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To find the other side: — 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 their difference...
Mathematics: Compiled from the Best Authors and Intended to be the Text-book ... - Page 17
1801

## 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.)...

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

William Galbraith - Astronomy - 1834 - 454 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...

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

Abel Flint - Geometry - 1835 - 368 pages
...the other angles 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, 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...

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

Mathematics - 1836 - 488 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...

## A complete treatise on practical land-surveying

Thomas Holliday - Surveying - 1838 - 404 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...

## A Course of Mathematics: Containing the Principles of Plane ..., Volumes 1-3

Jeremiah Day - Geometry - 1839 - 434 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.)...

## Crocker's Elements of land surveying. To which are added, Tables of six ...

Abraham Crocker - 1841 - 486 pages
...II Rule for the Second Case. As the sum of the two given sides is to the difference of those sides, so is the tangent of half the sum of their opposite angles, to the tangent of hajf their difference. This half-difference, added to the half sum, will give the greater angle * :...

## An Encyclopędia of Architecture: Historical, Theoretical, and Practical

Joseph Gwilt - Architects - 1842 - 1114 pages
...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...sum of their opposite angles To the tangent of half the difference of the same angles. Now the half sum of any two quantities increased by their half difference...