Search Images Maps Play YouTube News Gmail Drive More »
Sign in
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. "
Elements of Geometry and Trigonometry - Page 241
by Adrien Marie Legendre - 1837 - 359 pages
Full view - About this book

A Concise System of Mathematics ...

Alexander Ingram - Mathematics - 1830 - 458 pages
...sura. PROP. XXXIX. In any triangle ABC, of which the sides are unequal, the sum of the sides AC + AB is to their difference as the tangent of half the sum of the opposite angles B and C, to the tangent of half their difference. CA + AB : CA — AB : : tan. £ (B...
Full view - About this book

Elements of Surveying

Charles Davies - Surveying - 1830 - 390 pages
...should obtain, THEOREM. 44. In any plane triangle, the sum of tfte two sides containing either angle, is to their difference, as the tangent of half the sum of the other two angles, to the tangent of half their difference. Let ABC (PI. I. Fig. 3) be a triangle ;...
Full view - About this book

The Principles of Plane Trigonometry, Mensuration, Navigation and Surveying

Jeremiah Day - Measurement - 1831 - 520 pages
...equal to the sum, and FH to the difference of AC and AB. And by theorem II, (Art. 144.) the sum of the sides is to their difference; as the tangent of half the sum of the opposite angles, to the tangent <if half their difference. Therefore, R :tan(ACH-45°)::tan|(ACB +...
Full view - About this book

The Principles of Plane Trigonometry, Mensuration, Navigation and Surveying ...

Jeremiah Day - Measurement - 1831 - 394 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 Plane and Spherical Trigonometry: With Its Applications to the ...

John Radford Young - Astronomy - 1833 - 308 pages
...tan. i (A + B) a — b ~ "tan. i ( A — B j ' that is to say., in any plane triangle the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. By help of this rule we may determine the...
Full view - About this book

The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1834 - 518 pages
...given, the fourth is also given. PROPOSITION III. In a plane triangle, the sum of any two sides in to their difference, as the tangent of half the sum of the angle at Ihe base, to the tangent of half their difference. PROPOSITIONS III. IV. of the angles at...
Full view - About this book

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 540 pages
...half the difference, and it will give the less. PROP. III. FIG. 8. In a plane triangle, the sum of any two sides is to their difference, as the tangent of half the sum of the angles at the base, to the tangent of half their difference. Let ABC be a plane triangle, the sum of any two...
Full view - About this book

The Elements of Euclid: viz. the first six books, together with the eleventh ...

Robert Simson - Trigonometry - 1835 - 544 pages
...difference; and since BC, FGare parallel, (2. 6.) EC is to CF, as EB to BG; that is, the sum of the fides is to their difference, as the tangent of half the sum of the angles at the base to the tangent of half their difference. * PROP. IV. F1G. 8. In a plane triangle, the cosine...
Full view - About this book

The Element of Geometry

John Playfair - Geometry - 1836 - 148 pages
...triangle, any three being given, the fourth is also given. PROP. III. i In a plane triangle, the sum of any two sides is to their difference, as the tangent of half the sum of the angles at the base, to the tangent of half their difference. Let ABC be a plane triangle, the sum of any two...
Full view - About this book

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

John Playfair - Euclid's Elements - 1836 - 488 pages
...• . i . ..; . i. .• i » »i :*• <••! The sum of any two sides of a triangle is to theif difference, as the tangent of half the sum, of the angles opposite to those sides, to the tawgent of half their difference. '' •• i• . . .• ' * " i •' ' •...
Full view - About this book




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