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" TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE. "
A System of Geometry and Trigonometry: Together with a Treatise on Surveying ... - Page 34
by Abel Flint - 1825 - 241 pages
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Mathematical and Astronomical Tables: For the Use of Students in Mathematics ...

William Galbraith - Astronomy - 1834 - 428 pages
...45. In a plane triangle when the two sides and contained angle are given. I. As the sum of the given sides Is to their difference; So is the tangent of half the sum of the opposite angles To the tangent of half their difference. Half the difference added to half the sum...
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

Mathematics - 1836 - 472 pages
...are as their opposite sides. Theorem II. In any 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, to the tangent of half their difference. .Theorem III. As the largest side, to the...
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A System of Geometry and Trigonometry, with a Treatise on Surveying: In ...

Abel Flint - Geometry - 1837 - 272 pages
...30'. CASE III. Two sides and their contained angle given, to find the other angles and side. Fig. 48. The solution of this CASE depends on the following...DIFFERENCE TO HALF THE SUM OF THE ANGLES, AND YOU WILL RAVE THE GREATER ANGLE, AND SUBSTRACT THE HALF DIFFERENCE FROM THE HALF SUM, AND YOU WILL HAVE THE...
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A System of Geometry and Trigonometry: With a Treatise on Surveying; in ...

Abel Flint - Geometry - 1838 - 334 pages
...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...THE ANGLES, AND YOU WILL HAVE THE GREATER ANGLE, AND SUBSTRACT THE HALF DIFFERENCE FROM THE HALF SUM, AND YOU WILL HAVE THE LESSER ANGLE. In the triangle...
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A complete treatise on Practical Land-Surveying, etc

Thomas Holliday - Surveying - 1838 - 80 pages
...the angle contained between them are given, to find the rest. u2 Rule.—As the sum of the two given sides is to their difference, so is the tangent of half the sum of the unknown angles to the tangent of half their difference: this half difference being added to half the...
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A System of Geometry and Trigonometry: With a Treatise on Surveying, in ...

Abel Flint - Geometry - 1839 - 334 pages
...sides and their contained angle given, to find the other angles and side, fig. 48. The solution &f this CASE depends on the following PROPOSITION. IN...THEM. ADD THIS HALF DIFFERENCE TO HALF THE SUM OF THB .MJGLES, AND YOU WILI, HAVE THE GREATER ANGLE, AND SXTBSTRACT THE HALF DIFFERENCE FROM THE HALF...
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A Course of Mathematics: Containing the Principles of Plane Trigonometry ...

Jeremiah Day - Geometry - 1839 - 370 pages
...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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A Treatise on Plane and Spherical Trigonometry: Including the Construction ...

Enoch Lewis - Conic sections - 1844 - 228 pages
...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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The New American Practical Navigator; Being an Epitome of Navigation ...

Nathaniel Bowditch - 1846 - 451 pages
...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,...
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A Treatise of Plane Trigonometry, and the Mensuration of Heights and ...

Jeremiah Day - Logarithms - 1848 - 153 pages
...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 ; TO THE TANGENT OF HALF THEIR DIFFERENCE. Thus, the sum of AB and AC, is to their...
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