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The Regulated Area of the Circle; And the Area of the Surface of the Sphere

The Regulated Area of the Circle; And the Area of the Surface of the Sphere


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About the Book

Purchase of this book includes free trial access to www.million-books.com where you can read more than a million books for free. This is an OCR edition with typos. Excerpt from book: PART I. ON THE AREA OF THE CIRCLE. INTRODUCTION. Notwithstanding the various treatises that have been written on the subject of getting the area of the circle?which works, in many respects, were enveloped in mysticism, and are irrational and hypothetical?the ratio of the diameter to the circumference has, with all this irrational labor, been nearly ascertained; but the principal object which all previous authors have aimed at, has never been attained by any one, except the author of this work, viz: Of finding the true area of the circle in a rational and comprehensive manner, as will be perceived by a comparison of thii with other treatises. Others have taught that the circle is a polygon of an infinite number of sides, and yet a triangle, which has the circumference for its basis, while the radius of the circle is its altitude, and that the area of the circle is the product of its circumference by one-half of its radius; but a careful perusal of this work will satisfy the inquiring mind, that it is impossible to ascertain the area of the circle by multiplying its circumference by the half of its radius; by this mode the result will always be Jess than the amount of the true area of the circle, for the very reason that the curve line has the capacity of encompassing more area than can be effected by a member of rectilineal basis of triangles composing a polygon. For this cause, all previous mathematicians have and must/orever fail t PROPOSITION I. ?AUXILIARY THEOREM. Position 1. If one-half the difference of two unequal magnitudes be taken from the greater and added to the less, both magnitudes become equal to each other. DEMONSTRATION. Let the sum of A+ B be = D, yet A ?C being =B and B + C == A; but D being = A + B, D therefore will be = 2B + C. One- half D...


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Product Details
  • ISBN-13: 9780217606806
  • Publisher: General Books
  • Publisher Imprint: General Books
  • Height: 229 mm
  • No of Pages: 46
  • Spine Width: 3 mm
  • Width: 152 mm
  • ISBN-10: 0217606806
  • Publisher Date: 14 Oct 2010
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 82 gr


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