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" The cotangent of half the sum of the angles at the base, Is to the tangent of half their difference... "
Trigonometry, Plane and Spherical: With the Construction and Application of ... - Page 25
by Thomas Simpson - 1810 - 125 pages
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An introduction to the theory ... of plane and spherical trigonometry ...

Thomas Keith - 1839 - 498 pages
...to PROP, xxvi.) (413) In any spherical triangle, I. If the perpendicular fall within the triangle : The cotangent of half the sum of the angles at the base, Is to the tangent of half their difference, As the tangent of half the vertical angle, Is to tJie tangent of the excess of the greater of the two...
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A system of practical mathematics; being no.xvi. of a new series of school-books

Scottish school-book assoc - 1845 - 434 pages
...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...
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Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ...

Dennis M'Curdy - Geometry - 1846 - 166 pages
...the base EC : CF : : EB : BG; that is, 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. Tharefore, in any triangle, &o. QED . 5 Th. The base of a triangle is to the sum of both the sides,...
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The New American Practical Navigator; Being an Epitome of Navigation ...

Nathaniel Bowditch - 1846 - 864 pages
...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...
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A Treatise on Astronomy, Descriptive, Physical, and Practical: Designed for ...

Horatio Nelson Robinson - Astronomy - 1850 - 370 pages
...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....
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Mathematical Recreations: Containing Solutions of Many Very Difficult and ...

Horatio Nelson Robinson - Mathematics - 1851 - 96 pages
...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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Report of twenty-one years' experience of the Dick bequest for elevating the ...

Allan Menzies - 1854 - 520 pages
...then rule is, — Sum of the two sides (containing given angle) 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 ; half the sum = ^ (180 — angle C), then having found the half sum, J sum + diff. = greater angle,...
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Practical carpentry, joinery, and cabinet-making [by P. Nicholson. by P ...

Peter Nicholson - Cabinetwork - 1856 - 482 pages
...TRIGONOMETRY. — THEOREM 2. 151. 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. Let ABC be a triangle 4 then, of the two sides, CA and CB, let CB be the greater. Produce CA to E,...
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Examination papers used at the examinations for direct commissions [&c.].

War office - 1861 - 714 pages
...one side the base, prove that the sum of the other 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. 6. Observers on two ships a mile apart find the angles subtended by the other ship and a fort are respect...
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