 | Sir John Leslie - 1809 - 522 pągines
...dt 3"-V zp: « <f-*s"-*+n. n -- * 3 2 -7 s -6 &c . PROP. IV. THEOR. The sum of the sines of two arcs is to their difference, as the tangent of half the sum of the arcs to the tangent of half the difference. If A and B denote two arcs; the S,A + S,B : S, A — S,B... | |
 | Sir John Leslie - 1809 - 542 pągines
...even, and the lower signs when that half is odd. PROP. IV. THEOR. The sum of the sines of two arcs is to their difference, as the tangent of half the sum of the arcs to the tangent of half the difference. If A and B denote two arcs; the S,A + S,B :S,A. — S,B... | |
 | Euclid - 1810 - 554 pągines
...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 any two... | |
 | Francis Nichols - 1811 - 162 pągines
...of the angles at A and B, may be found by Cor. 32. 1. PROP VI. 61. In any 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. sum of the angles at the base."~ =^Let... | |
 | William Enfield - 1811 - 476 pągines
...side MR. In the triangle SRM, the sides RS, RM, being thus found, the sum of. the two sides RS, RM, is to their difference, as the tangent of half the sum of the angles at the base RSM, RMS, is to the tangent of half their difference. To half the sum add half the difference,... | |
 | Sir John Leslie - 1811 - 524 pągines
...cos7a + Jcot Sa + Zlcos 3a + 35c. &e. &c> &c «. PROP. IV. THEOR. The sum of the sines of two arcs is to their difference, as the tangent of half the sum of the arcs to the tangent of half the difference. If A and B denote two arcs; the sinA+sinV : si»A-«»B... | |
 | Charles Butler - 1814 - 528 pągines
...letting fall a perpendicular, as in the preceding article. 71. In a plane triangle, tte 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 the difference. Let ABC be a triangle, from C as a centre with... | |
 | Charles Butler - 1814 - 582 pągines
...letting fall a perpendicular, as in the preceding article. 72. 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 lose ; to the tangent of half the difference. Let ABC be a triangle, from C as a centre with... | |
 | Euclides - 1814 - 560 pągines
...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... | |
 | Robert Gibson - 1814 - 558 pągines
...filanc triangle ЛИС, the sum of the two given aide» AB and JBC, including a given angle ЛВС, is to their difference, as the tangent of half the sum of the two unknown angles Л and С is tt the tangent of half their difference. Produce AB, and make HB= BC,... | |
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in any triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite to those sides is to the tangent of half their difference. 
