| 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 - 428 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 - 513 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 - 114 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 - 359 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 - 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 - Geometry - 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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