 | Royal Society (Great Britain) - Meteorology - 1809 - 792 pages
...triangle described about the same circle, on the same principles as the preceding. PROP. 3. The square of the side of an equilateral triangle, inscribed in a circle, is equal to o rectangle under the diameter of the circle, and a perpendicular let fall from any angle of the triangle... | |
 | Charles William Hackley - Geometry - 1847 - 248 pages
...a given square, so as to form an equilateral and equiangular octagon. 38. Prove that the square of the side of an equilateral triangle, inscribed in a circle, is equal to three times the square of the radius. 39. To draw straight lines from the extremities of a chord to... | |
 | Charles Hutton - Mathematics - 1860 - 1020 pages
...angles of a given square, so as to fora an equilateral and equiangular octagon. (29.) The square of the side of an equilateral triangle, inscribed in a circle, is equal to three times the square of the radius. (30.) To draw straight lines from the extremities of a chord... | |
 | Euclides - 1862 - 140 pages
...circle, and having its sides respectively perpendicular to those of the first triangle. 3. The square of the side of an equilateral triangle inscribed in a circle is equal to three-fourths of the square of the dia meter. 4. The side of an equilateral triangle inscribed in a... | |
 | Samuel H. Winter - 1864 - 348 pages
...pentagon and a regular decagon, inscribed in the same circle, is equal to the square on the radius. 12. The side of an equilateral triangle inscribed in a circle is equal to a diagonal of a rhombus, each of whose sides is the radius of the circle. 13. If А, в, с are the... | |
 | Edward Olney - Geometry - 1872 - 562 pages
...tangent at the common point, the points being on the opposite side of the tangent from the circle. 641. The side of an equilateral triangle inscribed...other, and from either point of intersection a diameter he drawn in each, the other extremities of these diameters and the other point of intersection are... | |
 | Euclides - 1874 - 342 pages
...that they will form an equilateral triangle, whose area is four times the former. 8. The square on the side of an equilateral triangle inscribed in a circle is equal to three-fourths of the square on the diameter. 9. If an equilateral triangle be inscribed in a circle,... | |
 | Euclid, James Bryce, David Munn (F.R.S.E.) - Geometry - 1874 - 236 pages
...lines joining the corresponding extremities, triangles which shall be equiangular. 37. The square of the side of an equilateral triangle, inscribed in a circle, is equal to three times the square of the radius. 38. If from any point in the diameter of a semicircle, two straight... | |
 | Edward Olney - Geometry - 1879 - 502 pages
...tangent at the common point, the points being on the opposite side of the tangent from the circle. 641. The side of an equilateral triangle inscribed...diagonal and each of whose sides are equal to the radius. _ /\ 642. If two circumferences intersect each other, and from either point of intersection a diameter... | |
 | James Morton - Circle-squaring - 1881 - 236 pages
...triangles generally are to each other as the products of their bases and altitudes. The square of the one side of an equilateral triangle inscribed in a circle is equal to three-fourths the area of a square described without the circle and tangent thereunto. Therefore, by... | |
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... 641. The side of an equilateral triangle inscribed in a circle is equal to the diagonal of a rhombus, whose other diagonal and each of whose sides are equal to the radius. 
