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Βιβλία Βιβλία 1 - 10 από 21 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 Elements of Euclid: In which the Propositions are Demonstrated in a New ...

Euclid - 1776 - 264 σελίδες
...PROP. XXIH. TN every* fpherical triangle, the cotangent of half thefum of the * angles at the bafe, is to the tangent of half their difference ; as the tangent of half the vertical angle to the tangent of the angle that the perpendicular makes tuith the line bifecling the vertical angle....

Trigonometry, Plane and Spherical: With the Construction and Application of ...

Thomas Simpson - 1810 - 125 σελίδες
...of half £ THEOREM VII. In any spherical triangle, ABC (fig. 16.), it -will be, as the co-tangent 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 which the perpendicular CD...

Asiatick Researches: Or, Transactions of the Society Instituted in ..., Τόμος 10

Asiatick Society (Calcutta, India) - 1811
...Yerracondah, and the observed angles PSY and PYS, we have, the tangent of half the sum of the first, to the tangent of half their difference, as the tangent of half the sum of the second, to tangent of 2° 54' 25"-9^i their half difference : from which we get the greater...

A Treatise of Plane and Spherical Trigonometry: In Theory and Practice ...

Francis Nichols - 1811 - 128 σελίδες
...angle to the opposite side, or base, the cotangent of half the sum of the angles at the base will be to the tangent of half their difference, as the tangent of half the sum of the segments of the vertical angle is to the tangent of half their difference; that is, cot....

American Edition of the British Encyclopedia: Or, Dictionary of ..., Τόμος 12

William Nicholson - 1821
...difference of the same arches. In any spherical triangle, ABC (fig. 27,) it will be, as the co-tangent 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 which the perpendicular CD...

American Practical Navigator

1821
...of the same angles, (to the same radius,) and therefore (by art. :<:».) 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. I ed in it M : ABC, if the Hoe CD be....

Euclid's Elements of Geometry: The Six First Books. To which are Added ...

Rev. John Allen - 1822 - 494 σελίδες
...substituting the latter ratios for the former, the cotangent of the hull' sum of t!ie angles A and ABC is to the tangent of half their difference, as the tangent of the half sum of the angles ACD and BCD is to the tangent of half their difference; and, forming rectangles...

The new practical builder, and workman's companion, Τόμος 2

Peter Nicholson - 1823
...— THEOREM 2. 234. 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 ; then, of the two sides, CA and CB, let CB be the greater. Produce CA to E,...

A treatise on navigation, and nautical astronomy

Edward Riddle - 1824
...radius is to the tangent of the difference between this angle and half a right angle, as the tangent of half the sum of the angles at the base is to the tiuigcnt of half their difference. ELEMENTARY PRINCIPLES OP SPHERICAL TRIGONOMETRY. 1. A SPHERE is...

An Introduction to the Theory and Practice of Plain and Spherical ...

Thomas Keith - 1826 - 442 σελίδες
...the proper rules. RULE III. (X) When the three angles are given, to find the sides. The co-tangent of half the sum of the angles at the base, Is to the...half their difference; As the tangent of half the verticle angle, Is to the tangent of the excess of the greater of the two vertical angles (formed by...




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