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In any plane triangle, as twice the rectangle under any two sides is to the difference of the sum of the squares of those two sides and the square of the base, so is the radius to the cosine of the angle contained by the two sides.
Elements of Plane and Spherical Trigonometry: With Their Applications to ... - Pągina 19
per Olinthus Gregory - 1816 - 244 pągines
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - 1806 - 518 pągines
...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 of the angle included by...
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Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an ...

Sir John Leslie - 1809 - 493 pągines
...In any triangle, as twice the rectangle under two sides, is to the difference between their squares and the square of the base, so is the radius, to the cosine of the contained angle. In the triangle ABC, 2AB x BC : AB' + AC* — BC' R:Cos,BAC. For let fall the perpendicular...
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A Treatise of Plane and Spherical Trigonometry: In Theory and Practice ...

Francis Nichols - 1811 - 128 pągines
...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 contained by the two sides. Let ABC be any triangle; 2 AB. BC : difference between AB2+BC2 and AC2 :: R : cos. B. A A B D C B CD From A draw...
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An Easy Introduction to the Mathematics: In which the Theory and ..., Volum 2

Charles Butler - 1814
...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 the angle contai-ned by the...
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Easy Introduction to Mathematics, Volum 2

Charles Butler - 1814
...angles are found by this proposition. 71- In a plane triangle, twice the rectangle contained bjacj 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 the angle contained by the...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 528 pągines
...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 of the angle included by...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - 1827 - 513 pągines
...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 of the angle included by...
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Mathematics for Practical Men

Olinthus Gregory - 1833 - 427 pągines
...difference of the segments of the base made by a perpendicular let fall from the vertical angle. 18. In any plane triangle it will be, as twice the rectangle...the cosine of the angle contained by the two sides. Cor. When unity is assumed as radius, then if A c, AB, B c, are the sides of a triangle, this prop,...
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Mathematics for Practical Men: Being a Common-place Book of Principles ...

Olinthus Gregory - 1834 - 427 pągines
...difference of the segments of the base made by a perpendicular let fall from the vertical angle. 18. In any plane triangle it will be, as twice the rectangle...the cosine of the angle contained by the two sides. Cor. When unity is assumed as radius, then if A c, AB, B c, are the sides of a triangle, this prop,...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1834
...plane triangle, &c. Q. JE. a. PROPOSITION V. In any triangle, twice the rectangle contained by any tn-n 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 of the angle included by...
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