 | Francis Holliday - 1749 - 360 pàgines
...method offohing this qucjiion is thus : AS the fum of the ratios ( ij) is to their difference (3), fo is the tangent of half the fum of the angles at the bafe to the tangent of half their difference ; whence all the angles are known, and consequently the triangle. Mr J. lodd ingenioufly has lolved... | |
 | William Flower - 1768 - 276 pàgines
...hypothenufe, to the tang" ent of its adjacent perpendicular. Lemma, As the fum of tbeßnes of two unequal arcs is to their difference, fo is the tangent of half the fum of thofe arcs, to the tangent of half their difference. And, as the fum of their cq/ines is to their difference,... | |
 | Robert Simson - 1775 - 534 pàgines
...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 greater fide for... | |
 | Euclid - 1776 - 326 pàgines
...therefore the c 5. i. angles HBE, EBC, are likewife equal d; and, it BE be made ra- a 32 i dius, then EC is the tangent of half the fum of the angles at the bafe. Draw BD parallel to AC, then the angle DBC is equal to the angle ACB e. Take HF equal to DC, and join... | |
 | Euclid - 1776 - 318 pàgines
...therefore thec 5. j. angles HBE, EBC, arc likewife equal d; r.nd, if BE be made ra. j .^ 1t diuSj then EC is the tangent of half the fum of the angles at the bale. Draw BD parallel to AC, then the angle DEC is equal to the angle ACB e. Take KF equal to DC,... | |
 | Euclid - 1781 - 552 pàgines
...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 any two fides AB, AC will be to their difference as the tangent... | |
 | Robert Simson - 1781 - 534 pàgines
...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 greater fide for... | |
 | Vasiliĭ Nikitich Nikitin, Prokhov Ignatévich Suvorov - 1793 - 146 pàgines
...fum of the fides В A, AC, to their difference, fo is the cotangent of half the contained angle A, or the tangent of half the fum of the angles at the bafe, AC В, C В A, to the tangent of half the difference of thofe anles. О<, ED In every plane triangle... | |
 | Charles Hutton - 1788 - 728 pàgines
...Sides and the dngle Included by them, to find the reft. In a plane triangle, As the fum of any two fides is to their difference, fo is the tangent of half the fum of their oppofite angles, to the tangent of half their difference. Then the half difference added to the... | |
 | John McGregor (teacher of mathematics.) - 1792 - 532 pàgines
...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, the bafe is to... | |
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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. 
