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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.
Trigonometry, Plane and Spherical: With the Construction and Application of ... - Page 69
by Thomas Simpson - 1810 - 125 pages

## The New American Practical Navigator: Being an Epitome of Navigation ...

Nathaniel Bowditch - Nautical astronomy - 1826 - 764 pages
...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,...

## Mathematical and Astronomical Tables: For the Use of Students of Mathematics ...

William Galbraith - Astronomy - 1827 - 412 pages
...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...

## A Concise System of Mathematics ...

Alexander Ingram - Mathematics - 1830 - 458 pages
...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...

## The Principles of Plane Trigonometry, Mensuration, Navigation and Surveying

Jeremiah Day - Measurement - 1831 - 520 pages
...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...

## Mathematical and Astronomical Tables: For the Use of Students in Mathematics ...

William Galbraith - Astronomy - 1834 - 454 pages
...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...

## A System of Geometry and Trigonometry: With a Treatise on Surveying; in ...

Abel Flint - Geometry - 1835 - 342 pages
...CASE depends on the following PROPOSITION. IN EVERY 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. ADD THIS HALF DIFFERENCE TO HALF...

## The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

Mathematics - 1836 - 488 pages
...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...

## A complete treatise on practical land-surveying

Thomas Holliday - Surveying - 1838 - 404 pages
...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...