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Libros Libros 51 - 60 de 100 sobre AC, (Fig. 25.) is to their difference ; as the tangent of half the sum of the angles...
" AC, (Fig. 25.) is to their difference ; as the tangent of half the sum of the angles ACB and ABC, to the tangent of half their difference. "
Elements of Plane and Spherical Trigonometry: With Their Applications to ... - Página 18
por Olinthus Gregory - 1816 - 244 páginas
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A System of Geometry and Trigonometry: With a Treatise on Surveying; in ...

Abel Flint - 1838 - 334 páginas
...CASE depends on the following PROPOSITION. IN EVERY PLANE TRIANGLE, AS THE SUM OF ANY TWO SIDES ISTO THEIR DIFFERENCE, SO IS THE TANGENT OF HALF THE SUM OF THE TWO OPPOSITE ANGLES TO THE TANGENT OF HALF THE DIFFERENCE BETWEEN THEM. ADD THIS HALF DIFFERENCE TO...
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A Course of Mathematics: Containing the Principles of Plane ..., Partes2-4

Jeremiah Day - 1839 - 370 páginas
...other radius. (Art. 119.) THEOREM II. 144. In a plane triangle, As THE SUM OF ANY 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 sum of AB and AC, (Fig. 25.) is...
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An Encyclopædia of Architecture: Historical, Theoretical, and Practical

Joseph Gwilt - 1842 - 1089 páginas
...said unknown angles ; and using the following ratio, we have — As the sum of the two given sides Is to their difference, So is the tangent of half the sum of their opposite angles To the tangent of half the difference of the same angles. Now the half sum of...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1842 - 317 páginas
...then will the radius be to the tangent of the difference between that angle and half a right angle, as the tangent of half the sum of the angles, at the base of the triangle to the tangent of half their difference. Let ABC be a triangle, the sides of which...
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A Treatise on Plane and Spherical Trigonometry: Including the Construction ...

Enoch Lewis - 1844 - 228 páginas
...cos CAD : cos CAB : : tan AD : tan AB. QED ART. 72. As the sum of the sines of any two unequal arcs is to their difference, so is the tangent of half the sum of those arcs, to the tangent of half their difference. Let AB, AC be the arcs ; L the centre of the circle...
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Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ...

1845
...sine of half their difference: also, that the base is to the sum of the other two sides as the cosine of half the sum of the angles at the base, to the cosine of half their difference. Ex. 10. How must three trees, A, B, C, be planted, so that the angle...
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Higher Geometry and Trigonometry: Being the Third Part of a Series on ...

Nathan Scholfield - 1845 - 232 páginas
...sine of half their difference : also, that the base is to the sum of the other two sides as the cosine of half the sum of the angles at the base, to the cosine of half their difference. Ex. 10. How must three trees, A, B, C, be planted, so that the angle...
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A Series on Elementary and Higher Geometry, Trigonometry, and Mensuration ...

Nathan Scholfield - 1845
...Prove that, in any plane triangle, the base is to the difference of the other two sides, as the sine of half the sum of the angles at the base, to the sine of half their difference : also-, that the base is to the sum of the other two sides as the cosine...
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The New American Practical Navigator; Being an Epitome of Navigation ...

Nathaniel Bowditch - 1846 - 451 páginas
...same angles. Thus, in the triangle ABC, if we call AB the base, it will l>e, As the sum of AC and CB is to their difference, so is the tangent of half the sum of the angles ABC, ВАС, to the tangent of half their dinerence. DH Dem. With the longest leg, CB, as radius, describe...
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Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ...

Dennis M'Curdy - 1846 - 138 páginas
...J(AC-(AB): tan. J(AC—AB). QED 4 Th. In any triangle, the sum of two sides 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. Given the triangle ABC, the side AB being greater than...
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