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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. "
The Elements of Plane and Spherical Trigonometry - Page 64
by Thomas Ulvan Taylor, Charles Puryear - 1902 - 160 pages
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1806 - 546 pages
...a plane triangle, any three 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...
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A Treatise of Plane and Spherical Trigonometry: In Theory and Practice ...

Francis Nichols - Plane trigonometry - 1811 - 162 pages
...angle ACB, which is the supplement of the angles at A and B, may be found by Cor. 32. 1. PROP VI. 61. In any 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. Let ABC be the proposed...
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Easy Introduction to Mathematics, Volume 2

Charles Butler - 1814 - 582 pages
...this proposition, without letting fall a perpendicular, as in the preceding article. 72. 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 the difference. Let ABC be a triangle,...
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An Easy Introduction to the Mathematics: In which the Theory and ..., Volume 2

Charles Butler - Mathematics - 1814 - 528 pages
...proposition, without letting fall a perpendicular, as in the preceding article. 71. In a plane triangle, tte 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 the difference. Let ABC be a triangle,...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 588 pages
...in a plane triangle, any three 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...
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Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

Miles Bland - Euclid's Elements - 1819 - 444 pages
...found*. * The preceding expressions not being easy for calculation, values i . may PROP. XIII. (88.) In any triangle, the sum of any two sides is to their difference as the tangent of the semi-sum of the angles at the base is to the tangent of their semi-difference. Let ABC be any triangle,...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 1046 pages
...obtuse R 42. From the proportion AC + CB : AC— CB:: tangí (B+C) : tang-i (B—C) it follows that in any triangle the sum of any two sides is to their difference, as the tangent of half the sum of the two angles opposite these sides, is to the tangent of half the difference of these...
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An Introduction to the Theory and Practice of Plain and Spherical ...

Thomas Keith - Navigation - 1826 - 504 pages
...are to each other as the chords of double their opposite angles. PROPOSITION IV. (E) 1. In any plane triangle, the sum of any two sides is to their difference, as the tangent of half the sum of their ^opposite angles, is to the tangent of half their difference. Let ABC be any...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 546 pages
...in a plane triangle, any three 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...
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Elements of Plane and Spherical Trigonometry: With Its Applications to the ...

John Radford Young - Astronomy - 1833 - 308 pages
...two arcs to find the sine and cosine of their sum and difference . . .19 ARTIcLE. PAGE 19. In a plane triangle the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles to the tangent of half their difference . . . .21 20. Formulas...
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