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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

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 of the tangents of the adjacent parts. II. The sine of the middle part is equal to the product of the cosines...

An Elementary Treatise on Plane & Spherical Trigonometry: With Their ...

Benjamin Peirce - Trigonometry - 1861 - 396 pages
...— I. The sine of the middle part is equal to the product of the tangents of the two adjacent parts. II. The sine of the middle part is equal to the product of the manes of the two opposite parts. [B., p. 438.] Proof. To demonstrate the preceding rules, .it is only...

Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 532 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 results already...

Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 518 pages
...are called the opposite parts. Then, whatever be the middle part, we have as THE EULES OF 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...

Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1861 - 638 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...

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...

Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1863 - 504 pages
...are called the opposite parts. Then, whatever be the middle part, we have as THE RULES ov NAPIKR. 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...

Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - 1867 - 188 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 results already...

Treatise on Geometry and Trigonometry: For Colleges, Schools and Private ...

Eli Todd Tappan - Geometry - 1868 - 444 pages
...next to it are the adjacent parts, and the remaining two are the opposite parts. Napier's rule is : The sine of the middle part is equal to the product of the tangents of the adjacent parts, also to the product of the cosines of the opposite parts. The words...

Plane and Spherical Trigonometry, Part 1

Henry W. Jeans - 1873 - 272 pages
...substituted for cos. co. A ; cos. A for sin. co. A ; cot. A for tan. co. A, to. (See Part II.) KULE B. The sine of the middle part is equal to the product of the cosines of the two parts opposite to, or separated from it.* Having written down the equation according to the case, make...