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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. 642. If two circumferences intersect each other, and from either point of intersection...
The System of Calculating Diameter, Circumference, Area, and Squaring the ... - Σελίδα 11
των James Morton - 1881 - 216 σελίδες
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## The Philosophical Transactions of the Royal Society of London

...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...

## Elementary Course of Geometry ...

Charles William Hackley - 1847 - 103 σελίδες
...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...

## A Course of Mathematics: Composed for the Use of the Royal Military Academy

Charles Hutton - 1860 - 895 σελίδες
...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...

## Euclid's Elements of geometry, books i. ii. iii. iv

Euclides - 1862
...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 circle is equal to the perpendicular of an equilateral triangle described on the diameter. 5. If tangents be drawn through...

## Mathematical Exercises ...

Samuel H. Winter - 1864
...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...

## A Treatise on Special Or Elementary Geometry: An advanced course in geometry

Edward Olney - 1872 - 84 σελίδες
...circumference, their sum is least when they make equal angles with a tangent at the common point. 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. 642....

## A Treatise on Special Or Elementary Geometry, Τόμοι 1-2

Edward Olney - 1872
...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 in a circle is equal to the diagonal of a rhombus, whose other diagonal and each of whose sides are equal to the radius. 642....

## A TREATISE ON SPECIAL OR ELEMENTARY GEOMETFH.

EDWARD OLNEY - 1872
...circumference, their sum is least when they make equal angles with a tangent at the common point. . 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. 642....

## The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874
...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, and the adjacent...

## Elements of Euclid [selections from book 1-6] adapted to modern methods in ...

Euclides - 1874
...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...