# Treatise on Elementary Geometry

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## Description

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1905 edition. Excerpt: ...circle is regular if the number of its sides is odd. 4. An equiangular polygon circumscribed about a circle is regular. 5. The area of the 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 and circumscribed equilateral triangles. 8. A plane surface may be entirely covered (as in the construction of a pavement) by equal regular polygons of either three, four, or six sides. 9. A plane surface may be entirely covered by a combination of squares and regular octagons having the same side, or by dodecagons and equilateral triangles having the same side. 10. If squares be described on the sides of a regular hexagon, and their adjacent external vertices be joined, a regular dodecagon will be formed. 11 The diagonals of a regular pentagon form a regular pentagon. 12. The diagonals joining alternate vertices of a regular hexagon enclose a regular hexagon one-third as large as the original hexagon. u 15 169 13. The area of the regular inscribed octagon is equal to the product of the side of the inscribed square by the diameter. Suggestion. A quarter of the octagon is the sum of two triangles having as a common base the side of the inscribed square, and having the radius as the sum of their altitudes. 14. The area of a regular inscribed dodecagon is equal to three times the square of the radius. 15. Prove the correctness of the following construction: If AB and CD are two perpendicular diameters in a circle, and E the middle point of the radius OC, and if EF is taken equal to EA, then OF is equal to the side of the...show more

## Product details

• Paperback | 68 pages
• 189 x 246 x 4mm | 141g
• Miami Fl, United States
• English
• black & white illustrations
• 1236529529
• 9781236529527