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Bøker Bok 3140 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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The New American Practical Navigator: Being an Epitome of Navigation ...

Nathaniel Bowditch - 1826 - 617 sider
...the tame angla. Thus, in the triangle ABC, if we call AB the base, it will be 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 difference. Dan. With the longest leg CB as radius,...
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Mathematical and Astronomical Tables: For the Use of Students of Mathematics ...

William Galbraith - 1827 - 322 sider
...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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A concise system of mathematics

Alexander Ingram - 1830
...180°, and take half the remainder, to get half the sum of the unknown angles. Then as the sura 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. Having thus found the half difference, add...
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A System of Geometry and Trigonometry: With a Treatise on Surveying ... in ...

Abel Flint - 1830 - 284 sider
...side. Fig. 48. The solution of this CASE depends on the following PROPOSITION. IN EVERY PLANE TRIANGLE, AS THE SUM OF ANY TWO SIDES IS TO THEIR DIFFERENCE, SO IS THE TANQENT OF HALF THE SUM OF THE TWO OPPOSITE ANGLES TO THE TANGENT OF HALF THE DIFFERENCE BETWEEN THEM....
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The Principles of Plane Trigonometry, Mensuration, Navigation and Surveying

Jeremiah Day - 1831 - 370 sider
...other radius. (Art. 1 19.) 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 to...
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Mathematics for Practical Men

Olinthus Gregory - 1833 - 427 sider
...the tangent of the sum or difference of the arcs. 11. As the sum of the sines of two unequal arcs, is to their difference ; so is the tangent of half the sum of those two arcs to the tangent of half their difference. 12. Of any three equidifferentarcs,it will...
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Mathematical and Astronomical Tables: For the Use of Students in Mathematics ...

William Galbraith - 1834 - 428 sider
...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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A System of Geometry and Trigonometry: With a Treatise on Surveying; in ...

Abel Flint - 1835 - 334 sider
...and side. The solution of this CASE depends on the following PROPOSITION. ' IN EVERY PLANE TRIANGLE, AS THE SUM OF ANY TWO SIDES IS TO THEIR DIFFERENCE,...OF THE TWO OPPOSITE ANGLES TO THE TANGENT OF HALF THE DIFFERENCE BETWEEN THEM. ADD THIS HALF DIFFERENCE TO HALF THE SUM OF THE ANGLES AND YOU WILL HAVE...
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

1836 - 472 sider
...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, George Gillet - 1838 - 334 sider
...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 HALF THE SUM OF THE ANGLES, AND YOU WILL HAVE...
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