| Euclides - 1840 - 192 pages
...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 pages
...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 - Geometry - 1841 - 378 pages
...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 - Euclid's Elements - 1842 - 332 pages
...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 pages
...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 - Geometry - 1845 - 218 pages
...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 pages
...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.... | |
| Euclides, James Thomson - Geometry - 1845 - 382 pages
...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 - Euclid's Elements - 1846 - 334 pages
...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 - Conic sections - 1849 - 252 pages
...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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