| Edward Albert Bowser - Geometry - 1890 - 393 pages
...regular inscribed hexagon is twice the area of the inscribed equilateral triangle. 4. The area of the **regular inscribed hexagon is threefourths of that of the regular circumscribed hexagon.** 5. The area of the regular inscribed hexagon is a mean proportional between the areas of the inscribed... | |
| John Maximilian Dyer - Plane trigonometry - 1891 - 306 pages
...in its construction (Eue. IV. 11) ::,/5:1(8) The area of the regular hexagon inscribed in a circle **is a mean proportional between the areas of the inscribed and circumscribed equilateral triangles,** (9) One circle is inscribed in and another is circumscribed about a regular polygon of и sides. If... | |
| William Chauvenet - 1893 - 340 pages
...regular inscribed triangle is one-half the area of the regular inscribed hexagon. 6. The area of the **regular inscribed hexagon is three-fourths of that of the regular circumscribed hexagon.** 7. The area of the regular inscribed hexagon is a mean proportional between the areas of the inscribed... | |
| Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 320 pages
...apothems, their radii, or their sides. Proved with cor. 1. EXERCISES. 470. The area of an inscribed regular **hexagon is a mean proportional between the areas of...inscribed and circumscribed equilateral triangles.** 471. Show how, with compasses alone, to divide a circumference into six equal arcs. 472. Prove that... | |
| John Macnie - Geometry - 1895 - 392 pages
...equilateral triangle is to the radius of the circumscribing circle as 3 is to 2. 614. The area of the regular **hexagon is a mean proportional between the areas of...inscribed and circumscribed equilateral triangles.** 615. The square of a side of an inscribed equilateral triangle is equivalent to three times the square... | |
| Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 320 pages
...apothems, their radii, or their sides. Proved with cor. 1. EXERCISES. 470. The area of an inscribed regular **hexagon is a mean proportional between the areas of...inscribed and circumscribed equilateral triangles.** 471. Show how, with compasses alone, to divide a circumference into six equal arcs. 472. Prove that... | |
| George D. Pettee - Geometry, Plane - 1896 - 272 pages
...whose diameter is a chord of the outer circle, tangent to the inner circle. 396. The area of a regular **hexagon is a mean proportional between the areas of...inscribed and circumscribed equilateral triangles.** MAXIMA AND MINIMA 289. Definitions. Of magnitudes of the same kind, that which is greatest is a maximum;... | |
| George Albert Wentworth - Geometry - 1896 - 296 pages
...inscribed hexagon — J-RVS (Ex. 380). But TEACHERS EDITION. Ex. 392. The area of an inscribed regular **hexagon is a mean proportional between the areas of...inscribed and circumscribed equilateral triangles.** PROOF. Area of inscribed equilateral A whose sido is a = |xf R = ^~ x ^ - JR^Vs. (Ex.378) Area of circumscribed... | |
| Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 556 pages
...triangles be circumscribed about and inscribed in a given triangle, the area of the given triangle **is a mean proportional between the areas of the inscribed and circumscribed** triangles. 105. Any fourth point P is taken on the circumference of a circle through A, B, and C. Prove... | |
| Andrew Wheeler Phillips, Irving Fisher - Geometry, Modern - 1896 - 276 pages
...of those which fall upon the other side. 128. The area of any regular polygon inscribed in a circle **is a mean proportional between the areas of the inscribed and circumscribed** polygons of half the number of sides. 129. If, on the sides of a right triangle as diameters, semi-circumferences... | |
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