 | Euclid, John Playfair - Euclid's Elements - 1795 - 462 pages
...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 - Trigonometry - 1799 - 374 pages
...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 - Trigonometry - 1806 - 546 pages
...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 - Geometry, Analytic - 1809 - 542 pages
...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—... | |
 | Thomas Simpson - Trigonometry - 1810 - 168 pages
...tangent of half £ THEOREM VII. In any spherical triangle, ABC (fig. 16.), it -will be, as the co-tangent of half the sum of the angles at the base is to the tangent of half their difference, so is the tangent of half the vertical angle to the tangent 'of the... | |
 | Thomas Keith - Navigation - 1810 - 478 pages
...xxvi.) (H) In any spherical triangle, I. If the perpendicular fall within the triangle. The co-tangent of half the sum of the angles at the base, Is to tangent of half their difference ; As the tangent of half the •vertical angle, Is to the tangent... | |
 | John Dougall - 1810 - 734 pages
...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 - Astronomy - 1811 - 476 pages
...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 - 582 pages
...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 - 588 pages
...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... | |
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... 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. 
