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Llibres Llibres 81 - 90 de 188 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 and Trigonometry: From the Works of A.M. Legendre ...

Charles Davies, Adrien Marie Legendre - 1854 - 432 pągines
...also have (Art. 22), a + b : ab :: tan $(A + B) : ta.n$(A — B): tha| is, 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. 91. In case of a right•angled triangle,...
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A TREATISE OF PLANE TRIGONOMETRY

JEREMIAH DAY, D.D. LL.D., - 1855
...THE OPPOSITE ANGLES J To THE TANGENT OF HALF THEIR DIFFERENCE. Thus, the sum of AB and AC, ^ ^ ^ c is to their difference ; as the tangent of half the sum of the angles ACB and ABO, to the tangent of half their difference. Demonstration. Extend CA to G, making AG equal to AB;...
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A Treatise on Land-Surveying Comprising The Theory Developed from Five ...

W.M. Gillespie, A.M., Civ. Eng - 1855
...to each other as the opposite sides. THEOREM II. — In every plane 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 their difference. THEOREM III. — In every plane triangle,...
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Elements of Plane Trigonometry, Surveying and Navigation

William Smyth - 1855 - 223 pągines
...tan — ~ ; lU —4 a proportion, which we may thus enunciate ; the sum of two sides of a triangle is to their difference, as the tangent of half the sum of the opposite angles is to the tangent of half their difference. Ex. 1. Let AC (fig. 30) be 52. 96 -yds,...
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Elements of geometry and trigonometry: with applications in mensuration

1855 - 324 pągines
...sin A : sin BTheorems.THEOREM IIIn any triangle, the sum of the two sides contain1ng either angle, is to their difference, as the tangent of half the sum of the two other angles, to the tangent of half their differenceLet ACB be a triangle: then will AB + AC:AB-AC::t1M)(C+£)...
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Elements of Plane and Spherical Trigonometry: With Their Applications to ...

Elias Loomis - 1855 - 178 pągines
...i(A+B) . sin. A-sin. B~sin. i(AB) cos. i(A+B)~tang. i(AB) ' that is, The sum of the sines of two arcs is to their difference, as the tangent of half the sum of those arcs is to the tangent of half their difference. Dividing formula (3) by (4), and considering...
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Practical carpentry, joinery, and cabinet-making [by P. Nicholson. by P ...

Peter Nicholson - 1856
...+ BC :: AC-BC : AD — BD. TRIGONOMETRY. — THEOREM 2. 151. 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 4 then, of the two sides,...
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A Treatise on Land-surveying: Comprising the Theory Developed from Five ...

William Mitchell Gillespie - 1856 - 464 pągines
...to each other a* the opposite sides. THEOREM II. — In every plane 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 their difference. THEOREM III. — In every plane triangle,...
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PLANE AND SOLID GEOMETRY

GEORGE R. PERKINS - 1856
...(2.) In the same way it may be shown that THEOREM II. 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. By Theorem I., we have 5 : c : : sin. B...
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A Treatise on Land-surveying: Comprising the Theory Developed from Five ...

William Mitchell Gillespie - 1857 - 524 pągines
...to each other at the opposite sides. THEOREM II.— In every plane triangle, the turn of two tides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference. THEOREM III. — In every plane triangle,...
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