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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. "
The Field Engineer: A Handy Book of Practice in the Survey, Location, and ... - Página 13
por William Findlay Shunk - 1908 - 345 páginas
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1806 - 518 páginas
...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 ...

Sir John Leslie - 1809 - 524 páginas
...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 páginas
...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...
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An Easy Introduction to the Mathematics: In which the Theory and ..., Volumen2

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, Volumen2

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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Elements of Plane and Spherical Trigonometry: With Their Applications to ...

Olinthus Gregory - 1816 - 244 páginas
...GB :: BF : BE ; which agrees with the proposition. PROP. XVII. 17. In any plane triangle it will be, as twice the rectangle under any two sides, is to...the cosine of the angle contained by the two sides. Let ABC be a plane triangle. From A, C one extremity of the base AB, draw AD perpendicular to the opposite...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 528 páginas
...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 páginas
...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: Being a Common-place Book of ... Pure and ...

Olinthus Gregory - 1834 - 427 páginas
...base made by a perpendicular let fall from the vertical angle. 18. In any plane triangle it will be, as twice the rectangle under any two sides, is to...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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