Search Images Maps Play YouTube News Gmail Drive More »
Sign in
Books Books
" In any triangle, the sum of the two sides containing either angle, is to their difference, as the tangent of half the sum of the two other angles, to the tangent of half their difference. "
Elements of Surveying - Page 25
by Charles Davies - 1830 - 300 pages
Full view - About this book

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

Jeremiah Day - Geometry - 1838 - 416 pages
...therefore, from the preceding proposition, (Alg. 389.) that the sum of any two sides of a triangle, is to their difference ; as the tangent of half the sum of the opposite angles, to the tangent of half their difference. This is the second theorem applied to the...
Full view - About this book

Elements of Trigonometry, Plane and Spherical: Adapted to the Present State ...

Charles William Hackley - Trigonometry - 1838 - 338 pages
...tan £ (A -f- B) : tan \ (A — B) That is to say, the sum of two of the sides of a plane triangle is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. This proportion is employed when two sides...
Full view - About this book

Elements of Surveying: With a Description of the Instruments and the ...

Charles Davies - Surveying - 1839 - 376 pages
...AB : 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:...
Full view - About this book

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

Jeremiah Day - Geometry - 1839 - 434 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...
Full view - About this book

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:...
Full view - About this book

An introduction to the theory ... of plane and spherical trigonometry ...

Thomas Keith - 1839 - 498 pages
...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...
Full view - About this book

Elements of Surveying, and Navigation: With a Description of the Instruments ...

Charles Davies - Navigation - 1841 - 414 pages
...AB : 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. 58. Let ACB be a triangle : then will AB+AC:...
Full view - About this book

Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1842 - 332 pages
...parallel to FG, CE : CF : : BE ; BG, (2. 6.) that is, the sum of the two sides of the triangle ABC is to their difference as the tangent of half the sum of the angles opposite to those sides to the tangent of half their difference. PROP. V. THEOR. If a perpendicular...
Full view - About this book

A Treatise on Plane and Spherical Trigonometry: Including the Construction ...

Enoch Lewis - Conic sections - 1844 - 240 pages
...to any radius whatever (Art. 27). QED ART. 30. In any right lined triangle, the sum of any two sides is, to their difference, as the tangent of half the sum of the angles, opposite to those sides, to the tangent of half their difference. Let ABC be the triangle;...
Full view - About this book

Key to System of practical mathematics. 2 pt. No.xvii

Scottish school-book assoc - 1845 - 278 pages
...6 tan. 4(A — B) opposite to the angles A and B, the expression proves, that the sum of the sides is to their difference, as the tangent of half the sum of the opposite angles is to the tangent of half their difference, which is the rule. (7.) Let (AD— DC)...
Full view - About this book




  1. My library
  2. Help
  3. Advanced Book Search
  4. Download EPUB
  5. Download PDF