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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

Royal Society (Great Britain), Charles Hutton, Richard Pearson - 1809
...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...




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