 The cosine of half the sum of two sides of a spherical triangle is to the cosine of half their difference as the cotangent of half the included angle is to the tangent of half the sum of the other two angles.  Spherical trigonometry - Page 186by Benjamin Martin - 1736Full view - About this book
 | William Leybourn - Geometry - 1704 - 432 pages
...is divided into Two Parts, by .letting fell of a Pe rpendicxlar -, and by help of this - ANAL 0 G I. As the Tangent of half the Bafe, Is to the Tangent of half the Sura of the other Two Sides $ :So is theTangent of half the Difference of thofe Sides, To theTangent... | |
 | James Hodgson - Astronomy - 1723 - 724 pages
..."••'-• • • 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... | |
 | Antoine-René Mauduit - Spherical trigonometry - 1768 - 252 pages
...upon the oppoßteßde or bafe, В С, (produced if necejfary), we ¡hall always bave this analogy -, as the tangent of half the bafe is to the tangent of half the fum of the other two ß des, fo is the tangent of half the difference of thefe fides to the tangent... | |
 | William Flower - Mathematical instruments - 1768 - 276 pages
...cotangents, it follows, that tangent AD : tangent AB+BE :: tangen t AB -BE : tangent CD. That i г is, the tangent of half the bafe is to the tangent of half the fum of the fides, as the tangent of half the difference of the fides, is to the tangent of the diftance... | |
 | James Atkinson - Navigation - 1770 - 514 pages
...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 ;... | |
 | John Wright (Mathematician) - Perspective - 1772 - 298 pages
...3.] the redangle HCL is equal to the redangle KCM; and [14. 6.] CH is to CK, as CM to CL ; that is, the tangent of half the bafe is to the tangent of half the fum of the two fides, as the tangent of half the difference of the fides to the tangent of half the... | |
 | Alexander Ingram - Trigonometry - 1799 - 374 pages
...res5.Cor.io. ciprocally proportional to their cotangents '. Wherefore, i&c. Def. t. T. CoK. Hence, the tangent of half the bafe is to the tangent of half the fum of the fides, as the tangent of half the difference of the fidis to tlu tangent of half the difference... | |
 | Francis Nichols - Plane trigonometry - 1811 - 162 pages
...any two sides is to the cosine of half their difference, as the cotangent of half the included angle is to the tangent of half the sum of the other two angles. 78. Remark. From this proposition and cor. we obtain half the sum S, and half the difference... | |
 | 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 of the... | |
 | Benjamin Peirce - Spherical trigonometry - 1836 - 92 pages
...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 + c) : cos. ¿ (a — c) ' : : cotau. ¿ B : tang. J (A... | |
| |
