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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

Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Trigonometry - 1876 - 208 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...

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 of the cosines...

The Civil-engineer & Surveyor's Manual

Michael McDermott - Civil engineering - 1879 - 540 pages
...angle. We will arrange Napier's rules as follows, where co. = complement of the angles or hypothenuse. Sine of the middle part, Is equal to the product of the tangents of the adjacent parts. Is equal to the product of the cosines of the opposite parts. Sine comp. A. Sin. comp....

The Elements of Plane and Spherical Trigonometry

Eugene Lamb Richards - Trigonometry - 1879 - 232 pages
...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 of the opposite parts. Let ABC be a spherical triangle right-angled at B. We shall take each...

Plane and Spherical Trigonometry

George Albert Wentworth - Trigonometry - 1882 - 162 pages
...parts immediately adjacent are called adjacent parts, and the other two are called opposite parts. Rule I. The sine of the middle part is equal to the product of the tangents of the aAjacent parts. Rule II. The sine of the middle part is equal to the product of the cosines of the...

Plane and Spherical Trigonometry

George Albert Wentworth - Trigonometry - 1882 - 234 pages
...parts immediately adjacent are called adjacent parts, and the other two are called opposite parts. Eule I. The sine of the middle part is equal to the product of the tsngents of the aAjacent parts. Eule II. The sine of the middle part is equal to the product of the...

Plane and Spherical Trigonometry: G. A. Wentworth ...

George Albert Wentworth - Trigonometry - 1884 - 328 pages
...parts immediately adjacent are called adjacent parts, and the other two are called opposite parts. Rule I. The sine of the middle part is equal to the product of the \asigents of the aAjacent parts. Rule II. The sine of the middle part is equal to the product of the...

Five-place Logarithmic and Trigonometric Tables

George Albert Wentworth - 1887 - 346 pages
...The sine of the middle part is equal to the product of the tangents of the adjacent parts. Rule II. The sine of the middle part is equal to the product of the famines, of the opposite parts. These Rules are easily remembered by the expressions, tan. ad. and...

The Essentials of Plane and Spherical Trigonometry

Webster Wells - Trigonometry - 1887 - 202 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. 146. Napier's rules may be proved by taking each of the circular parts...

Thomas Marcus Blakslee - Trigonometry - 1888 - 56 pages
...the complements of the opposite angles, and the complement of the hypotenuse. His rules are : RULE I. The sine of the middle part is equal to the product of the tangents of the adjacent parts. By (1) (6) sin a = sin A sin h = tan 6 cot B sin b — sin B sin A = tan a cot A cos...