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" The rectangle of the radius, and sine of the middle part, is equal to the rectangle of the tangents of the two EXTREMES CONJUNCT, and to that of the cosines of the two EXTREMES DISJUNCT. "
Trigonometry, Plane and Spherical: With the Construction and Application of ... - Page 28
by Thomas Simpson - 1810 - 125 pages
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A Treatise on Plane and Spherical Trigonometry: Including the Construction ...

Enoch Lewis - Conic sections - 1844 - 240 pages
...two are termed the opposite extremes. Then Napier's rules are : 1. The rectangle of radius and the sine of the middle part is equal to the rectangle of the tangents of the adjacent extremes. 2. The rectangle of radius and the sine of the middle part is equal...
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Elements of Geometry and Trigonometry Translated from the French of A.M ...

Charles Davies - Trigonometry - 1849 - 384 pages
...A=90, we have sin B sin C cos a = R cos B cos C, or R cos a=cot B cot C; that is, radius into the sine of the middle part is equal to the rectangle of the tangent of the complement of B into the tangent of the complement of C, that is, to the rectangle of...
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A Treatise on Trigonometry, Plane and Spherical: With Its Application to ...

Charles William Hackley - Trigonometry - 1851 - 524 pages
...angled triangle may be expressed in the two following rules of Napier : 1. Radius multiplied by the sine of the middle part is equal to the rectangle of the tangents of the adjacent parts. 2. Radius multiplied by the sine of the middle part is equal to the...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1852 - 436 pages
...sin B sin 0 cos a — cos B cos G, or, cos a — cot B cot (7; that is, radius, which is 1, into the sine of the middle part is equal to the rectangle of the tangent of the complement of B, into the tangent of the complement of (7, that is, to the rectangle...
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The Writings of Thomas Jefferson: Correspondence, cont

Thomas Jefferson - United States - 1854 - 630 pages
...EXTREMES disjunct from the middle or EXTREMES DISJUNCT. He then laid down his catholic rule, to wit : " The rectangle of the radius, and sine of the middle part, is equal to the rectangle of the tangents of the two EXTREMES CONJUNCT, and to that of the cosines of the two EXTREMES DISJUNCT." And...
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The Writings of Thomas Jefferson: Correspondence, cont

Thomas Jefferson - United States - 1854 - 636 pages
...EXTREMES disjunct from the middle or EXTREMES DISJUNCT. He then kid down his catholic rule, to wit : " The rectangle of the radius, and sine of the middle part, is equal to the rectangle of the tangents of the two EXTREMES CONJUNCT, and to that of the cosines of the two EXTREMES DISJUNCT." And...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1854 - 436 pages
...which, it must be remembered, apply to the circular parts, as already defined. 1st. Radius inlo the sine of the middle part is equal to the rectangle of the tangents of the adjacent parts. 2d. Radius into the sine of the middle part is equal to the tidangle...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1872 - 464 pages
...= tan (90-a) tan b • ' • • (10.) Comparing these formulas with the figure, we see that, The sine of the middle part is equal to the rectangle of the tangents of the adjacent parts. These two rules are called Napier'a rales for Circular Parts, and they...
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Elements of Geometry and Trigonometry: From the Works of A.M. Legendre

Adrien Marie Legendre - Geometry - 1874 - 512 pages
...tan (90- a) tan 1> • • • • (10.) Comparing these formulas with the figure, wo seo that, The sine of the middle part is equal to the rectangle of the tangents of the adjacent parts. These two rules are called Napier's rules for Circular Parts, and they...
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Manual of Geometry and Conic Sections: With Applications to Trigonometry and ...

William Guy Peck - Conic sections - 1876 - 376 pages
...(10) Comparing these formulas with the diagram, we see that the following rule is always true: 2d. The sine of the middle part is equal to the rectangle of the tangents of the adjacent parts. Discussion. 48. In applying Napier's rules, the required part is always...
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