 | Sir John Leslie - 1820 - عدد الصفحات: 482
...that of its supplement arc the same. PROP. X. THEOR. v In any triangle, the sum of two sides is to the difference, as the tangent of half the sum of the...the base, to the tangent of half their difference. In the triangle ABC, AB+AC : AB-AC : : From the vertex A, with a distance equal to the greater side... | |
 | Euclid, Robert Simson - 1821 - عدد الصفحات: 514
...AC, and CF their 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...the base to the tangent of half their difference. PROP. IV. FIG. 18. IN any plane triangle BAC, whose two sides are BA, AC, and base BC. the less of... | |
 | 1821 - عدد الصفحات: 708
...(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 - عدد الصفحات: 394
...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 - عدد الصفحات: 516
...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... | |
 | Charles Hutton - 1822 - عدد الصفحات: 680
...that the base is to the sum of the other two sides as ^ SPHERICAL TRIGONOMETRY. 25 | as the cosine of half the sum of the angles at the base, to the if cosine of half their difference. . I Ex. 14. How must three trees, A, B, c, be planted, so that... | |
 | Peter Nicholson - 1823 - عدد الصفحات: 210
...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... | |
 | Jeremiah Day - 1824 - عدد الصفحات: 440
...construction, 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-450): :Tan i(ACB+B)... | |
 | 1824 - عدد الصفحات: 492
...because DA C = AC B, (Euc. 1. 29.) Therefore, DAC+ DCA = 130o, and consequently ADC = of any triangle is to their difference, as the tangent of half the sum of the angles opposite them, is to the tangent of half their difference. Therefore, by logarithms, As, CD + DA =... | |
 | Edward Riddle - 1824 - عدد الصفحات: 572
...angle. Shew that radius is to the tangent of the difference between this angle and half a right angle, as the tangent of half the sum of the angles at the base is to the tiuigcnt of half their difference. ELEMENTARY PRINCIPLES OP SPHERICAL TRIGONOMETRY. 1. A... | |
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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 II. we have a : b : : sin. A : sin. B. 
