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" 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 to the tangent of half their difference. "
A Complete Treatise on Practical Mathematics: Including the Nature and Use ... - Page 38
by John McGregor (teacher of mathematics.) - 1792 - 431 pages
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The Doctrine of Plain and Spherical Trigonometry: With Its Application and ...

William Hawney - 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...
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A Compleat Treatise of Practical Navigation Demonstrated from It's First ...

Archibald Patoun - 1734 - 568 pages
...In any plain Triangle, as ABC, thefum of the fides, AB and BC, is to the difference of thefe fides, as the Tangent of half the fum of the Angles at the bafe, viz. A and C, is to the Tangent of half the difference of thefe Angles. Demon. Produce AB and make...
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Miscellanea Curiosa Mathematica: Or, The Literary Correspondence ..., Volume 1

Francis Holliday - 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....
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A New & Complete Treatise of Spherical Trigonometry: In which are Contained ...

Antoine-René Mauduit - 1768 - 252 pages
...the tangent of half the difference cf the fegments of the bafe-, and the fécond this ; The coßne of half the fum of the angles at the bafe is to the coftne cf half their difference, as the tangent of half the difference of their oppofttefides is io...
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A Key to the Modern Sliding-rule: Containing the Description and Exlpanation ...

William Flower - 1768 - 276 pages
...point from the middle of the bafe. TbeoretQ VII. In any fpberic triangle it will be, as the cotangent of half the fum of the angles, at ' the bafe is to the tangent of half their difference* fo is the tangent of half the vertical angle to the tangent of the...
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A Compendious Course of Practical Mathematics: Particularly Adapted to the ...

Paul Hoste - 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 angle C....
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A New System of Mathematics: Containing Plane Geometry; General ...

John Muller - 1769 - 152 pages
...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 the...
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New Elements of Mathematics: Or Euclid Corrected. Containing Plane Gometry ...

John Muller - 1773 - 202 pages
...: 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...
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The Elements of Euclid, Viz: The Errors, by which Theon, Or Others, Have ...

Robert Simson - 1775 - 534 pages
...; and fince BC, FG are parallel (2.6.) EC is to CF, asEB to BG; that is, the fum of the H h 3 fides 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. PROP. IV. FIG. 18. TN any plain triangle BAC, whole two fides...
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The Elements of Euclid: In which the Propositions are Demonstrated in a New ...

Euclid - 1776 - 326 pages
...angle BIC, 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 any two of its...
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