 | Jeremiah Day - 1824 - 440 σελίδες
...the sum, and FH to the difference of AC and AB. And by theorem II, [Art. 1 44.] the sum of the sides is to their difference ; as the tangent of half the sum of the opposite angles, to the tangent of half their difference. Therefore, R : Tan (ACH-45°): :Tan ^(ACB+B)... | |
 | Peter Nicholson - 1825 - 1046 σελίδες
...: 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 then'AC=a,... | |
 | Nathaniel Bowditch - 1826 - 732 σελίδες
...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... | |
 | Thomas Keith - 1826 - 504 σελίδες
...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... | |
 | Nathaniel Bowditch - 1826 - 764 σελίδες
...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... | |
 | Silvestre François Lacroix - 1826 - 190 σελίδες
...^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... | |
 | Robert Simson - 1827 - 546 σελίδες
...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... | |
 | Dionysius Lardner - 1828 - 434 σελίδες
...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,... | |
 | 1829 - 536 σελίδες
...first of these cases is shewn to depend on the theorem, that, " the sum of two sidi\s 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 half difference added to half the sum,... | |
 | Alexander Ingram - 1830 - 458 σελίδες
...sura. PROP. XXXIX. In any triangle ABC, of which the sides are unequal, the sum of the sides AC + AB is to their difference as the tangent of half the sum of the opposite angles B and C, to the tangent of half their difference. CA + AB : CA — AB : : tan. £ (B... | |
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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. 
