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

Benjamin Peirce - Trigonometry - 1852 - 408 pages
...sine of the middle part is equal to the product of the tangents of the two adjacent parts. IL TJie sine of the middle part is equal to the product of the cosines of the two opposite parts. [B. p. 436.] Proof. To demonstrate the preceding rules, it is only necessary to compare all the equations...
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A Treatise on Plane and Spherical Trigonometry

William Chauvenet - 1852 - 268 pages
...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 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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An Elementary Treatise on Plane and Spherical Trigonometry: With Their ...

Benjamin Peirce - Trigonometry - 1852 - 382 pages
...parts ; and the other two parts are called the opposite parts. The two theorems are as follows. 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...
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Elements of Plane and Spherical Trigonometry: With Their Applications to ...

Elias Loomis - Trigonometry - 1855 - 192 pages
...part required may then be found by the following RULE OF NAPIER. (211.) The product of the radius and the sine of the middle part, is equal to the product of the tangents of the adjacent parts, or to the product of the cosines of the opposite parts. It will assist...
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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - Geometry - 1856 - 460 pages
...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 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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Plane and spherical trigonometry. [With] Solutions of problems

Henry William Jeans - 1858 - 106 pages
...selected is called the middle part. Eule A will apply to the former case, Eule B to the latter. RULE A. The sine of the middle part is equal to the product of the tangents of the two parts adjacent to it. EULE B. The sine of the middle part is equal to the product...
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Tables of Logarithms of Numbers and of Sines and Tangents for Every Ten ...

Elias Loomis - Logarithms - 1859 - 372 pages
...part required may then be found by the following RULE OF NAPIER. (211.) The product of the radius and the sine of the middle part, is equal to the product of the tangents of the adjacent parts, or to the product of the cosines of the opposite parts. It will assist...
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The Mathematical Monthly, Volume 1

John Daniel Runkle - Mathematics - 1859 - 478 pages
...RULES. BY TUI MAN HENRY 8AFFORD. IN the form in which they are usually given, the rules are — I. The sine of the middle part is equal to the product of tlie tangents of tJie adjacent parts. II. T/te sine of the middle part is equal to tJic product of...
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The Mathematical Monthly, Volume 2

1860 - 462 pages
...— RULE I. The sine of the middle pari 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. That the second of these rules may be deduced from the first has been...
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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - Geometry - 1860 - 470 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...
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