 | Euclides - 1840 - 192 pagine
...since each of its angles is double of the angle of an equilateral triangle, it is also equiangular. PROP. XVI. PROB. To inscribe an equilateral and equiangular quindecagon in a given circle (ABCD). Let AB and BD be the sides of an equilateral pentagon inscribed in the given circle, and let... | |
 | Euclides - 1840 - 82 pagine
...equiangular pentagon. PROP. XV. PROB. To inscribe an equilateral and equiangular hexagon in a given circle. A PROP. XVI. PROB. To inscribe an equilateral and equiangular quindecagon in a given circle. BOOK VI. PROP. I. THEOR. Triangles and parallelograms having the same altitude, are to one another... | |
 | Euclides - 1841 - 378 pagine
...lines touching the circle, an equilateral and equiangular hexagon will be described about it, which may be demonstrated from what has been said of the...like to that used for the pentagon. PROP. XVI. PROB. 'In inscribe an equilateral and equiangular quindecayon in a given circle. Let ABCD be the given circle;... | |
 | John Playfair - 1842 - 332 pagine
...lines touching the circle, an equilateral and equiangular hexagon shall be described about it, which may be demonstrated from what has been said of the...method like to that used for the pentagon. PROP. XVI. PROS. To inscribe an equilateral and equiangular qumdecagon in a given circle. Let ABCD be the given... | |
 | Euclides - 1842 - 316 pagine
...lines touching the circle, an equilateral and equiangular hexagon shall be described about it, which may be demonstrated from what has been said of the...circumscribed about it, by a method like to that used for a pentagon. NB In practice it will evidently suffice to inscribe in the circle a line equal to the... | |
 | Euclid - 1845 - 218 pagine
...lines touching the circle, an equilateral and equiangular hexagon shall be described about it, which may be demonstrated from what has been said of the...it, by a method like to that used for the pentagon. PROPOSITION XVI. PBOB. — To inscribe an equilateral and equiangular quindecagon in a given circle.... | |
 | Euclides - 1845 - 546 pagine
...lines touching the circle, an equilateral and equiangular hexagon will be described about it, which may be demonstrated from what has been said of the...it, by a method like to that used for the pentagon. PROPOSITION XVI. PROBLEM. To inscribe an equilateral and equiangular quindecagon in a given circle.... | |
 | Euclid, James Thomson - 1845 - 382 pagine
...equal lines FB, GC, &c. Therefore, if any equilateral, &c. PROP. VI. PROR. — To inscribe a square in a given circle. Let ABCD be the given circle ; it is required to inscribe a square in it. Draw two diameters AC, BD at right angles to one another ; and join AB, BC, CD, DA;... | |
 | Euclid, John Playfair - 1846 - 334 pagine
...is to the radius, as the square root of 2, is to unity. PROP. VII. PROB. To describe a square about a given circle. Let ABCD be the given circle ; it is required to describe a square about it. Draw two diameters AC, BD of the circle ABCD, at right angles to one another,... | |
 | Elias Loomis - 1849 - 252 pagine
...equal, and the figure ABCDEF will be a regular polygon. PROPOSITION III. PROBLEM. To inscribe a square in a given circle. Let ABCD be the given circle ; it is required to inscribe a square in it. Draw two diameters AC, BD at right angles to each other; and join AB, BC, CD, DA. Because... | |
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... may be demonstrated from what has been said of the pentagon : and likewise a circle may be inscribed in a given equilateral and equiangular hexagon, and circumscribed about it, by a method like to that used for the pentagon. 
