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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. "
A Compleat Treatise of Practical Navigation Demonstrated from It's First ... - Page 41
by Archibald Patoun - 1734 - 414 pages
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Miscellanea Curiosa Mathematica: Or, The Literary Correspondence ..., Volume 1

Francis Holliday - Mathematics - 1749 - 360 pages
...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...
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A Key to the Modern Sliding-rule: Containing the Description and Exlpanation ...

William Flower - Mathematical instruments - 1768 - 276 pages
...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,...
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The Elements of Euclid, Viz: The Errors, by which Theon, Or Others, Have ...

Robert Simson - Trigonometry - 1775 - 534 pages
...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...
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The Elements of Euclid: In which the Propositions are Demonstrated in a New ...

Euclid - Geometry - 1776 - 326 pages
...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...
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The Elements of Euclid,: In which the Propositions are Demonstrated in a New ...

Euclid - Geometry - 1776 - 318 pages
...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,...
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The First Six Books: Together with the Eleventh and Twelfth

Euclid - 1781 - 552 pages
...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...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1781 - 534 pages
...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...
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Elements of Plane and Spherical Trigonometry,: Written Originally in Russian ...

Vasiliĭ Nikitich Nikitin, Prokhov Ignatévich Suvorov - Geometry - 1793 - 146 pages
...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...
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A Treatise on Mensuration, Both in Theory and Practice

Charles Hutton - Measurement - 1788 - 728 pages
...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...
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A Complete Treatise on Practical Mathematics: Including the Nature and Use ...

John McGregor (teacher of mathematics.) - Mathematics - 1792 - 532 pages
...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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