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" In any plane triangle, the sum of any two sides is to their difference, as the tangent of half the sum of the opposite angles is to the tangent of half their difference. "
A Course of Mathematics: In Three Volumes : Composed for the Use of the ... - Page 63
by Charles Hutton - 1811
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 588 pages
...being given, the fourth is also given. PROP. III. FIG. 8. IN a plane triangle, the sum of any two sides is to their difference, as the tangent of half the sum of the angles at the base, to the tangent of half their difference. . Let ABC be a plane triangle, the...
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Elements of Geometry and Plane Trigonometry: With an Appendix, and Copious ...

Sir John Leslie - 1817 - 456 pages
...cos la + 7 cos5a + 21 cos3a + 35c. ' &e. &c. &c. PROP. IV. THEOR. The sum of the sines of two arcs is to their difference, as the tangent of half the sum of those arcs to the tangent of half the difference. If A and B denote two arcs ; smA+«'wB : sin A— «'wB A—...
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A Course of Mathematics: For the Use of Academies, as Well as ..., Volume 2

Charles Hutton - 1818 - 652 pages
...This equation is readily converted into a very useful proportion, viz. The sum of the sines of two ara or angles, is to their difference, as the tangent...angles, is to the tangent of half their difference. 26. Operating with the third and fourth formulae of the preceding article, as we have already done...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1819 - 350 pages
...the difference between either of them and 45o. * PROP. IV. The sum of any troo sides of a triangle is to their difference, as the tangent of half the sum of the angles opposite to those sides, to the tangent of half their difference. Let ABC be any plane triangle...
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New Series of The Mathematical Repository, Volume 4

Thomas Leybourn - 1819 - 430 pages
...: AC*. Required a proof. 8. Prove, geometrically, that in any plane triangle, the sum of the sides is to their difference as the tangent of half the sum of the angles at the base to the tangent of half their difference. 9. Shew that tan.* 60 = 3 tan. 60 to...
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A Course of Mathematics for the Use of Academies, as Well as Private Tuition

Charles Hutton - 1822 - 680 pages
...• '• .--""•'"• This equation is readily converted into a very useful proportion, viz. Tlie sum of the sines of two arcs or angles, is to their difference r,- a$ the tangent of: half the sum of those arcs or angles, is to the tangent of half their difference....
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - 1822 - 394 pages
...principles of Art. 42 and 43 are easily deducible. XL VII. In any rectilineal triangle, the sum of two sides is to their difference, as the tangent of half the sum of the angles opposite those sides is to the tangent of half the difference of those same angles. From...
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Euclid's Elements of Geometry: The Six First Books. To which are Added ...

Rev. John Allen - 1822 - 516 pages
...legs AC and CB, and AD their difference ; therefore the sum of the legs AC, CB of the triangle ABC is to their difference, as the tangent of half the sum of the angles CAB and CBA at the Ijase is tQ the tangent of half their difference. PROP. VII. THEOR. If...
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The New Practical Builder and Workman's Companion, Containing a Full Display ...

Peter Nicholson - 1823 - 210 pages
...BC : : AC - BC : AD - BD. TRIGONOMETRY. — THEOREM 2. 234. The sum of the two sides of a triangle is to their difference as the tangent of half the sum of the angles at the base is to the tangent of half their difference. Let ABC be a triangle ; then, of...
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Glasgow Mechanics' Magazine, and Annals of Philosophy, Volume 1

1824 - 492 pages
...because DA C = AC B, (Euc. 1. 29.) Therefore, DAC+ DCA = 130o, and consequently ADC = of any triangle is to their difference, as the tangent of half the sum of the angles opposite them, is to the tangent of half their difference. Therefore, by logarithms, As,...
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