Books Books In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference. A Treatise of Plane and Spherical Trigonometry: In Theory and Practice ... - Page 12
by Francis Nichols - 1811 - 128 pages ## Elements of Surveying: Including a Description of the Instruments and the ...

Charles Davies - Navigation - 1837 - 336 pages
...AC :: sin C : sin B. THEOREM II. In any triangle, the sum of the two sides containing eithet angle, is to their difference, as the tangent of half the sum of the two other angles, to the tangent of half their difference. 58. Let ACB be a triangle : then will AB+AC:... ## The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1837 - 410 pages
...sine of a right angle is equal to the radius. PROP. III. THEOR. THE sum of any two sides of a triangle is to their difference, as the tangent of half the sum of the angles opposite to those sides, is to the tangent of half their difference. Let ABC be a triangle,... ## Elements of Plane Geometry According to Euclid

Andrew Bell - Euclid's Elements - 1837 - 290 pages
...demonstrated that AB : BC = sin C : sin A. PROPOSITION VI. THEOREM. The sum of two sides of a triangle is to their difference as the tangent of half the sum of me angles at the base to the tangent of half their difference. Let ABC be any triangle, then if B and... ## A Course of Mathematics: Containing the Principles of Plane Trigonometry ...

Jeremiah Day - Geometry - 1838 - 416 pages
...THE OPPOSITE ANGLES ; To THE TANGENT OF HALF THEIR DIFFERENCE. Thus, the sum of AB and AC, (Fig. 25.) is to their difference ; as the tangent of half the sum of the angles ACB and ABC, to the tangent of half their difference. Demonstration . Extend CA to G, making... ## An introduction to the theory ... of plane and spherical trigonometry ...

Thomas Keith - 1839 - 498 pages
...are to each other as the chords of double their opposite angles. PROPOSITION IV. (115) In any plane triangle, the sum of any two sides is to their difference, as the tangent of half the sum of their opposite angles is to the tangent of half their difference, Let ABC be any triangle ; make BE... ## Elements of Surveying: With a Description of the Instruments and the ...

Charles Davies - Surveying - 1839 - 376 pages
...AC :: sin C : 'sin B. THEOREM II. In any triangle, the sum of the two sides containing eithei angle, is to their difference, as the tangent of half the sum of the two other angles, to the tangent of half their difference. 53. Let ACB be a triangle : then will AB+AC:... ## A Course of Mathematics: Containing the Principles of Plane ..., Volumes 1-3

Jeremiah Day - Geometry - 1839 - 432 pages
...THE OPPOSITE ANGLES J To THE TANGENT OF HALF THEIR DIFFERENCE. Thus, the sum of AB and AC, (Fig. 25.) is to their difference ; as the tangent of half the sum of the angles ACB and ABC, to the tangent of half their difference. Demonstration. Extend CA to G, making... ## Elements of Surveying: With a Description of the Instruments and the ...

Charles Davies - Surveying - 1839 - 376 pages
...AC :: sin C : sin B. THEOREM II. In any triangle, the sum of the two sides containing eithei angk, is to their difference, as the tangent of half the sum of the two other angles, to the tangent of haJ/ their difference. 58. Let ACB be a triangle : then will AB+AC:... ## Pantology: Or, A Systematic Survey of Human Knowledge; Proposing a ...

Roswell Park - Best books - 1841 - 626 pages
...an oblique angled triangle, the sides are proportional to the sines of the opposite angles : also, the sum of any two sides is to their difference, as the tangent of the half sum of the two opposite angles, is to the tangent of their half difference : and finally,... 