 | Alexander Ingram - 1830 - 458 pàgines
...sura. PROP. XXXIX. In any triangle ABC, of which the sides are unequal, the sum of the sides AC + AB is to their difference as the tangent of half the sum of the opposite angles B and C, to the tangent of half their difference. CA + AB : CA — AB : : tan. £ (B... | |
 | Jeremiah Day - 1831 - 520 pàgines
...if the sines be adapted to any other radius. (Art. 1 19.) THEOREM II. 144. In a plane triangle, AS THE SUM OF ANY TWO OF THE SIDES, To THEIR DIFFERENCE...sides AB and AC. On AB set off AD equal to AC ; then DB it the difference of the sides AB and AC. The sum of the two angles ACB and ABC, is equal to the... | |
 | Jeremiah Day - 1831 - 394 pàgines
...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... | |
 | John Radford Young - 1833 - 286 pàgines
...4 tan. a — 4 ~~ tan. J(A — B) ' that is to say, 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 help of this rule we may determine the... | |
 | Euclides - 1834 - 518 pàgines
...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 pàgines
...difference ; and since BC, FG are parallel, (2. 6.) EC is to CF, as EB to BG; that is, the sum of the 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. * PROP. IV. FIG. 8. In a plane triangle, the cosine... | |
 | Jeremiah Day - 1836 - 418 pàgines
...TWO OF THE SIDES, To THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES j To THE TANGENT OF HALF THEIR DIFFERENCE. Thus the...sides AB and AC. On AB set off AD equal to AC ; then DB is the difference of the sides AB and AC. < The sum of the two angles ACB and ABC, is equal to the... | |
 | Adrien Marie Legendre - 1836 - 394 pàgines
...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... | |
 | John Playfair - 1836 - 148 pàgines
...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... | |
 | Euclid, James Thomson - 1837 - 410 pàgines
...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... | |
| |
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. 
