 | Euclid, John Playfair - 1795 - عدد الصفحات: 462
...tangent of a certain angle ; then will the radius be to the tangent of the difference between, that angle and half a " right angle, as the tangent of half the fum of the angles at the bafe of the triangle to the tangent of half their difference. TLet ABC be... | |
 | Alexander Ingram - 1799 - عدد الصفحات: 374
...angle be found fuch, that the radius is to its tangent, as one of the fides to the other ; then the radius is to the tangent of the difference between...and half a right angle, as the tangent of half the fum of the angles at the tafe, to the tangent of half their difference. Let ABC be a triangle of which... | |
 | Robert Simson - 1806 - عدد الصفحات: 546
...is to the tangent of an anjjle, and the radius is to the tangent of the excess of this angle above half a right angle as the tangent of half the sum of the angles B and C at the base, is to the tangent of half their difference. At the point A, draw the straight... | |
 | Sir John Leslie - 1809 - عدد الصفحات: 542
...AB : BC :: S,C : S, A. PROP. X. THEOR. In any triangle, the sum of two sides, is to the difference, as the tangent of half the sum of the angles at the base, to the tangent of half their difference. In the triangle ABC, AB + AC : AB-AC : : T,°-±?: 2 IT" O—... | |
 | John Dougall - 1810 - عدد الصفحات: 734
...to EF; AD, however, is the sum of the sides, and AE their difference; while DC was shown above to be the tangent of half the sum of the angles at the base, and EF is the tangent of rulf their difference ; the proposition is, therefore, demonstrated. PROP.... | |
 | William Enfield - 1811 - عدد الصفحات: 476
...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, and... | |
 | Charles Butler - 1814 - عدد الصفحات: 582
...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 base : to the tangent of half the difference. Let ABC be a triangle, from € as a centre with the least... | |
 | Euclides - 1816 - عدد الصفحات: 588
...are parallel (2. 6.), EC is to CF, as EB to BG; that is, the sum of the 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. PROP. IV. FIG. 18. IN any plane triangle BAG, whose two sides... | |
 | Olinthus Gregory - 1816 - عدد الصفحات: 278
...triangle it will be, as the sum of the sides about the vertical angle, is to their difference, so is the tangent of half the sum of the angles at the base, to the tangent of half their difference. By the preceding prop. AC : BC :: sin B : sin A, .-. by comp.... | |
 | Sir John Leslie - 1817 - عدد الصفحات: 456
...supplement are the same. PROP. X. THEOR. In any triangle, the sum of two sides, is to the difference, as the tangent of half the sum of the angles at the base, to the tangent of half their difi ference. In the triangle ABC, AB+AC : AB— AC : : From the vertex... | |
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... angle and half a right angle, as the tangent of half the sum of the angles, at the base of the triangle to the tangent of half their difference. 
