 | William Hawney - Astronomy - 1725 - 504 pages
...The Demon ftr At ion of this fecond Axiom is briefly thus. I fay, the fum of the Legs of any Angle a, is to their Difference, as the Tangent of half the fum of their oppofite Angles, is to the Tangent of half their Difference. Let Let A* B and C represent the... | |
 | Paul Hoste - Mathematics - 1769 - 294 pages
...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 - Mathematics - 1773 - 202 pages
...BE :: BF : BG, or BA:BC + CA: : 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 as the... | |
 | Robert Simson - Trigonometry - 1775 - 534 pages
...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 of... | |
 | Euclid - Geometry - 1776 - 326 pages
...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 of... | |
 | Euclid - 1781 - 552 pages
...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 of... | |
 | Robert Simson - Trigonometry - 1781 - 534 pages
...tangent of half their difference. Let ABC be a plain triangle, the fum of any two fides AB, AC will be to their difference as the tangent of half the fum of the angles at the bafe ABC, ACB to the tangent of half their difference. About A as a center, with AB the... | |
 | William Nicholson - Navigation - 1784 - 462 pages
...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 thofe... | |
 | David Stewart Erskine Earl of Buchan, Walter Minto - Logarithms - 1787 - 164 pages
...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.) - Mathematics - 1792 - 532 pages
...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 triangle,... | |
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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. 
