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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. "
Trigonometry, Plane and Spherical: With the Construction and Application of ... - Página 28
por Thomas Simpson - 1810 - 125 páginas
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A System of the Mathematics: Containing the Euclidean Geometry ..., Volumen2

James Hodgson - 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...
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Euclid's Elements of Geometry: From the Latin Translation of Commandine. To ...

John Keill - 1733 - 397 páginas
...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,...
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Euclid's Elements of Geometry: From the Latin Translation of Commandine, to ...

John Keill - 1782 - 399 páginas
...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...
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Mathematics: Compiled from the Best Authors and Intended to be the ..., Volumen2

1801 - 426 páginas
...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.*...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1806 - 518 páginas
...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:...
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Mathematics: Compiled from the Best Authors, and Intended to be ..., Volumen2

Samuel Webber - 1808
...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...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1810 - 518 páginas
...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...
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A Treatise of Plane and Spherical Trigonometry: In Theory and Practice ...

Francis Nichols - 1811 - 128 páginas
...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....
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 528 páginas
...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...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 317 páginas
...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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