 The lateral area of a cylinder is equal to the product of the perimeter of a right section of the cylinder by an element. Hyp. S is the lateral area, P the perimeter of a right .section, and E an element of the cylinder AK; S...  Solid Geometry - Seite 395von Clara Avis Hart, Daniel D. Feldman, Virgil Snyder - 1912 - 188 SeitenVollansicht - Über dieses Buch
 | William Chauvenet - 1871 - 380 Seiten
...parallel to the base, is equal to the base. PROPOSITION II.— THEOREM. 16. The lateral area of a prism is equal to the product of the perimeter of a right section of the prism by a lateral edge. Let AD' be a prism, and GHIKL a right section of it ; then, the area... | |
 | William Chauvenet - 1872 - 382 Seiten
...regular polygons inscribed in a circle. PROPOSITION II.— THEOREM. 8. The lateral area of a cylinder is equal to the product of the perimeter of a right section of the cylinder by an element of the surface. Let ^.BCZXEFbethe base &ndAA' any element of a cylinder,... | |
 | Aaron Schuyler - 1876 - 384 Seiten
...sections parallel to the bases. (?) 431. Proposition III.— Theorem. The lateral area of a cylinder is equal to the product of the perimeter of a right section by an element. -JT Let I denote the lateral area of the cylinder AG ; p, the perimeter of a right section... | |
 | George Albert Wentworth - 1877 - 436 Seiten
...s, and the perimeter of its right section by p. Then s=p XA A', §524 (the lateral area of a prism is equal to the product of the perimeter of a right section by a lateral edge). Now let the number of lateral faces of the inscribed prism be indefinitely increased,... | |
 | William Henry Harrison Phillips - 1878 - 236 Seiten
...prism whose homologous edge ab — 5 inches ? IX. Theorem. The lateral surface of any prism (cylinder) is equal to the product of the perimeter of a right section by a lateral edge. HYPOTH. abcde is a right section, and A A', a lateral edge, of the prism ABCDE-A'.... | |
 | William Chauvenet, William Elwood Byerly - 1887 - 331 Seiten
...made by a plane parallel to the base is equal to the base. PROPOSITION II. The lateral area of a prism is equal to the product of the perimeter of a right section of the prism by a lateral edge. Corollary. The lateral area of a right prism is equal to the product... | |
 | Edward Albert Bowser - 1890 - 420 Seiten
...remains. . •. prism AI = prism AT. QED ^ Proposition 4. Theorem. 591. 'The lateral area of a prism is equal to the product of the perimeter of a right Section by a lateral edge. B Hyp. Let FGHIK be a rt. section, and AA' a lateral edge of the prism AD'. To prove... | |
 | William Chauvenet - 1893 - 340 Seiten
...rigorous proof has been given in Book V. PROPOSITION II.—THEOREM. 8. The lateral area of a cylinder is equal to the product of the perimeter of a right section of the cylinder by an element of the surface. Let ABCDEF be the base and AA' any element of a cylinder,... | |
 | William C. Bartol - 1893 - 106 Seiten
...+ BK + CG = S; hence, S = I (DE + EE + ED). QED 95. COROLLARY 1. The lateral surface of a cylinder is equal to the product of the perimeter of a right section by an element of the surface. THE ELEMENTS OF SOLID GEOMETRY. 96. COROLLARY 2. The lateral surface... | |
 | John Macnie - 1895 - 386 Seiten
...similar, (Hyp.) ami T: T'= ' R) : = H2:Il'-= R2:S'2. 674. SCHOLIUM. The lateral. area of any cylinder is equal to the product of the perimeter of a right section of the cylinder by an element of its surface. This may be proved by a method similar to that employed... | |
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