 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...  Easy Introduction to Mathematics - Σελίδα 353των Charles Butler - 1814Πλήρης προβολή - Σχετικά με αυτό το βιβλίο
 | Jeremiah Day - 1815 - 388 σελίδες
...equal to the sum, and FH to the difference of AC and AB. And by theorem II, [Art. 144.] the sum of the sides is to their difference ; as the tangent of half the sum of the opposite angles, to the tangent of half their difference. Therefore, R:Tan (ACH-45°;::Tan A(ACB +... | |
 | Euclides - 1816 - 588 σελίδες
...tangent of half their difference. . Let ABC be a plane triangle, the sum of any two sides AB, AC will be to their difference as the tangent of half the sum of the angles at the base ABC, ACB to the tangent of half their difference. About A as a centre, with AB the greater side for... | |
 | Olinthus Gregory - 1816 - 276 σελίδες
...cosines being the sines of the complements, it follows from the proposition that the sum of the cosines, is to their difference, as the tangent of half the sum of the complements, is to the tangent of halt' their difference. But half the sum of the complements of two... | |
 | Sir John Leslie - 1817 - 456 σελίδες
...cos la + 7 cos5a + 21 cos3a + 35c. ' &e. &c. &c. PROP. IV. THEOR. The sum of the sines of two arcs is to their difference, as the tangent of half the sum of those arcs to the tangent of half the difference. If A and B denote two arcs ; smA+«'wB : sin A—... | |
 | Miles Bland - 1819 - 444 σελίδες
...* The preceding expressions not being easy for calculation, values i . may PROP. XIII. (88.) In any triangle, the sum of any two sides is to their difference as the tangent of the semi-sum of the angles at the base is to the tangent of their semi-difference. Let ABC be any triangle,... | |
 | John Playfair - 1819 - 350 σελίδες
...the difference between either of them and 45o. * PROP. IV. The sum of any troo 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... | |
 | 1821 - 708 σελίδες
...(supposing arty tide to be the bast, and calling the other two the sides) the sum of the sides is to th-ir difference, as the tangent of half the sum of the angles at the base is to the tangent of half the difference of the same angle*. Thus, in the triangle ABC, if we call... | |
 | Adrien Marie Legendre - 1822 - 394 σελίδες
...principles of Art. 42 and 43 are easily deducible. XL VII. In any rectilineal 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 the difference of those same angles. From the proportion... | |
 | Rev. John Allen - 1822 - 516 σελίδες
...legs AC and CB, and AD their difference ; therefore the sum of the legs AC, CB of the triangle ABC is to their difference, as the tangent of half the sum of the angles CAB and CBA at the Ijase is tQ the tangent of half their difference. PROP. VII. THEOR. If to half the... | |
 | Peter Nicholson - 1823 - 210 σελίδες
...BC : : AC - BC : AD - BD. TRIGONOMETRY. — THEOREM 2. 234. 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 ; then, of the two sides, CA and... | |
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