The Mathematics Teacher Volume 5

The Mathematics Teacher Volume 5

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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1913 edition. Excerpt: ... polar triangles each angle of the one is the supplement of the opposite side in the other. K7. 6. Vertical spherical triangles are symmetrical and equivalent. C8, no.. _ (The relation between the areas and volumes of similar solids may be treated as corollaries in individual cases. See preface, article 3. It is understood that certain statements concerning limits may be assumed either explicitly or implicitly; these are not stated as theorems. See Q3, 4. 9, R9. 10-) 1. An oblique prism is equivalent to a right prism whose base is a right section of the oblique prism and whose altitude is a lateral edge of the oblique prism. C4. 2. A plane passed through two diagonally opposite edges of a parallelepiped divides it into two equivalent triangular prisms. C6. 3. The lateral area of a prism is the product of a lateral edge and the perimeter of a right section. Q1. (Corollary of Plane Geometry.) 4. The lateral area of a regular pyramid is one half the product of the slant height and the perimeter of the base. Q2-l (Corollary of Plane Geometry.) ' 5. The lateral area of a right circular cylinder is the product of the altitude and the circumference of the base; i. e., s=21rrh. Q5-6. The lateral area of a right circular cone is one half the product of the slant height and the circumference of the base; i. e., s=1rrl. Q6. 7. The lateral area of a frustum of a regular pyramid is one half the product of the slant height and the sum of the perimeters of the bases. IQ87. The lateral area of a frustum of a right circular cone is one half the product of the slant height and the sum of the circumferences of the bases. Q8 (a). 9. The area of a zone is the product of its altitude and the circumference of a great circle; i. e., s=21i-rh. Q1o. (Lemma for IO below.)...show more

Product details

  • Paperback | 90 pages
  • 189 x 246 x 5mm | 177g
  • Rarebooksclub.com
  • Miami Fl, United States
  • English
  • black & white illustrations
  • 1236559983
  • 9781236559982