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Llibres Llibres 51 - 60 de 184 sobre C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides....
" C' (89) (90) (91) (92) (93) 112. 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 Treatise of Plane Trigonometry: To which is Prefixed, a Summary View of ... - Pągina 66
per Jeremiah Day - 1815 - 126 pągines
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - 1837 - 318 pągines
...difference between either of them and 45°. PROP. IV. THEOR. The sum of any two 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 ; CA+AB...
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Elements of Surveying: Including a Description of the Instruments and the ...

1837 - 249 pągines
...AC :: sin C : sin B. THEOREM II. In any triangle, the sum of the two sides containing eithet angle, is to their difference, as the tangent of half the sum of the two other angles, to the tangent of half their difference. 58. Let ACB be a triangle : then will AB+AC:...
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Elements of Plane Geometry According to Euclid

Andrew Bell - 1837 - 240 pągines
...demonstrated that AB : BC = sin C : sin A. PROPOSITION VI. THEOREM. The sum of two sides of a triangle is to their difference as the tangent of half the sum of me angles at the base to the tangent of half their difference. Let ABC be any triangle, then if B and...
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Elements of Trigonometry, Plane and Spherical: Adapted to the Present State ...

Charles William Hackley - 1838 - 307 pągines
...tan £ (A -f- B) : tan \ (A — B) That is to say, the sum of two of the sides of a plane triangle is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. This proportion is employed when two sides...
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A Course of Mathematics: Containing the Principles of Plane ..., Volums 1-3

Jeremiah Day - 1838
...therefore, from the preceding proposition, (Alg. 389.) that the sum of any two sides of a triangle, is to their difference ; as the tangent of half the sum of the opposite angles, to the tangent of half their difference. This is the second theorem applied to the...
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A Course of Mathematics: Containing the Principles of Plane ..., Parts 2-4

Jeremiah Day - 1839 - 370 pągines
...therefore, from the preceding proposition, (Alg. 389.) that the sum of any two sides of a triangle, is to their difference ; as the tangent of half the sum of the opposite angles, to the tangent of half their difference. This is the second theorem applied to the...
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Elements of Surveying: With a Description of the Instruments and the ...

Charles Davies - 1839 - 261 pągines
...AC :: sin C : 'sin B. THEOREM II. In any triangle, the sum of the two sides containing eithei angle, is to their difference, as the tangent of half the sum of the two other angles, to the tangent of half their difference. 53. Let ACB be a triangle : then will AB+AC:...
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An introduction to the theory ... of plane and spherical trigonometry ...

Thomas Keith - 1839
...double their opposite angles. PROPOSITION IV. (115) 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 triangle ; make BE...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1842 - 317 pągines
...difference between either of them and 45°. PROP. IV. THE OR. The sum of any two 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 ofhalftlteir difference. Let ABC be any plane triangle...
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A Treatise on Plane and Spherical Trigonometry: Including the Construction ...

Enoch Lewis - 1844 - 228 pągines
...to any radius whatever (Art. 27). QED ART. 30. In any right lined triangle, the sum of any two sides 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 the triangle; AC, AB,...
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