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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 ... - Σελίδα 25
των Thomas Simpson - 1810 - 125 σελίδες
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The British encyclopedia, or, Dictionary of arts and sciences, Τόμος 6

William Nicholson - 1809
...the tangent of half the difference of the same arches. In any spherical triangle A li С (fig. 27), it will be, as the cotangent of half the sum of the angle», at the base, is to tlie tañe ent of half their difference, »o ii tin- tangent of halt" the...

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

Thomas Keith - 1810 - 420 σελίδες
...Fig. to PROP, xxvi.) (H) In any spherical triangle, I. If the perpendicular fall within the triangle. The co-tangent of half the sum of the angles at the base, Is to tangent of half their difference ; As the tangent of half the •vertical angle, Is to the tangent...

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

Francis Nichols - 1811 - 128 σελίδες
...any spherical triangle, if a perpendicular arc be drawn from an 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...

British Encyclopedia: Or, Dictionary of Arts and Sciences ..., Τόμος 12

William Nicholson - 1821
...to the tangent of half the 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 case is to the tangent of half their difference, so is the tangent of half the vertical angle to the...

American Practical Navigator

1821
...difference 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....

The New Practical Builder and Workman's Companion, Containing a Full Display ...

Peter Nicholson - 1823 - 596 σελίδες
...TRIGONOMETRY. — 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 - 551 σελίδες
...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
...tang ECD, the same expression as when the perpendicular falls within the triangle. (Y) COROLLARY II. The co-tangent 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 tangent of half the difference between the two...

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...

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...




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