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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 ... - Página 28
por Thomas Simpson - 1810 - 125 páginas
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ELEMENTS OF PLANE AND SPHERICAL TRIGONOMETRY

ELIAS LOOMIS, LL.D. - 1859
...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

Adrien Marie Legendre - 1869 - 455 páginas
...-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
...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 - 1872 - 455 páginas
...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
...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 - 1874 - 455 páginas
...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 - 1876 - 366 páginas
...(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 - 1885 - 512 páginas
...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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