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The area of a regular inscribed hexagon is a mean proportional between the areas of the inscribed and circumscribed equilateral triangles.
Elements of Plane and Solid Geometry - Page 221
by George Albert Wentworth - 1877 - 398 pages

Elements of Geometry

George Washington Hull - Geometry - 1897 - 408 pages
...thirds of the area of the regular hexagon inscribed in the circle. 816. The area of an inscribed regular hexagon is a mean proportional between the areas of...inscribed and circumscribed equilateral triangles. 317. The square inscribed in a semicircle is equivalent to two fifths of the square inscribed in the...

Plane and Solid Geometry

James Howard Gore - Geometry - 1898 - 232 pages
...inscribed hexagon = - V3. §3 3. Find the area of a square inscribed in a circle whose radius is 6. 4. Show that the area of a regular inscribed hexagon is a mean proportional between the areas of an inscribed, and of a circumscribed, equilateral triangle. PROPOSITION IX. THEOREM. 304. The area...

Essentials of Geometry (plane).

Webster Wells - Geometry - 1898 - 282 pages
...(Prove, by aid of § 164, that a O can be inscribed in FGHKL ; then use Ex. 7, p. 198.) E" - "D 25. The area of a regular inscribed hexagon is a mean proportional between the areas of an inscribed, and of a circumscribed equilateral triangle. (Prove, by aid of Exs. 8, 10, and 11, p....

The Essentials of Geometry

Webster Wells - Geometry - 1899 - 450 pages
...pentagon. A (Prove, by aid of § 164, that a O can be inscribed in FGHKL ; then use Ex. 7, p. 198.) 25. The area of a regular inscribed hexagon is a mean proportional between the areas of an inscribed, and of a circumscribed equilateral triangle. (Prove, by aid of Exs. 8, 10, and 11, p....

New Plane and Solid Geometry

Wooster Woodruff Beman, David Eugene Smith - Geometry - 1899 - 416 pages
...circumference in C, D ; draw CD, DB, BC, and prove A BCD equilateral. 444. The area of an inscribed regular hexagon is a mean proportional between the areas of...inscribed and circumscribed equilateral triangles. 445. Show how, with compasses alone, to divide a circumference into six equal arcs. 446. Prove that...

The Elements of Plane Geometry

Charles Austin Hobbs - Geometry, Plane - 1899 - 240 pages
...equal to one half the area of the inscribed regular hexagon. Ex. 659. The area of an inscribed regular hexagon is a mean proportional between the areas of...inscribed and circumscribed equilateral triangles. Proposition 217. Theorem. 254. The area of a circle is equal to one half the product of its circumference...

The Essentials of Geometry

Webster Wells - Geometry - 1899 - 424 pages
...pentagon. (Prove, by aid of § 164, that a 0 can be inscribed in FGHKL ; then use Ex. 7, p. 198.) E" "D 25. The area of a regular inscribed hexagon is a mean proportional between the areas of an inscribed, and of a circumscribed equilateral triangle. (Prove, by aid of Exs. 8, 10, and 11, p....

New Plane Geometry

Wooster Woodruff Beman, David Eugene Smith - Geometry, Modern - 1899 - 272 pages
...circumference in C, D; draw CD, DB, BC, and prove A BCD equilateral. 444. The area of an inscribed regular hexagon is a mean proportional between the areas of...inscribed and circumscribed equilateral triangles. 445. Show how, with compasses alone, to divide a circumference into six equal arcs. 446. Prove that...