...from three given points and from a given straight line. When is it impossible to do so ? Q. Prove that the perimeters of two regular polygons of the same number of sides are to one another as the radii of their circumscribing circles. Prove that in a given circle the perimeter...

...to any vertex of a regular polygon bisects the angle at the vertex. 143. The perimeters of regular polygons of the same number of sides are to each other as any two homologous sides. 144. Find the area of a square inscribed in a circle whose radius is 6. 145....

...Hence .Kand Kf are similar. Art. 321. QED 268 BOOK V. PLANE GEOMETRY PROPOSITION VI. THEOREM 434. I. The perimeters of two regular polygons of the same...other as the radii of their circumscribed circles, or as the radii of their inscribed circles; II. Their areas are to each other as the squares of these...

...homologous sides proportional. Hence K and K' are similar. Art. 321. QED PROPOSITION VI. THEOKEM 434. I. The perimeters of two regular polygons of the same...other as the radii of their circumscribed circles, or as the radii of their inscribed circles; II. Their areas are to each other as the squares of these...

...O'A' = OM : O'M'. § 445 §364 § 431 § 436 Also, . § 357 §351 § 361 Ax. 1 QED 448. COR. The areas of two regular polygons of the same number of sides are to each other as the squares of the radii of the circumscribed circles, and of the inscribed circles. § 413 PROPOSITION...

...PLANE GEOMETRY PROPOSITION VI. THEOREM 484. I. The perimeters of two regular polygons of the stone number of sides are to each other as the radii of their circumscribed circles, or as the radii of their inscribed circles; II. Their areas are to each other as the squares of these...

...equivalent to a given square and having the difference of its base and altitude equal to a given line. 4. The perimeters of two regular polygons' of the same number of sides are in the same ratio as the radii of the inscribed or circumseribed circles. 5. To construct a circle...

...of double the number of sides will be inscribed. PLANE GEOMETRY— BOOK V PROPOSITION V. THEOREM 448 The perimeters of two regular polygons of the same number of sides are to each other as their radii or as their apothems. HYPOTHESIS. P and P' are the perimeters, O and O' the centers, OA...

...double the number of sides will be inscribed. PLANE GEOMETRY — BOOK V PROPOSITION V. THEOREM 448 The perimeters of two regular polygons of the same number of sides are to each other as their radii or as their apothems. B' HYPOTHESIS. P and P' are the perimeters, O and 0' the centers,...

...according to its reading we would find ourselves doing the impossible. As for example take the theorem, " The perimeters of two regular polygons of the same...and also as the radii of their inscribed circles." The phrase " Of the same number of sides " might be omitted and the untrained pupil would scarcely...