Books Books
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 Theory and Practice of Surveying: Containing All the Instructions ...

Robert Gibson - Surveying - 1814 - 558 pages
...as their halves, that is, AH : IH: : CE : ED, that is as the sum of the two sides AB and BC, is to their difference ; so is the tangent of half the sum of the two unknown angles A and G, to the tangent of half their difference. QED THEO. III. Fig. 12. In any right...

## A Treatise on Surveying, Containing the Theory and Practice: To which is ...

John Gummere - Surveying - 1814 - 398 pages
...of the two unknown angles. Then ; • * * * * • * As the sum of the two given sides, „• Is to their difference ; ,. % So is the tangent -of half the sum of the two uuknown angles, To the tangent of half their difference.* This half difference of the two unknown angles,...

## A Practical Application of the Principles of Geometry to the Mensuration of ...

Jeremiah Day - Measurement - 1815 - 388 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, !Ło the tangent of half their difference. Thus the sum of AB and AC (Fig. 25.) is...

## A Treatise of Plane Trigonometry: To which is Prefixed, a Summary View of ...

Jeremiah Day - Logarithms - 1815 - 172 pages
...radius. (Art. 11 9.) THEOREM II. ..* 144. In a plane triangle, Jl 3 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...

## Elements of Plane and Spherical Trigonometry

Olinthus Gregory - Plane trigonometry - 1816 - 278 pages
...•. 15. In any plane triangle it will be, as the sum of the sides about the vertical angle, is to their difference, so is the tangent of half the sum of the angles at the base, to the tangent of half their difference. By the preceding prop. AC : BC :: sin...

## A Treatise on Practical Surveying: Which is Demonstrated from Its First ...

Robert Gibson - Surveying - 1818 - 502 pages
...are as their halves, ie AH : IH : : CE : ED, that is, as the snm of the two sides AB and BC, is to their difference ; so is the tangent of half the sum of the two unknown angles A and C, to the tangent of half their difference. QED THEOREM HI. In any right-lined...

## American Edition of the British Encyclopedia: Or, Dictionary of ..., Volume 12

William Nicholson - Natural history - 1821 - 356 pages
...spherical triangle, ABC (fig. 27,) it will be, as the co-tangent of half the sum of the angles at the base is to the tangent of half their difference, so is the tangent of half the vertical angle to the tangent of the angle which the perpendicular CD makes with the line CF, bisecting...

## British Encyclopedia: Or, Dictionary of Arts and Sciences ..., Volume 12

William Nicholson - Natural history - 1821 - 356 pages
...spherical triangle, ABC (fig. 27,) it will be, as the co-tangent of half the sum of the angles at the case is to the tangent of half their difference, so is the tangent of half the vertical angle to the tangent of the angle which the perpendicular CD makes with the line CF, bisecting...