 | Henry Pearson - Algebra - 1833 - 164 pages
...the opposite sides. tan a + b ab tan Or the sum of two sides of a triangle is to their difference, or the tangent of half the sum of the angles opposite...to them is to the tangent of half their difference. 8. c = i/(a* + b2 - 2 ab cos C). This is an expression for a side of a triangle in terms of the remaining... | |
 | William Galbraith - Astronomy - 1834 - 454 pages
...the cosine of half their difference as the cotangent of half the angle contained between them is to the tangent of half the sum of the angles opposite to them, t or sin \ (AB + AC) : sin \ (AB<»BC) : : cot \ A : tan } (B</)C); cos 4 (AB+AC) : cos \ (ABcn BC)... | |
 | Euclides - 1834 - 518 pages
...given, the fourth is also given. PROPOSITION III. In a plane triangle, the sum of any two sides in to their difference, as the tangent of half the sum of the angle at Ihe base, to the tangent of half their difference. PROPOSITIONS III. IV. of the angles at... | |
 | Euclid - 1835 - 540 pages
...from half the sum subtract half the difference, and it will give the less. 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 sum of any two... | |
 | Robert Simson - Trigonometry - 1835 - 544 pages
...difference; and since BC, FGare parallel, (2. 6.) EC is to CF, as EB to BG; that is, the sum of the fides is to their difference, as the tangent of half the sum of the angles at the base to the tangent of half their difference. * PROP. IV. F1G. 8. In a plane triangle, the cosine... | |
 | John Playfair - Geometry - 1836 - 148 pages
...opposite to them, in r. plane triangle, any three being given, the fourth is also given. PROP. III. i 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 sum of any two... | |
 | Adrien Marie Legendre - Geometry - 1836 - 394 pages
...6 — c=2p — 2c, a+c — 6=2p — 26; hence THEOREM V. In every rectilineal triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides, to the tangent of half their difference. For. AB : BC : : sin C : sin A (Theorem III.).... | |
 | John Playfair - Euclid's Elements - 1836 - 488 pages
...• . i . ..; . i. .• i » »i :*• <••! The sum of any two sides of a triangle is to theif difference, as the tangent of half the sum, of the angles opposite to those sides, to the tawgent of half their difference. '' •• i• . . .• ' * " i •' ' • -•... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...sine of a right angle is equal to the radius. PROP. III. 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, is to the tangent of half their difference. Let ABC be a triangle, a, b any two of its... | |
 | John Playfair - Euclid's Elements - 1837 - 332 pages
...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 : CA-AB... | |
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In the same way it may be proved that a : b : : sin. A : sin. B, and these two proportions may be written a : 6 : c : : sin. A : sin. B : sin. C. THEOREM III. t8. In any plane triangle, the sum of any two sides is to their difference as the tangent of... 
