 | Horatio Nelson Robinson - Geometry - 1860 - 470 pages
...Thus, if n be the number of sides of the polygon, the angle at the center will be expressed , 360° by~ inscribed polygon of double the number of sides. Thus,...circumscribed polygon is but a part of one having h«»lf the number of sides BOOK V. ON THE PKOPOKT10NALITIES AND MEASUREMENT OF POLYGONS AND CIRCLES.... | |
 | Horatio Nelson Robinson - Conic sections - 1865 - 474 pages
...inscribed polygon be bisected, and the chords of these semi-arcs be drawn, we shall have a regular inscribed polygon of double the number of sides. Thus,...PROPORTIONALITIES AND MEASUREMENT OF POLYGONS AND CIRCLES. PROPOSITION I. — THEOREM. The area of any circle is equal to the product of its radius by one half... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 336 pages
...number of sides. EXERCISE. Theorem.—If a regular polygon is inscribed in a circle, the tangents drawn at the middle points of the arcs subtended by the sides of the inscribed polygon form a circumscribed regular polygon, whose sides are parallel to the sides of the inscribed... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...follows that GS = HK, etc. 3. COROLLARY I. If the vertices of a regular inscribed polygon are joined with the middle points of the arcs subtended by the sides of the polygon, the joining lines will form a regular inscribed polygon of double the number of sides. 4.... | |
 | William Chauvenet - Geometry - 1887 - 364 pages
...follows that GH=HK,6tc. 3. COROLLARY I. If the vertices of a regular inscribed polygon are joined with the middle points of the arcs subtended by the sides of the polygon, the joining lines will form a regular inscribed polygon of double the number of sides. 4.... | |
 | George Albert Wentworth - Geometry - 1888 - 264 pages
...between 0° and 90° as limits. 259. Again, suppose a square A BCD inscribed in a circle, and E, F, lf, K the middle points of the arcs subtended by the sides of the square. If we draw the straight lines AE, EB, BF, etc., we shall have an inscribed polygon of double... | |
 | George Irving Hopkins - 1891 - 210 pages
...to those of the latter. 488. If the vertices of a regular inscribed polygon of n sides are joined to the middle points of the arcs subtended by the sides of the .polygon, the lines thus drawn will form a regular inscribed polygon of 2n sides. 489. If tangents... | |
 | William Chauvenet - 1893 - 340 pages
...circumscribed about the circle. Corollary I. If the vertices of a regular inscribed polygon are joined with the middle points of the arcs subtended by the sides of the polygon, the joining lines will form a regular inscribed polygon of double the number of sides. Corollary... | |
 | Charles Ambrose Van Velzer, George Clinton Shutts - Geometry - 1894 - 416 pages
...the number of sides. 301. COROLLARY V. If a regular polygon is inscribed in a circle, tangents drawn at the middle points of the arcs subtended by the sides of the inscribed polygon, form a regular circumscribed polygon whose sides are parallel to the sides of the inscribed... | |
 | Webster Wells - Geometry - 1894 - 256 pages
...Therefore, the polygon FGHKL is regular. (§ 341.) PROPOSITION III. THEOREM. 346. Tangents to a circle at the middle points of the arcs subtended by the sides of a regular inscribed polygon, form a regular circumscribed polygon. D' H C' Let ABCDE be a regular polygon... | |
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If the vertices of a regular inscribed polygon are joined with the middle points of the arcs subtended by the sides of the polygon, the joining lines will form a regular inscribed polygon of double the number of sides. 
