...the same number of sides are proportional to their sides ; and the same is true of their apothems. The areas of two regular polygons of the same number of sides are proportional to the squares of their sides, or the squares of their radii, or the squares of their...

...spheres upon which they are situated. COmpare § 206. ^ 308. COR. 3. The surfaces of two spheres are to each other as the squares of their radii, or as the squares of their diameters. V ^ 309. COR. 4. The area of a zone is equal to the product of its altitude % the circumference...

...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 ; and their areas are...

...Then, But, Whence, AB* AW*' K' AB ^R_ A'B' ~ R' K ^ R2 _ Iff 7? '2 ~ .A. Ji (§ 320.) ,.'2 That is, the areas of two regular polygons of the same number...radii, or as the squares of their apothems. PROPOSITION VI. THEOREM. 351. The area of a regular polygon is equal to one-half the product of its perimeter and...

...parallelogram. State the difference in the meaning of the word equal here and in question 2. 6. The perimeters of two regular polygons of the same number of sides are to each other as their radii or as their apothems. Define regular polygons, their radii, their apothems. CORNELL UNIVERSITY,...

...K' denote the areas of the polygons AE and A'-E'. Then, 7 JF = §-?. Whence, ^-_^^rj. That is, £Ae areas of two regular polygons of the same number of sides are to each other ax the squares of their radii, or as the squares of their apothems. PROPOSITION VI. THEOREM. 351. The...

...the same number of sides are proportional to their sides ; and the same is true of their apothems. The areas of two regular polygons of the same number of sides are proportional to the squares of their sides, or the squares of their radii, or the squares of their...

...sphere although they are equal. Exercises. — 1. Show that the surfaces of any two spheres are to each other as the squares of their radii, or as the squares of any corresponding lines. 2. Find the surface of a sphere, the diameter of which is one and a half feet....

...Whence O'B' Therefore the triangles are similar. AB OA Hence And A'B' AB O'A' OF §466 §150 §285 §274 §290 A'B' O'F' QED 482. COR. I. The perimeters of...same number of sides are to each other as the squares of tlieir radii or as the squares of their apothems. PROPOSITION V. THEOREM 484. The circumference...

...same number of sides are to each other as the squares of any two homologous sides. 413. The perimeters of two regular polygons of the same number of sides are to each other as the radii of their circumscribed circles, and also as the radii of their inscribed circles. 414. Cor. The...