 | Horatio Nelson Robinson - Geometry - 1860 - 470 pages
...16, 32, etc., sides. To get the corresponding circumscribed polygons, we have merely to draw tangents at the middle points of the arcs subtended by the sides of the inscribed polygons. Cor. 5. It is plain that each inscribed polygon is but a part of one having twice the number... | |
 | Horatio Nelson Robinson - Geometry - 1868 - 276 pages
...16, 32, etc., sides. To get the corresponding circumscribed polygons, we have merely to draw tangents at the middle points of the arcs subtended by the sides of the inscribed polygons. Cor. 5. It is plain that each inscribed polygon is but a part of one having twice the number... | |
 | 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
...regular polygon. §395 QED 407. COR. 2. 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 polygon form a circumscribed regular polygon, whose sides are parallel to the sides of the inscribed... | |
 | 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... | |
 | 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... | |
 | George Albert Wentworth - Mathematics - 1896 - 68 pages
...the same number of sides. 407. Cor. 2. 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 polygon form a circumscribed regular polygon, whose sides are parallel to the sides of the inscribed... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 276 pages
...apothem of the inscribed. 506. If the sides of a regular circumscribed polygon are tangent to the circle at the middle points of the arcs subtended by the sides of a similar inscribed polygon, then the sides of the circumscribed figure are parallel to those of the... | |
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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. 
