Books Books In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference. A Treatise of Plane and Spherical Trigonometry: In Theory and Practice ... - Page 12
by Francis Nichols - 1811 - 128 pages ## Glasgow Mechanics' Magazine, and Annals of Philosophy, Volume 1

Industrial arts - 1824 - 492 pages
...because DA C = AC B, (Euc. 1. 29.) Therefore, DAC+ DCA = 130o, and consequently ADC = of any triangle is to their difference, as the tangent of half the sum of the angles opposite them, is to the tangent of half their difference. Therefore, by logarithms, As, CD... ## The Second [-fifth and Sixth] Part of A Course of Mathematics: Adapted to ...

Jeremiah Day - Geometry - 1824 - 440 pages
...THE OPPOSITE ANGLES ; To THE TANGENT OF HALF THEIR DIFFERENCE. Thus the sum of AB and AC (Fig. 25) is to their difference ; as the tangent of half the sum of the angles ACB and ABC. to the tangent of half their difference. Demonstration. Extend CA to G, making... ## A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 1046 pages
...obtuse R 42. From the proportion AC + CB : AC— CB:: tangí (B+C) : tang-i (B—C) it follows that in any triangle the sum of any two sides is to their...difference, as the tangent of half the sum of the two angles opposite these sides, is to the tangent of half the difference of these same angles. Let... ## An Introduction to the Theory and Practice of Plain and Spherical ...

Thomas Keith - Navigation - 1826 - 504 pages
...are to each other as the chords of double their opposite angles. PROPOSITION IV. (E) 1. In any plane triangle, the sum of any two sides is to their difference, as the tangent of half the sum of their ^opposite angles, is to the tangent of half their difference. Let ABC be any triangle; make BE... ## The New American Practical Navigator: Being an Epitome of Navigation ...

Nathaniel Bowditch - Nautical astronomy - 1826 - 732 pages
...any triangle (supposing any side to be the basr, and calling the other two the sides) the sum of the sides is to their difference, as the tangent of half the sum of the angles at the base is to the tangent of half the difference of the tame angles. Thus, in the triangle... ## The New American Practical Navigator: Being an Epitome of Navigation ...

Nathaniel Bowditch - Nautical astronomy - 1826 - 782 pages
...triangle (supposing any aide to be the base, and calling the other two the tide*) the sum of the sida is to their difference, as the tangent of half the sum of tht ongfcs at the base is to the tangent of half the difference of the tame angla. Thus, in the triangle... ## An Elementary Treatise on Plane and Spherical Trigonometry and on the ...

Silvestre François Lacroix - Geometry, Analytic - 1826 - 190 pages
...^r;» ^'otn which tang i (a' -f- 6') sin a' + sin 6' we infer, that the sum of the sines of two arcs is to their difference, as the tangent of half the sum of these arcs is to the tangent of half their difference, is obtained immediately by a very elegant geometrical... ## The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 546 pages
...in a plane triangle, any three being given, the fourth is also given. PROP. III. FIG. 8. In a plane triangle, the sum of any two sides is to their difference, as the tangent of half the sum of the angles at the base, to the tangent of half their difference. Let ABC be a plane triangle, the sum of... ## An Analytical Treatise on Plane and Spherical Trigonometry, and the Analysis ...

Dionysius Lardner - Plane trigonometry - 1828 - 434 pages
...plane triangle are as the sines of the opposite angles. (73.) The sum of two sides of a plane triangle is to their difference as the tangent of half the sum of the opposite angles to the tangent of half their difference. •* ^74.) Formulae for the sine, cosine, tangent, and cotangent... 