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" 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. "
Elements of Plane and Spherical Trigonometry: With Practical Applications - Page 85
by Benjamin Greenleaf - 1867 - 170 pages
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A Treatise on Plane and Spherical Trigonometry

William Chauvenet - 1852 - 268 pages
...right angle not being considered, the two sides including it are regarded as adjacent. The rules are : I. The sine of the middle part is equal to the product...the product of the cosines of the opposite parts. The correctness of these rules will be shown by taking each of the five parts as middle part, and comparing...
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Mathematical Dictionary and Cyclopedia of Mathematical Science: Comprising ...

Charles Davies, William Guy Peck - Mathematics - 1855 - 628 pages
...middle pari is equal to the products of the tangents of the adjacent parís. 2. The tine of the muidle part is equal to the -product of the cosines of the opposite part* : thus, sin (90° - «) = tan (90° - B) tan (90° - C), and sin (90° — it) = cos e cos 4....
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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - Geometry - 1856 - 460 pages
...and which are opposite, when either of the five parts is chosen as the middle part. NAPIER'S RULES, I. The sine of the middle part is equal to the product...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 apply these Eules, we shall obtain...
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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - Geometry - 1860 - 472 pages
...opposite, when either of the five parts is chosen as the middle part. 90°-B 90° -T NAPIER'S RULES. I. The sine of the middle part is equal to the product...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 apply these Rules, we shall obtain...
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Elements of Geometry, and Plane and Spherical Trigonometry: With Numerous ...

Horatio Nelson Robinson - Geometry - 1860 - 470 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 by that distinguished mathematician,...
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A Treatise on Plane and Spherical Trigonometry

William Chauvenet - Trigonometry - 1863 - 272 pages
...»in» of the middle part и equal to the product of the tangents of the adjacent parte. II. The »ine of the middle part is equal to the product of the cosines of the opposite parts. The correctness of these rules will be shown by taking each of the five parts as middle part, and comparing...
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A Treatise on Plane and Spherical Trigonometry

William Chauvenet - Trigonometry - 1924 - 268 pages
...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...the product of the cosines of the opposite parts. The correctness of these rules will be shown by taking each of the fife parts as middle part, and comparing...
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Elements of Plane and Solid Geometry: And of Plane and Spherical ...

Gerardus Beekman Docharty - Geometry - 1867 - 474 pages
...to the product of the tangents of the adjacent parts. . 2. The product of sin. M and tabular radius is equal to the product of the cosines of the opposite parts. In order to make these rules clearly understood, we will show the manner in which they are applied...
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Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - 1869 - 516 pages
...two parts are called the opposite parts. Then, whatever be the middle part, we have as THE RULES OF NAPIER. -I. The sine of the middle part is equal to...results already established, Art. 165. Thus, 1. Let 6 be taken for the middle part ; then p and the complement of A will be the adjacent parts, and the...
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A Treatise on Plane and Spherical Trigonometry

William Chauvenet - Trigonometry - 1871 - 268 pages
...considered, the two sides including it are regarded as adjacent parts. The rules are : I. The tine of the middle part is equal to the product of the...the product of the cosines of the opposite parts. The correctness of these rules will be shown by taking each of the five parts aa middle part, and comparing...
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