| William Frothingham Bradbury - Geometry - 1872 - 262 pages
...As the triangles 0 AB, 0 BC, 0 CD, &c. are equal, their altitudes are equal, that is, the bases are **equidistant from the vertex 0. 35. Scholium. 0 is...XVIII. 37. The area of a regular polygon is equal to** half the product of its perimeter and apothem. For the area of each triangle of which the polygon is... | |
| William Chauvenet - Geometry - 1872 - 382 pages
...or CD : C'D', etc. Therefore the polygons fulfill the two conditions of similarity. 10. Corollary. **The perimeters of regular polygons of the same number of sides are** to each other as the radii of the circumscribed circles, or as the radii of the inscribed circles;... | |
| Edward Olney - Geometry - 1872 - 472 pages
...sides are to each other as the corresponding diagonals (35O), p : P : : r : HQED , .g,370. COR. 1. — **The perimeters of regular polygons of the same number of sides are** to each other as the apothems of the polygons. For the apothems are to each other as the sides of the... | |
| William Frothingham Bradbury - Geometry - 1873 - 288 pages
...bases are equidistant from the vertex 0. 35. Scholium. 0 is called the centre, and the perpendicular OG **the apothem of the polygon. 36. Corollary. In regular...of regular polygons of the same number of sides are** аt their apothems ; and the polygons as the squares of their apothems. THEOREM XVIII. 37. The area... | |
| Harvard University - 1874 - 668 pages
...impossible ! Why ? Given any curve, to ascertain whether it is the arc of a circle or not. 6. Prove that **the perimeters of regular polygons of the same number of sides are** proportional to the iliiimeiers of their inscribed or circumscribed circles. Go on to prove that the... | |
| 1875 - 256 pages
...impossible 1 Why 1 Given any curve, to ascertain whether it is the arc of a circle or not. 6. Prove that **the perimeters of regular polygons of the same number of sides are** proportional to the diameters of their inscribed or circumscribed circles. Go on to prove that the... | |
| William Frothingham Bradbury - Geometry - 1880 - 260 pages
...Scholium. 0 is called the centre, 0 B the radius, and the perpendicular 0 G the apothem of the polygon. 84. **Corollary. In regular polygons of the same number...polygons as the squares of their apothems. THEOREM** XXXVII. 85. The area of a regular polygon is equal to half the product of its perimeter and apothem.... | |
| Edward Olney - Geometry - 1882 - 262 pages
...homologous sides are to each other as the corresponding diagonals (350), p : P : : r : RQED 370. COR. 1. — **The perimeters of regular polygons of the same number of sides are** to each other as the apothems of the polygons. For the apothems are to each other as the sides of the... | |
| Edward Olney - Geometry - 1886 - 348 pages
...the homologous sides are to each other as the corresponding diagonals (387), pr 416. COROLLARY 1. — **The perimeters of regular polygons of the same number of sides are** to each other as the apothems of the polygons (382)417. COROLLARY 2. — The circumferences of circles... | |
| William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...inscribed in it. PROPOSITION III. Regular polygons of the same number of sides are similar. Corollary. **The perimeters of regular polygons of the same number of sides are** to each other as the radii of the circumscribed circles, or as the radii of the inscribed circles ;... | |
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