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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 Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1806 - 546 pages
...half their difference. Therefore) in any plane triangle, 8cc. QED PROP. V. FIG. 9, 10. IN any plane 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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An Easy Introduction to the Mathematics: In which the Theory and ..., Volume 2

Charles Butler - Mathematics - 1814 - 528 pages
...the three sides of a triangle are given, the angles are found by this proposition. 71. In a plane' 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 radius to the co-sine of...
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A Treatise of Plane Trigonometry: To which is Prefixed, a Summary View of ...

Jeremiah Day - Logarithms - 1815 - 172 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 Practical Application of the Principles of Geometry to the Mensuration of ...

Jeremiah Day - Measurement - 1815 - 388 pages
...different way, by the following proposition. THEOREM B. In a plane triangle, tivice 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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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 588 pages
...half their difference. Therefore, in any plane triangle, &c. Q. E, D. PROP. V. FIG. 9. and 10. 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 cosine...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 354 pages
...as the difference of the sides to the difference of the segments of the base. Q, ED PROP. VI. 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 AB3+BC3 and...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Circle-squaring - 1819 - 350 pages
...the sides to the difference of the segments of the base. Q, ED PROP. VI. /ğ ağu triangle, twice tlu rectangle contained by any two sides is to the difference...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 AB3+BCa and...
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The Second [-fifth and Sixth] Part of A Course of Mathematics: Adapted to ...

Jeremiah Day - Geometry - 1824 - 440 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 of the squares oj those sides, and the square of the third side, as radius to the tosine of the angle included between...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Circle-squaring - 1826 - 326 pages
...PROP; VI. THEOR. In any triangle, twiee the reetangle eontained by any two sid.es is to the differenee between the sum of the squares of those sides, and the square of the base, as the radius to the eosine of the angle ineluded by the two sidesi Let ABC be any triangle, 2AB.BC is to the differenee...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 546 pages
...of half their difference. Therefore, in any plane triangle, Sic. QED PROP. V. FIG. 9 and 10. 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 cosine...
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