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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 ... - Σελίδα 59
των Archibald Patoun - 1734 - 414 σελίδες
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Miscellanea Curiosa Mathematica: Or, The Literary Correspondence of ..., Τόμος 1

Francis Holliday - 1749 - 316 σελίδες
...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...

A Key to the Modern Sliding-rule: Containing the Description and Exlpanation ...

William Flower - 1768 - 228 σελίδες
...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,...

The Elements of Euclid, Viz: The Errors, by which Theon, Or Others, Have ...

Robert Simson - 1775 - 520 σελίδες
...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...

The Elements of Euclid: In which the Propositions are Demonstrated in a New ...

Euclid - 1776 - 264 σελίδες
...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...

The First Six Books: Together with the Eleventh and Twelfth

Euclid - 1781 - 520 σελίδες
...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...

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

Robert Simson - 1781 - 466 σελίδες
...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...

Elements of Plane and Spherical Trigonometry,: Written Originally in Russian ...

Vasiliĭ Nikitich Nikitin, Prokhov Ignatévich Suvorov - 1793 - 101 σελίδες
...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...

A Treatise on Mensuration, Both in Theory and Practice

Charles Hutton - 1788 - 703 σελίδες
...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...

A Complete Treatise on Practical Mathematics: Including the Nature and Use ...

John McGregor (teacher of mathematics.) - 1792 - 431 σελίδες
...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...

Elements of Geometry;: Containing the First Six Books of Euclid, with Two ...

Euclid, John Playfair - 1795 - 400 σελίδες
...will the radius be to the tangent of the difference between, that angle and half a " right angle, as the tangent of half the fum of the angles at the bafe of the triangle to the tangent of half their difference. TLet ABC be a triangle, the fides of which...




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