 | John Harris - 1706 - 298 sider
...DEMONSTRATION. I fay the Sum of the Legs of any Angle <*, is to their Difference : : as the Tangent of i the Sum of their oppofite Angles, is to the Tangent of half their Difference. Produce O one of the given Legs of the Angle given, till af become equal to H or C «, and then bifeft... | |
 | John Muller - 1769 - 152 sider
...BC-CA: BD + DA. PROP. Fig. 27. 80. In any unequal Jided triangle ABC, the fum of the fides BC, AC, is to their difference, as the tangent of half the fum of the oppofae angles A, B, is to the tangent of half their difference. Let the fame conftru&ion be as... | |
 | Paul Hoste - 1769 - 294 sider
...confequently, fince (by 4. AE is to DA, as CE toDF, it is certain, tha* the fum of the fides BA, BC, is to their difference, as the tangent of half the fum of the angles A and C, is to the tangent of an angle, which added to the faid half, will make the greater... | |
 | John Muller - 1773 - 202 sider
...: BC-CA:BD + DA. PROP. Fig. 27: 80. In any unequal fided triangle ABQ the fum of the fides BC, AC, is to their difference, as the tangent of half the fum of the oppofite angles A, B, is to the tangent of half their difference. Let the fame conftruction be... | |
 | Robert Simson - 1775 - 534 sider
...being given, the fourth is alfo given. PROP. III. FIG. 8. TN a plain triangle, the fum of any two fules is to their difference, as the tangent of half the fum of the angles at the bafe, to the tangent of half their difference. Let ABC be a plain triangle, the fum... | |
 | Euclid - 1776 - 326 sider
...or BAC f. Wherefore, Sec, f fcho1PROP. Ill, TN any right lined triangle, ths fum of any two fides., is to their •*• difference, -as the tangent of half the fum of the angles at the kafe, is to the tangent of half their difference. Let ABC be the triangle, the fum... | |
 | Euclid - 1781 - 552 sider
...given, the fourth is aid » given. PROP. III. FIG. 8. IN a plain triangle, the fum of any two fides is to their difference, as the tangent of half the fum of the angles at the bafe, to the tangent of half their difference. Let ABC be n plain triangle, the fum... | |
 | William Nicholson - 1784 - 462 sider
...the fame proportion as their halves, it will follow that, , The fum of any two fides .... . • ! i Is to their difference, ., , . . . As the tangent of half the fum of the angles not included between the two afTumed fides, Is to the tangent of half the difference of... | |
 | David Stewart Erskine Earl of Buchan, Walter Minto - 1787 - 164 sider
...Cof af-cof b : cof a — cof b : : cot ^ : tang t±?. (4) Lem. 3. The fum of the fines of two arcs is to their difference as the tangent of half the fum of thofe arcs is to the tangent of half their their difference. * Sin a + fin b : fin a — fin b : :... | |
 | John McGregor (teacher of mathematics.) - 1792 - 532 sider
...their difference; and fince EG and BC are parallel, EC : CF as EB :. BG, that is, the fum of the fides is to their difference : as the tangent of half the fum of the angles at the bafe, is to the tarn. Cent of half their difference. THEOTHEOREM III. in a plane... | |
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IN a plain triangle, the fum of any two fides is to their difference, as the tangent of half the fum of the angles at the bafe, to the tangent of half their difference. 
