| Peter Nicholson - 1823 - 596 páginas
...40, page 41) AD+BD : AC + BC : : AC - BC : AD - BD. TRIGONOMETRY. — THEOREM 2. 234. The sum of the **two sides of a triangle is to their difference as the tangent of half the sum of the** angles at the base is to the tangent of half their difference. Let ABC be a triangle ; then, of the... | |
| 1824
...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... | |
| Jeremiah Day - 1824
...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... | |
| Peter Nicholson - 1825 - 372 páginas
...: 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... | |
| Nathaniel Bowditch - 1826 - 617 páginas
...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... | |
| Silvestre François Lacroix - 1826 - 165 páginas
...^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... | |
| Nathaniel Bowditch - 1826 - 617 páginas
...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... | |
| Thomas Keith - 1826 - 442 páginas
...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... | |
| Euclid, John Playfair - 1826 - 320 páginas
...differenee as the radius to the tangent of the differenee between either of them and 45°. PROP. IV. **The sum of any two sides of a triangle is to their** differeuee, as the tangent of half the sum of the angles opposite to those sides, to the tangent of... | |
| Robert Simson - 1827 - 513 páginas
...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... | |
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