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Llibres Llibres 41 - 50 de 193 sobre C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides....
" C' (89) (90) (91) (92) (93) 112. 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. "
A Treatise of Plane Trigonometry: To which is Prefixed, a Summary View of ... - Pāgina 66
per Jeremiah Day - 1815 - 126 pāgines
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A concise system of mathematics

Alexander Ingram - 1830
...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. Ŗ (B...
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The Principles of Plane Trigonometry, Mensuration, Navigation and Surveying

Jeremiah Day - 1831 - 370 pāgines
...if the sines be adapted to any other radius. (Art. 1 19.) THEOREM II. 144. In a plane triangle, AS THE SUM OF ANY TWO OF THE SIDES, To THEIR DIFFERENCE...sides AB and AC. On AB set off AD equal to AC ; then DB it the difference of the sides AB and AC. The sum of the two angles ACB and ABC, is equal to the...
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The Principles of Plane Trigonometry, Mensuration, Navigation and Surveying

Jeremiah Day - 1831 - 370 pāgines
...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...
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Elements of Plane and Spherical Trigonometry: With Its Applications to the ...

John Radford Young - 1833 - 264 pāgines
...4 tan. a — 4 ~~ tan. J(A — B) ' 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...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1834
...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...
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The Elements of Euclid: viz. the first six books, together with the eleventh ...

Euclid, Robert Simson - 1835 - 513 pāgines
...difference ; and since BC, FG are parallel, (2. 6.) EC is to CF, as EB to BG; that is, the sum of the 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. * PROP. IV. FIG. 8. In a plane triangle, the cosine...
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The Principles of Plane Trigonometry, Mensuration, Navigation and Surveying ...

Jeremiah Day - 1836
...TWO OF THE SIDES, To THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES j To THE TANGENT OF HALF THEIR DIFFERENCE. Thus the...sides AB and AC. On AB set off AD equal to AC ; then DB is the difference of the sides AB and AC. < The sum of the two angles ACB and ABC, is equal to the...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - 1836 - 359 pāgines
...c=2p — 2c, a+c — 6=2p — 26; hence THEOREM V. In every rectilineal triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides, to the tangent of half their difference. For. AB : BC : : sin C : sin A (Theorem...
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The Element of Geometry

John Playfair - 1836 - 114 pāgines
...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...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid - 1837 - 390 pāgines
...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, a, b any...
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