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" In a right angled spherical triangle, the rectangle under the radius and the sine of the middle part, is equal to the rectangle under the tangents of the adjacent parts ; or', to the rectangle under the cosines of the opposite parts. "
Trigonometry, Plane and Spherical: With the Construction and Application of ... - Page 28
by Thomas Simpson - 1810 - 125 pages
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Tables of Logarithms of Numbers and of Sines and Tangents for Every Ten ...

Elias Loomis - Logarithms - 1859 - 372 pages
...value of the part required may then be found by the following RULE OF NAPIER. (211.) The product of the radius and the sine of the middle part, is equal to the product of the tangents of the adjacent parts, or to the product of the cosines of the opposite parts....
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies, Adrien Marie Legendre - Geometry - 1869 - 472 pages
...-C) = cose cos (90 -2?) • • • • (5.) Comparing these formulas with the figure, we see that, The sine of the middle part is equal to the rectangle of cosines of the opposite parts. Formulas (8), (7), (4), (6), and (3), of Art. 72. may bo written as...
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A Treatise on Plane and Spherical Trigonometry

Enoch Lewis - 1872 - 238 pages
...extremes; and the other two are termed the opposite extremes. Then Napier's rules are: 1. The^rectangle of radius and the sine of the middle part is equal to the rectangle of the tangents of the adjacent extremes. part is equal to the rectangle of the cosines of the opposite extremes....
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1872 - 464 pages
...C) = tan (90-a) tan b • ' • • (10.) Comparing these formulas with the figure, we see that, The sine of the middle part is equal to the rectangle of the tangents of the adjacent parts. These two rules are called Napier'a rales for Circular Parts, and they...
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Tables for travellers

Charles Ramsay Drinkwater Bethune - 1872 - 102 pages
...if only two are adjacent, they are extremes, and the opposite part is the middle part. The product of Radius and the Sine of the middle part is equal to the products of the tangents of the adjacent extremes, or of the cosines of the opposite extremes : (tan....
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Elements of Geometry and Trigonometry: From the Works of A.M. Legendre

Adrien Marie Legendre - Geometry - 1874 - 512 pages
...cos c cos (90— 2?) • • • • (5.) Comparing tLese formulas with the figure, we see that. The sine of the middle part is equal to the rectangle of Ike cosines of the opposite parts. Let us now take the same middle parts, and the other parts adjacent....
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Manual of Geometry and Conic Sections: With Applications to Trigonometry and ...

William Guy Peck - Conic sections - 1876 - 376 pages
...(5) Comparing these formulas with the diagram, we see that the following rule is always true : 1st. The sine of the middle part is equal to the rectangle of the cosine of the opposite parts. 2. From formulas (7), (6), (8), (10), and (9), of Art. 46, we have,...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...sin (90 - C) = cose cos (90 - B). .... (5.) Comparing these formulas with the figure, we see that The sine of the middle part is equal to the rectangle of the cosines of the opposite parts. Let us now take the same middle parts, and the other parts adjacent....
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