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" II. The sine of the middle part is equal to the product of the cosines of the opposite parts. "
First Part of an Elementary Treatise on Spherical Trigonometry - Page 8
by Benjamin Peirce - 1836 - 71 pages
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The Mathematical Monthly, Volume 2

John Daniel Runkle - Mathematics - 1860 - 590 pages
...RULE I. The sine of the middle part equals the product of the cosines of the opposite parts, RULE II. The sine of the middle part is equal to the product of the tangents of the adjacent parts. It must be remembered that, instead of the hypothenuse and the two acute angles, their...
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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - Geometry - 1860 - 443 pages
...RULES. I. The sine of the middle part is equal to the product of the tangents of the adjacent parts. II. The sine of the middle part is equal to the product of the cosines of the opposite parts. If now we take in turn each of the five parts as the middle part, and...
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Elements of Geometry, and Plane and Spherical Trigonometry: With Numerous ...

Horatio Nelson Robinson - Geometry - 1860 - 453 pages
...of the middle part is equal to the product of the tangents of the adjacent parts. 2. The radius into the sine of the middle part is equal to the product of the cosines of the opposite parts. These rules are known as .Napier's Rules, because they were first given...
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Lessons on plane trigonometry

Edward Butler (A.M.) - 1862
...in the following rule, which is called Napier's Rule of circular parts :— The sine of a circular part is equal to the product of the tangents of the two adjacent circular- parts, or to the product of the cosines of the opposite circular parts. Suppose a and b given,...
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Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 520 pages
...NAPIER. I. The sine of the middle part is equal to the product of the tangents of the adjacent parts. II. The sine of the middle part is equal to the product of the cosines of the opposite parts. 168. Napier's rules may be proved by showing that they agree with the...
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Elements of Plane and Spherical Trigonometry: With Their Applications to ...

Elias Loomis - Plane trigonometry - 1862 - 202 pages
...required may then be found by the following i RULE OF NAPIER. (211.) The product of the radius and the sine of the middle part, is equal to the product of the t&ngents of the adjacent parts, or to the product of the cosines of the opposite parts. It will assist...
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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 514 pages
...NAPIER. I. The sine of the middle part is equal to Hie product of tlte tangents of the adjacent parts. IL The sine of the middle part is equal to the product of the cosines of the opposite parts. 168. Napier's rules may be proved by showing that they agree with the...
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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1861 - 628 pages
...NAPIER. I. The sine of the middle part is equal to the product of the tangents of the adjacent parts. II. The sine of the middle part is equal to the product of tJie cosines of the opposite parts. 168. Napier's rules may be proved by showing that they agree with...
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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1863 - 320 pages
...I. The sine of the middle part is equal to the product of the tangents of the adjacent parts. . II. The sine of the middle part is equal to the product of the cosines of the opposite parts. 168. Napier's rules may be proved by showing that they agree with the...
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A Treatise on Plane and Spherical Trigonometry

William Chauvenet - Trigonometry - 1924 - 268 pages
...angle not being considered, the two sides including it are regarded as adjacent parts. The rules are : I. The sine of the middle part is equal to the product of the tangente of the adjacent parts. II. The sine of the middle part is equal to the product of the cosines...
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