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" The last statement involves the assertion that the three angles of a spherical triangle determine the sides, whereas we are accustomed to say in Plane Trigonometry, that, at least one given part of a plane triangle must be a side, in order that the triangle... "
Elements of Trigonometry: Plane and Spherical - Page 72
by Edward Olney - 1885 - 201 pages
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The Modern Preceptor ; Or, a General Course of Education, Volume 2

John Dougall - 1810 - 660 pages
...side common to both. The other skies may therefore readily be found by employing the proportion that the sides are to each other as the sines of the angles opposite to each respectively ; and the manner of performing the whole problem may be seen in Example 5th of...
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Encyclopędia Americana: A Popular Dictionary of Arts, Sciences ..., Volume 11

Francis Lieber, Edward Wigglesworth, Thomas Gamaliel Bradford, Henry Vethake - Encyclopedias and dictionaries - 1832 - 616 pages
...are to each other as the sines of the opposite angles; in spherical triangles, however, the sines of the sides are to each other as the sines of the angles opposite to these sides. Hence tt appears how important the sine is for finding certain parts of triangles,...
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Encyclopędia Americana: A Popular Dictionary of Arts, Sciences ..., Volume 11

Francis Lieber, Edward Wigglesworth - Encyclopedias and dictionaries - 1835 - 624 pages
...are to each other as the sines of the opposite angles ; in spherical triangles, however, the sines of the sides are to each other as the sines of the angles opposite to these sides. Hence it appear) how important the sine is for finding certain parts of triangles,...
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A Series on Elementary and Higher Geometry, Trigonometry, and Mensuration ...

Nathan Scholfield - Conic sections - 1845 - 542 pages
...BA = AC cos. A = AC sin ..A) ,cj CB - BA tan. A = BA cot. C PROPOSITION II. In any plane triangle, the sides are to each other as the sines of the angles opposite to them. We shall, frequently in treating of triangles, make use of the following notation ; denoting...
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Higher Geometry and Trigonometry: Being the Third Part of a Series on ...

Nathan Scholfield - Conic sections - 1845 - 244 pages
...AC cos. A = AC sin. C CB = BA tan. A = BA cot. C = cot. C PROPOSITION H. In any plane triangle, tJie sides are to each other as the sines of the angles opposite to tltem. We shall, frequently in treating of triangles, make use of the following notation ; denoting...
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The Mechanic's Assistant: A Thorough Practical Treatise on Mensuration and ...

D. M. Knapen - Measurement - 1849 - 300 pages
...equal 12 feet, gt 8 feet, and BC 90 feet; required the height of AC. Am. 60 feet. In all triangles, the sides are to each other as the sines of the angles opposite the said sides ; and any given side is to the sine of the angle opposite said side, as any other given...
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Encyclopędia Americana: A Popular Dictionary of Arts, Sciences ..., Volume 11

Francis Lieber, Edward Wigglesworth, Henry Vethake - Encyclopedias and dictionaries - 1851 - 624 pages
...are to each other as tho eines of the opposite angles ; in spherical triangles, however, the sines of the sides are to each other as the sines of the angles opposite to these sides. Hence it appears how important the sine is for finding certain parts of triangles,...
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Encyclopędia Americana: A Popular Dictionary of Arts, Sciences ..., Volume 11

Francis Lieber - Encyclopedias and dictionaries - 1851 - 618 pages
...to each other as the sines of the opposite angles ; in spherical' triangles, however, the sines of the sides are to each other as the sines of the angles opposite to these sides. Hence it appears how important the sine is for fmding certain parts of triangles, from...
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Elements of Geometry, Plane and Spherical Trigonometry and Conic Sections

Horatio Nelson Robinson - Conic sections - 1854 - 350 pages
...this explanatory remark, we give, PROPOSITION 9. THEOREM. 3. In all spherical triangles, the sines of the sides are to each other, as the sines of the angles opposite to them. This was proved in relation to right angled triangles in theorem 2, and we now apply the principle...
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The Practice of Engineering Field Work, Applied to Land, Hydrographic, and ...

W. Davis Haskoll - Civil engineering - 1858 - 422 pages
...angles ; and since the sides of triangles subtend the opposite angles, that in all plane triangles the sides are to each other as the sines of the angles. In any circle, C, Fig. 96, inscribe a triangle ABD, and draw the radii CA, CB, CD ; bisect these three...
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