 | Archibald Patoun - 1770 - 578 pàgines
...at the Bafe. The Triangles A HD, AEF are flmilar^ and confequently (by Art. 73. &?#.!.) AD : AE : : DH : AF or HB ; that is AD, the Sum of the Legs А С and С В, is to AE, the Difference of thofe Legs, as •DH the Tangent of half the Sum of the... | |
 | Robert Simson - 1806 - 546 pàgines
...Let ABC be a plane triangle, live sura of any two sides, AB, AC will be to their difiV.-rt.-nce as the tangent of half the sum of the angles at the base ABC, ACB to the tangent of half their difference. About A as a centre, with AB the greater side for... | |
 | Sir John Leslie - 1809 - 522 pàgines
...consequently 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, : f ., ( ,—... | |
 | John Dougall - 1810 - 734 pàgines
...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 - 476 pàgines
...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 pàgines
...6.) and AF : AE:: FB : ED (16. 5.) ; 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. QED When two sides and the included angle are given, the... | |
 | Euclides - 1816 - 588 pàgines
...difference. . Let ABC be a plane triangle, the sum of any two sides AB, AC will be to their difference as the tangent of half the sum of the angles at the base ABC, ACB to the tangent of half their difference. About A as a centre, with AB the greater side for... | |
 | Olinthus Gregory - 1816 - 278 pàgines
...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 - 456 pàgines
...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... | |
 | John Playfair - 1819 - 350 pàgines
...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 sum of 'the angles at t,he base of the triangle to the tangent of half their difference. Let ABC be a triangle, the sides of which... | |
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In any plane triangle, 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. 
