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" In any triangle, twice the rectangle contained by any two sides is to the difference between the sum of the squares of those sides, and the square of the base, as the radius to the cosine of the angle included by the two sides. Let ABC be any triangle,... "
A Treatise of Plane and Spherical Trigonometry: In Theory and Practice ... - Page 13
by Francis Nichols - 1811 - 128 pages
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The Principles of Plane Trigonometry, Mensuration, Navigation and Surveying ...

Jeremiah Day - Measurement - 1831 - 394 pages
...a different way, by the following proposition. THEOREM B. In a plane triangle, twice the product of any two sides, is to the difference between the sum...the squares of those sides, and the square of the third side, as radius to the cosine of the angle included between the two sides. In the triangle ABC,...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - Euclid's Elements - 1832 - 358 pages
...the base. QED PROP. VI. THEOR. In any triangle, twice the rectangle contained by any two sides is !o the difference between the sum of the squares of those...the base, as the radius to the cosine of the angle included by the two sides. LetABCbeanytriangIe,2AB.BCis to the difference 'between ABa+BCa and AC*...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 540 pages
...&c. QED PROP. VI. FIG. 9. & 10. In any triangle, twice the rectangle contained by any two adjacent sides is to the difference between the sum of the squares of these two sides, and the square of the base, as the radius is to the cosine of the angle included by...
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The Elements of Euclid: viz. the first six books, together with the eleventh ...

Robert Simson - Trigonometry - 1835 - 544 pages
...&c. QED PROP. VI. FIG. 9. & 10. In any triangle, twice the rectangle contained by any two adjacent sides is to the difference between the sum of the squares of these two sides, and the square of the base, as the radius is to the cosine of the angle included by...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1836 - 488 pages
...of the sides to the difference of the segments of the base. QE Don PROP. VI. t . . In any trianglei twice the rectangle contained by any two sides is...the base, as the radius to the cosine of the angle included by the two sides. Let ABC be any triangle, 3AB.BC is to the difference between AB2 + BC2 and...
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

Mathematics - 1836 - 488 pages
...opposite angles, to the tangent of half their difference. In a plane triangle, twice the product of any two sides, is to the difference between the sum...the squares of those sides, and the square of the third side, as radius to the cosine of the angle included between the two sides. CONIC SECTIONS. 16th...
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The Element of Geometry

John Playfair - Geometry - 1836 - 148 pages
...to the tangent of half their difference. Therefore, in any plane triangle, &c. QED PROP. V. In any triangle, twice the rectangle contained by any two sides is to the difference of the sum of the squares of these two sides, and the square of the base, as the radius is to the co-sine...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - Euclid's Elements - 1837 - 332 pages
...the difference of the sides to the difference of the segments of the base. PROP. VI. THEOR. In, any triangle, twice the rectangle contained by any two...the base, as the radius to the cosine of the angle included by the two sides. • Let ABC be any triangle, 2AB.BC is to the difference between AB2+BC2...
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A Course of Mathematics: Containing the Principles of Plane ..., Volumes 1-3

Jeremiah Day - Geometry - 1838 - 416 pages
...a different way, by the following proposition. THEOREM B. In a plane triangle, twice the product of any two sides, is to the difference between the sum...the squares of those sides, and the square of the third side, as radius to the cosine of the angle included between the two sides. In the triangle ABC,...
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A Course of Mathematics: Containing the Principles of Plane ..., Volumes 1-3

Jeremiah Day - Geometry - 1839 - 434 pages
...a different way, by the following proposition. THEOREM B. In a plane triangle, twice the product of any two sides, is to the difference between the sum...the squares of those sides, and the square of the third side, as radius to the cosine of the angle included between the two sides. In the triangle ABC,...
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