pages
...— с) ~ tang. ¿ (Л — C)' 77. Theorem. The cosine of half the sum of two sides of a triangle is to the cosine of half their difference, as the cotangent of half the included angle (852) is to the tangent of half the sum of the other two angles, or in (figs. 4. and 5.), cos. ¿ (a... | |
| Benjamin Peirce - Spherical trigonometry - 1836 - 84 pages
...cosine 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)... | |
| John Playfair - Euclid's Elements - 1837 - 332 pages
...difference of the angles opposite to them : and also that the cosine of half the sum of these sides, is to the cosine of half their difference, as the cotangent of half the angle contained between them, to the tangent of half the sum of the angles opposite to them. COR. 2.... | |
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