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Bøker Bok 4150 av 76Plane Triangle, As the Sum of any two Sides ; Is to their Difference ; So is the...
" Plane Triangle, As the Sum of any two Sides ; Is to their Difference ; So is the Tangent of half the Sum of the two opposite Angles ; To the Tangent of half the Difference between them. "
Trigonometry, Plane and Spherical: With the Construction and Application of ... - Side 5
av Thomas Simpson - 1810 - 125 sider
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A complete treatise on practical land-surveying

Thomas Holliday - 1838
...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 Course of Mathematics: Containing the Principles of Plane ..., Deler 2-4

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

Enoch Lewis - 1844 - 228 sider
...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 sider
...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 - 1848 - 153 sider
...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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An elementary course of practical mathematics

James Elliot - 1851
...the remainder will be the sum of the two required angles. Then say,— As the sum of the two given sides is to their difference, so is the tangent of half the sum of the two required angles, to the tangent of half their difference. Having found the said half difference, add...
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A complete system of mensuration, with additions by J. Trotter

Alexander Ingram - 1851
...180°, and take half the remainder, to get half the sum of the unknown angles. Then as the sum of the sides is to their difference, so is the tangent of half the sum of the unknown angles to the tangent of half their difference (Theor. 4. Trig.) Having thus found the half...
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A Manual of Surveying for India, Detailing the Mode of Operations on the ...

Sir Henry Edward Landor Thuillier - 1851 - 718 sider
...angle between them, to find the other two angles and the third side. 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. Half the difference thus found added to half...
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A course of mathematics: containing the principles of plane trigonometry ...

Jeremiah Day - 1851
...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, (Fig. 25.) is...
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