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" PROPOSITION XV. PROBLEM. To inscribe an equilateral and equiangular hexagon in a given circle. Let ABCDEF be the given circle. "
Euclid's Elements of geometry, the first three books (the fourth, fifth, and ... - Página 160
por Euclides - 1846
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Euclid's Elements of geometry, transl. To which are added, algebraic ...

Euclides - 1826 - 226 páginas
...circumscribed, let it be circumscribed, and let it be ABCDE. Therefore a circle has been circumscribed, &c. QEF PROPOSITION XV. PROBLEM. To inscribe an equilateral and equiangular hexagon in a given circle. Let ABCDEF be the given circle; it is required to inscribe an equilateral and equiangular hexagon in...
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Elements of Geometry, Containing the First Six Books of Euclid

Euclid - 1826 - 234 páginas
...let it be circumscribed, and let it be ABCDE. Therefore a circle has been circumscribed, &c. g. EF PROPOSITION XV. PROBLEM. To inscribe an equilateral and equiangular hexagon in a given circle. Let ABCDEF be the given circle ; it is required to inscribe an equilateral and equiangular hexagon...
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Elements of Arithmetic, Algebra, and Geometry

George Lees - 1826 - 276 páginas
...diagonals is the centre, and its distance from one of the angular points the radius. • PROP. XVIII. PROBLEM. To inscribe an equilateral and equiangular hexagon in a given circle. The radius of the circle is the side. » PROP. XIX. PROBLEM. To describe an equilateral and equiangular...
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The First Six Books of the Elements of Euclid: With Notes

Euclid - 1833 - 216 páginas
...circle can be circumscribed about any equilateral and equiangular figure. PROP. XV. PROB. Fig. 17. To inscribe an equilateral and equiangular hexagon in a given circle (ABCDEF). Let G be the centre of the given circle, draw any diameter AGD ; from the centre A with the radius...
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Elements of Plane Geometry According to Euclid

Andrew Bell - 1837 - 290 páginas
...extremities of the other four, and be described about the equilateral and equiangular pentagon ABCDE. PROPOSITION XV. PROBLEM. To inscribe an equilateral and equiangular hexagon in a given circle. Let ABCDEF be the given circle ; it is required to inscribe an equilateral and equiangular hexagon...
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A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - 1837 - 112 páginas
...any one of them, will pass through the points A, B, c, D, K and bedescribed about the given pentagon. PROPOSITION XV. Problem. To inscribe an equilateral and equiangular hexagon in a '^ given circle. Steps of the Demonstration. 1. Prove that A EGD is equilateral, 2. that Z EGD = ^ of 2 right Zs, and...
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - 546 páginas
...extremities of the other four, and be described about the equilateral and equiangular pentagon ABCDE. QEF PROPOSITION XV. PROBLEM. To inscribe an equilateral and equiangular hexagon in a given circle. Let ABCDEF be the given circle. It is required to inscribe an equilateral and equiangular hexagon in...
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Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ...

Dennis M'Curdy - 1846 - 168 páginas
...which was to be done (d). Recite (a) p. 9, 1; (4) p. 4, 1; (c)p. 6, 1; (d), ' I def. I ,3,4. 15 P. To inscribe an equilateral and equiangular hexagon in a given circle (ABCDEF). Let G be the centre of the given circle, and draw the diameter AGD (a): Again, on the point D, where...
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The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848 - 52 páginas
...PROP. XIV. PROBLEM. To describe a circle about a given equilateral and equiangular pentagon. PROP. XV. PROBLEM. To inscribe an equilateral and equiangular hexagon in a given circle. COR. From this it is manifest, that the side of the hexagon is equal to the straight line from the...
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The first six books of the Elements of Euclid, with numerous exercises

Euclides - 1853 - 178 páginas
...four, and be described about the equilateral and equiangular pentagon ab С d e. Which was to be done. PROPOSITION XV. — PROBLEM. To inscribe an equilateral and equiangular hexagon in a given circle. LET ab С def be the given circle ; it is required to inscribe an equilateral and equiangular hexagon...
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