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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

## A Treatise of Plane Trigonometry, and the Mensuration of Heights and ...

Jeremiah Day - Logarithms - 1848 - 354 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...

## A Manual of Surveying for India, Detailing the Mode of Operations on the ...

Sir Henry Edward Landor Thuillier - Surveying - 1851 - 826 pages
...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...

## A Complete System of Mensuration ...

Alexander Ingram - 1851 - 202 pages
...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...

## An elementary course of practical mathematics, Part 3

James Elliot - 1851 - 162 pages
...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,...

## A Course of Mathematics: Containing the Principles of Plane Trigonometry ...

Jeremiah Day - Geometry - 1851 - 418 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, (Fig. 25.)...

## A Complete Epitome of Practical Navigation ...

John William Norie - Nautical astronomy - 1852 - 844 pages
...triangle. II. When two Sides and the Angle contained between them are given. 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 added to half the...

## The Computist's Manual of Facts: And Merchant's and Mechanic's Calculator ...

Ezra S. Winslow - Business mathematics - 1853 - 264 pages
...any angle = cos of that angle. That is, A being the angle — 1 — 2 sin2 of 4 A = cos A. In every plane triangle, as the sum of any two sides is to their difference, so is the natural tangent of half the sum of the angles opposite those sides to the natural tangent of half their...

## A Course of Mathematics: Containing the Principles of Plane Trigonometry ...

Jeremiah Day - Mathematics - 1853 - 288 pages
...radius. (Art. 119.) ff THEOREM II. /? 144. In a plane triangle, \. As THE SU^I OF ANY TWO OF THE SIDES, To THEIR DIFFERENCE ] So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITK ANGLKS; To THE TANGENT OF HALF THEIR DIFFERENCE. Thus, the sum of AB and AC, (Fig. 25.)...