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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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A System of the Mathematics: Containing the Euclidean Geometry ..., Volume 2

James Hodgson - Astronomy - 1723
...t,zxct,7<r— Axes, bac; that is the Radius multiplied into the Sine of the Complement of the Angle a or Sine of the Middle Part, is equal to the Product of the Tangent of ab one of the Extreams, into the Tangent of the Complement of л с the other Extream. By...
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Euclid's Elements of Geometry,: From the Latin Translation of Commandine. To ...

Euclid, John Keill - Geometry - 1733 - 397 pages
...S, CF=Cof. BC and T, DF = Cot. B. Wherefore R x Cof. BC=Cot. Cx Cot. B ; that is, Radius drawn into the Sine of the. middle Part, is equal to the Product of the Tangents of the adjacent extreme Parts. : X And And BA, AC, are the oppofite Extremes to the faid middle...
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Mathematics: Compiled from the Best Authors and Intended to be the ..., Volume 2

Mathematics - 1801
...solutions of all the cases of right-angled spherical triangles. THEOREM VII. The product of radius and the sine of the middle part is equal to the product of the tangents of the conjunct extremes, or to that of the cosines of the disjunct extremes.* NOTE. * DEMONSTRATION....
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The Complete Mathematical and General Navigation Tables: Including ..., Volume 1

Thomas Kerigan - Nautical astronomy - 1828 - 776 pages
...parts are to be computed by the two following equations ; viz., 1st. — The product of radius and the sine of the middle part, is equal to the product of the tangents of the extremes conjunct2d. — The product of radius and the sine of the middle part, is...
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First Part of an Elementary Treatise on Spherical Trigonometry

Benjamin Peirce - Spherical trigonometry - 1836 - 84 pages
...; and the other two parts are called the opposite parts. The two theorems are as follows. (474) I. The sine of the middle part is equal to the product of the tangents of the two adjacent parts. (47e) II. The sine of the middle part is equal to the product of...
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The Complete Mathematical and General Navigation Tables: Including Every ...

Thomas Kerigan - Nautical astronomy - 1838
...parts are to be computed by the two following equations ; viz., 1st. — The product of radius and the sine of the middle part, is equal to the product of the tangents of the extremes conjunct. 2d. — Tlie product of radius and the sine of the middle part,...
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Plane and Spherical Trigonometry ...

Henry W. Jeans - Trigonometry - 1842 - 138 pages
...= cos- P/=cos. co. A. CP C/P/ PN P/N, tan. A = — = = cot. P,= cot. co. A Are. CN C,N, Gl RULE I. The sine of the middle part is equal to the product of the tangents of the two parts adjacent to it. RULE II. The sine of the middle part is equal to the product...
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An Elementary Treatise on Plane & Spherical Trigonometry: With Their ...

Benjamin Peirce - Plane trigonometry - 1845 - 449 pages
...the middle part is equal to Ike product of the tangents of the two adjacent parts. Napier's Rules. II. The 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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An Elementary Treatise on Plane & Spherical Trigonometry: With Their ...

Benjamin Peirce - Plane trigonometry - 1845 - 498 pages
...the other two parts are called the opposite parts. The two theorems are as follows. Napier's Rules. II. The 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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The Elements of Spherical Trigonometry

James Hann - Spherical trigonometry - 1849 - 84 pages
...two are called extremes disjunct*. These things being understood, the following is the general rule. The sine of the middle part is equal to the product of the tangents of the extremes conjunct. * Thus, if in figure page 12 we suppose В С, the angle B, and...
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