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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. "
A System of Geometry and Trigonometry: Together with a Treatise on Surveying ... - Σελίδα 27
των Abel Flint - 1804 - 168 σελίδες
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The New American Practical Navigator; Being an Epitome of Navigation ...

Nathaniel Bowditch - 1846 - 854 σελίδες
...same angles. Thus, in the triangle ABC, if we call AB the base, it will l>e, 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 dinerence. DH Dem. With the longest leg, CB, as radius,...

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

Jeremiah Day - 1848 - 354 σελίδες
...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...

An elementary course of practical mathematics, Μέρος 3

James Elliot - 1851 - 162 σελίδες
...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, add...

A complete System of Mensuration ... With many ... Additions ... by J. Trotter

Alexander Ingram - 1851 - 204 σελίδες
...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 half...

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

Sir Henry Edward Landor Thuillier - 1851 - 826 σελίδες
...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 half...

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

Jeremiah Day - 1851 - 418 σελίδες
...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.) is...

A Complete Epitome of Practical Navigation ...

John William Norie - 1852 - 838 σελίδες
...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 sum...

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

Jeremiah Day - 1853 - 288 σελίδες
...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.) is...

The Practical Surveyor's Guide: Containing the Necessary Information to Make ...

Andrew Duncan (Surveyor) - 1854 - 156 σελίδες
...sides and their included angle are given to find the other angles and side. RULE. — As the sum of the sides is to their difference so is the tangent of half the sum of the opposite angles to the tangent of half the difference ; this half difference added to half the sum...

The Elements of Plane Trigonometry

James Hann - 1854 - 140 σελίδες
...+ b tan By Art. 19, —jjHence the following rule : As the sum of any two sides of a plane triangle is to their difference, so is the tangent of half the sum of their opposite angles to the tangent of half their difference. By Art. 16, .-. a2 - o2 = c2 - 2bc cos...




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