 | James Hodgson - Astronomy - 1723
...the Angle с the other Extream ; wherefore, &c, as was to be proved. Rule i. The Rectangle under the Radius and the Sine of the Middle Part, is equal to the Produft of the Co-fines of the Extreams Disjunct, thus if the Complement of ac be taken for the Middle... | |
 | John Keill - Trigonometry - 1733 - 448 pages
...Part. Thefe Things premifed. RULE I. In any right-angled fpherical Triangle, the ReBangle under the Radius, and the Sine of the middle Part, is equal to the Reftangle under the Iangents of the adjacent Parts, RULE RULE II. Ibe ReEf angle under the Radius,... | |
 | John Keill - Geometry - 1782 - 399 pages
...Part. Thcfc Things premifed, RULE I. In any Right-angled Spherical Triangle, the Re£langle under the Radius, and the Sine of the middle Part, is equal to the ReSlangle under the Tangents of the adjactnt Parts. RULE \ RULE II. Reffangle under the Radius, and... | |
 | Mathematics - 1801 - 658 pages
...sufficient for the 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.*... | |
 | Robert Simson - Trigonometry - 1806 - 518 pages
...rectangle contained by the tangents o' the adjacent parts. RULE IT. The rectangle contained by the radius, and the sine of the middle part is equal to the rectangle contained by the co-sines of the opposite parts. These rules are demonstrated in the following manner:... | |
 | Samuel Webber - Mathematics - 1808 - 522 pages
...sufficient for the solutions of all the cases of right.angled spheric triangles. THEOREM VII. . The product of radius and the sine of the middle part is equal to tht- product of the tangents* of the adjacent extremes, or to that of the cosines of the apposite extremes.f... | |
 | Euclid - Geometry - 1810 - 518 pages
...angled spherical triangles are resolved with the greatest ease. RULE I. The rectangle contained by the radius and the sine of the middle part, is equal to the rectwpgle contained by the tangents of the adjaeent parts. '/ RULE II. The rectangle contained by the... | |
 | Francis Nichols - Plane trigonometry - 1811 - 128 pages
...in the following proposition. 100. In a right-angled spherical triangle, the rectan* gle under the radius and the sine of the middle part is equal to the rectangle under the tangents of the adjacent parts, or to the rectangle under the cosines of the opposite parts.... | |
 | Euclides - 1816 - 528 pages
...angled spherics! triangles are resolved with the greatest ease. RULE I. The rectangle contained by the radius and the sine of the middle part, is equal to the rectangle contained by the tangents of the adjacent parts. RULE II. The rectangle contained by the radius and... | |
 | John Playfair - 1819 - 317 pages
...in the following PROPOSITION. In a right angled spherical triangle, iht rectangle under the radivs and the sine of the middle part, is equal to the rectangle under the tangents of the adjacent parts ; or to the rectangle under the cosines of the opposite parts.... | |
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In a right angled spherical triangle, the rectangle under the radius and the sine of the middle part, is equal to the rectangle under the tangents of the adjacent parts ; or', to the rectangle under the cosines of the opposite parts. 
