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Βιβλία Βιβλία 11 - 20 από 22 για The sum of the two sides of a triangle is to their difference as the tangent of half....
" The sum of the two sides of a triangle is to their difference as the tangent of half the sum of the angles at the base is to the tangent of half their difference. "
An Introduction to the Theory and Practice of Plane and Spherical ... - Σελίδα 199
των Thomas Keith - 1810 - 420 σελίδες
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The New American Practical Navigator: Being an Epitome of Navigation ...

Nathaniel Bowditch - 1826 - 617 σελίδες
...difference of the same angles, (to the same radius,) and therefore (by art. 55) as the tabular tangent of half the sum of the angles at the base is to the tabular tangent of half the difference of the same angles. t In any plane triangle ABC, if the line...

The New American Practical Navigator: Being an Epitome of Navigation ...

Nathaniel Bowditch - 1826 - 617 σελίδες
...difference of the same angles, (to the same radius,) and therefore (by art. 55) as the tabular tangent of half the sum of the angles at the base is to the tabular tangent of half the difference of the same angles. ьх. In any plane triangle ABC, if the...

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

Thomas Keith - 1839
...III. (483) When the three angles are given, to find the sides. The cotangent of half the sum of die angles at the base, Is to the tangent of half their difference, As die tangent of half the vertical angle, Is to the tangent of die excess of die greater of the two vertical...

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

Enoch Lewis - 1844 - 228 σελίδες
...vertex on the base, and an arc described bisecting the vertical angle ; it will be, as the cotangent of half the sum of the angles at the base is to the tangent of half their difference, so is the tangent of half the vertical angle to the tangent of the angle formed by the perpendicular...

A system of practical mathematics; being no.xvi. of a new series of school-books

1845
...difference of the segments of the base made by a perpendicular upon it from the vertex, as the cosine of half the sum of the angles at the base, is to the cosine of half their difference. Also, that the sum of the sides, is to the lifference of the segments...

Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ...

Dennis M'Curdy - 1846 - 138 σελίδες
...i(AC— AB). QED 4 Th. In any triangle, the sum of two sides is to their difference, as the tangent of half the sum of the angles at the base is to the tangent of half their difference. Given the triangle ABC, the side AB being greater than AC; AB+AC : AB— AC : : tan. J(ACB+ABC) : tan....

The New American Practical Navigator; Being an Epitome of Navigation ...

Nathaniel Bowditch - 1846 - 451 σελίδες
...difference of the same angles (to the same radius) ; and therefore (by Art. 55) as the tabular tangent of half the sum of the angles at the base is to the tabular tangent of half the difference of the same angles. LX. In any plane triangle, ABC, if the line...

An Elementary Treatise of Spherical Geometry and Trigonometry

Anthony Dumond Stanley - 1848 - 122 σελίδες
...tanj(A + B) tanj(a + ft). that is, The tangent of half the sum of any two sides of a spherical triangle is to the tangent of half their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. 38. In the following articles...

A TREATISE OF ASTRONOMY, DESCRIPTIVE, PHYSICAL, AND PRACTICAL DESIGNED FOR ...

H.N. ROBINSON - 1850
...45°, and call the difference «. Lastly, radius is to the tangent, «, as the tangent of the half sum of the angles at the base is to the tangent of half their difference. III. Resolution of right-angled spherical triangles. side, #.a given angle, and x the quantity sought....

MATHEMATICAL RECREATIONS: CONTAINIG SOLUTIONS OF MANY VERY DIFFUCULT AND ...

H.N. ROBINSON - 1851
...theorem : In any plane triangle, the sum of the sides is to their difference., as the tangent of the half sum of the angles at the base, is to the tangent of half their difference. This theorem is demonstrated in some form in every treatise on trigonometry. 5. Give a geometrical...




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