 | James Hodgson - Astronomy - 1723 - 724 pages
...t,¿z¿xct,í7<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... | |
 | Euclid, John Keill - Geometry - 1733 - 444 pages
...But 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... | |
 | Mathematics - 1801 - 658 pages
...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.... | |
 | 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... | |
 | Adrien Marie Legendre - Geometry - 1836 - 394 pages
...circular parts, as already defined. 1st. Radius into 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 rectangle of the cosines of the opposite parts. These rules are proved by assuming each of the five... | |
 | 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... | |
 | Benjamin Peirce - Spherical trigonometry - 1836 - 92 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. (475) II. The sine of the middle part is equal to the product of... | |
 | Thomas Kerigan - Nautical astronomy - 1838 - 804 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 conjunct. 2d. — Tlie product of radius and the sine of the middle part,... | |
 | 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... | |
 | Benjamin Peirce - Plane trigonometry - 1845 - 498 pages
...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... | |
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I. The sine of the middle part is equal to the product of the tangents of the adjacent parts. 
