Books Books C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. The New Practical Builder and Workman's Companion, Containing a Full Display ... - Page 81
by Peter Nicholson - 1823 - 596 pages ## Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1822 - 367 pages
...principles of Art. 42 and 43 are easily deducible. XL VII. In any rectilineal 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 the difference of those same angles. From the proportion... ## The Second [-fifth and Sixth] Part of A Course of Mathematics: Adapted to ...

Jeremiah Day - Geometry - 1824 - 440 pages
...opposite angles. It follows, therefore; from the preceding proposition, (Alg. 339.) 'et the sum of any two sides of a triangle, is to their difference ; as the tangent of half the sum of the opposite angles, to the tangent of half their difference. This is thesecoud theorem applied to the... ## Glasgow Mechanics' Magazine, and Annals of Philosophy, Volume 1

Industrial arts - 1824 - 492 pages
...DCA= BCD, 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 + DA =... ## A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 372 pages
...: 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 - 442 pages
...OF THE DIFFERENCES OF ARCS. PROPOSITION xiii. (Plate L Fig. 2.J (P) The sum of the sines of two arcs is to their difference, as the tangent of half the sum of those arcs is to the tangent of half their difference. Let BA and во be the two arcs ; draw the diameter... ## 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 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... ## The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 513 pages
...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 any two sides AB,... ## An Analytical Treatise on Plane and Spherical Trigonometry, and the Analysis ...

Dionysius Lardner - Plane trigonometry - 1828 - 438 pages
...of a 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,... 