Hirsch's Geometry; Or, a Sequel to Euclid - Bookswagon UAE
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Hirsch's Geometry; Or, a Sequel to Euclid

Hirsch's Geometry; Or, a Sequel to Euclid


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About the Book

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. 1827 Excerpt: ...This assumption gives, --= iw = 0785..., Cos. ii = 0707...; whence we 180 4 r conclude, that i/, is actually less than 45, but cannot be widely different from it, because these two magnitudes first differ in the second decimal place. If.. we put = 40; then we have--= It = 0-698..., and Cos. L=0-766..., 180 and consequently p 40. After having in this way previously convinced ourselves, that the value of p lies between 40 and 45; we can then approximate it more nearly by means of the proportional parts. To effect this, try the two assumptions xp = 41, p = 43. 343370: 231186 = 2: 1V20', nearly. 3. We have... p = 41 +1. 20'. Since this value differs but very little from the true one, as the following calculation shews, calculate, in the second place, on the assumption ip = 42. 21'. yfi = 42. 20'. /Oll=0-8685598 1 log.Cos.xp = 9-8687851-10 Error 2253 Subtract-608 Error 2861 Difference of errors. Again, put 2861: 2253 = l': 47', nearly. We obtain.. = 42. 20'. 47, and in this value the seconds are perfectly right, of which we can be convinced, by assuming xp greater or less by, and making the trial with it. However, the approximation cannot be continued further, for then it would be necessary to make use of logarithms with more than seven decimal places. Euler, in the above-cited work, by these means finds P = 42. 20'. 47. 14w. From this value of i/, we further obtain 0 = + 90 = 132. 20'. 47. 14w. Remark. Kaistncr treats this problem in a similar but more general way (Geometrical Treatise, 2nd Collection, p. 129, &c), for he gives a method how to find a segment having a given proportion to the area of the circle. SECTION LXV. Peob. Two circles intersect each other; the radii of these circles, together with the line which joins th...


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Product Details
  • ISBN-13: 9781130180589
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 40
  • Spine Width: 2 mm
  • Width: 189 mm
  • ISBN-10: 1130180581
  • Publisher Date: 01 Mar 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 91 gr


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