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" I. The sine of the middle part is equal to the product of the tangents of the adjacent parts. "
First Part of an Elementary Treatise on Spherical Trigonometry - Page 8
by Benjamin Peirce - 1836 - 71 pages
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Surveying and Navigation, with a Preliminary Treatise on Trigonometry and ...

Aaron Schuyler - Measurement - 1864 - 506 pages
...OZi = OE= cos A = sin (90— A). . • . (5) sin (900— A) = tan (90— Б) tan (90— P). 2. The sine of the middle part is equal to the product of the cosines of the opposite parts. OE=cos EOD X OD, or cos A = cos b cos p. ... (6) sin (90— A) = cos b cos p. DB...
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Surveying and Navigation: With a Preliminary Treatise on Trigonometry and ...

Aaron Schuyler - Navigation - 1873 - 536 pages
...cosEODxOD=OE=coa h = sin (90— A). . • . (5) sin (90— A) = tan (90— B) tan (90— P). 2. Sine of the middle part is equal to the product of the co-sines of the opposite parts. = cos EOD X OD, or cos h = cos 6 cos p. ... (6) sin (90— A) = cos 6 cos p. DB=EB...
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Surveying and Navigation, with a Preliminary Treatise on Trigonometry and ...

Aaron Schuyler - Measurement - 1873 - 520 pages
...90— h, b. 9. 90— h, 90— P, b. 10. 90— P, 90— B, p. 126. Napier's Principles. 1. The sine of the middle part is equal to the product of the tangents of the adjacent parts. Draw BD and DE, respectively perpendicular to OH and OP, and draw BE....
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Plane and spherical trigonometry. [With] Solutions of problems. [Followed by ...

Henry William Jeans - 1873 - 288 pages
...selected is called the middle part. Eule A will apply to the former case, Eule B to the latter. EULE A. The sine of the middle part is equal to the product of the tangents of the two parts adjacent to it. * The complement of an angle is what it wants of 90 ; thus,...
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Surveying and Navigation, with a Preliminary Treatise on Trigonometry and ...

Aaron Schuyler - Measurement - 1864 - 506 pages
.../< = sin (90- A). . . . (5) sin (9<P— A) = tan (90— B) tan (90- P). 2. TVtf si.nf of </ie middle part is equal to the product of the co-sines of the opposite parts. OE=cos EOD X #>, or cos h — cos b cos p. .-. (6) sin (90— h) = cos 6 cos p....
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Plane and Spherical Trigonometry and Mensuration

Aaron Schuyler - Measurement - 1875 - 276 pages
...90— Л, b. 9. 90— A, 90'— P, b. 10. 90— P, 90— B, p. 126. Napier's Principles. 1. The sine of the middle part is equal to the product of the tangents of the adjacent parts. Draw BD and DE, respectively perpendicular to OH and OP, and draw BE....
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Key to Robinson's New Geometry and Trigonometry, and Conic Sections and ...

Horatio Nelson Robinson - 1875 - 288 pages
...will be two adjacent parts, and two opposite parts. Then we can easily remember, that 1st. Radius into the sine of the middle part, is equal to the product of the tangents of the adjacent parts. 2d. Radius into the sine of the middle part, is equal to the product...
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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Trigonometry - 1876 - 208 pages
...are called the opposite parts. Then, whatever be the middle part, we have as THE RULES OP 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...
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A New Treatise on Surveying and Navigation, Theoretical and Practical: With ...

Horatio Nelson Robinson - Navigation - 1878 - 564 pages
...that it corresponds to one of the following invariable and comprehensive rides. 1. The radius into the sine 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 io> the product...
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The Elements of Plane and Spherical Trigonometry

Eugene Lamb Richards - Trigonometry - 1879 - 232 pages
...adjacent parts are a, 90—b; opposite parts are c, 90— A. 115. Napier's rule of the Circular Parts. The sine of the middle part is equal to the product of the tangents of the adjacent parts; and the sine of the middle part is equal to the product of the cosines...
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