 The lateral area of a circular cylinder is equal to the product of the perimeter of a right section of the cylinder by an element. Let S denote the lateral area, P the perimeter of a right section, and E an element of the cylinder AC.  Plane and Solid Geometry - Page 340by Edward Rutledge Robbins - 1907 - 412 pagesFull view - About this book
 | William Chauvenet - Geometry - 1871 - 380 pages
...case of 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 AB CDEF be the base and AA ' any •_ element of a cylinder, and. let the curve... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...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 of the... | |
 | William Chauvenet - Geometry - 1872 - 382 pages
...case of 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, and let the curve abcdef be... | |
 | William Chauvenet - Mathematics - 1872 - 382 pages
...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 GHJKL a right section of it; then, the area of the... | |
 | Aaron Schuyler - Geometry - 1876 - 384 pages
...of all 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 - Geometry - 1877 - 426 pages
...sections are the bases of the cylinder A С'. PROPOSITION XXIX. THEOREM. 619. 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. EL, Let AB С DE be the base, and A A' any element of the cylinder A C" ; and let the... | |
 | George Albert Wentworth - Geometry - 1877 - 436 pages
...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 - Geometry - 1878 - 236 pages
...similar 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 - Geometry - 1884 - 384 pages
...polygons inscribed in a circle. PROPOSITION II.— THEOREM. 8. The lateral area of a cylinder is equal io the product of the perimeter of a right section of the cylinder by an element of the surface. Let AB CDEF be the base and AA ' any F> E> element of a cylinder, and let the curve... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...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 of the... | |
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