Observations on the Nature of Demonstrative Evidence; With an Explanation of Certain Difficulties Occurring in the Elements of Geometry, and Reflections on Language
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Observations on the Nature of Demonstrative Evidence; With an Explanation of Certain Difficulties Occurring in the Elements of Geometry, and Reflections on Language

Observations on the Nature of Demonstrative Evidence; With an Explanation of Certain Difficulties Occurring in the Elements of Geometry, and Reflections on Language


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About the Book

This historic book may have numerous typos, missing text or index. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. 1793. Not illustrated. Excerpt: ... Euclid's 20th definition of book the 7th, the first number is the same multiple, or part of the second, as the third is of the fourth; we, say, that the first bears the fame proportion to the second, that the third bears to the fourth. In making experiments upon any four magnitudes, of which we perceive the first to be exactly as great, when compared to the second, as the third compared to the fourth; we shall quent demand, it is convenient to have ready bundled up for exchange in conversation, to save the trouble of counting them out, one by one. In algebra the signs are arbitrary; and hence their force is perfectly clear. The fense is not obscured by the intrusion of any collateral signification, nor do we pre-suppose that knowledge of the import of the terms, which often with respect to complex terms, does not exist, but assign it precisely beforehand. Mr. Ludlam informs his readers, " that the idea of ratio is a simple idea," p. 166. Such is his appre-i hension of the nature of terms. find, that when we double the first and third upon themselves any equal number of times, they will for ever be respectively as great, when compared to the second and fourth, either remaining as at first, or alfa doubled upon themselves any equal number of times; so that having clearly conceived this by the help of trials upon various magnitudes, we shall be aslured, that if the first and third of four magnitudes, be taken any equal number of times, and the magnitudes thence resulting shall not be exactly as great, when respectively compared to the second and fourth, or their equimultiples, the one as the other, then the original four magnitudes cannot have been exactly as great, the first compared to the second, as the third compared to the fourth. From this constant correspo...


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Product Details
  • ISBN-13: 9781151321916
  • Publisher: General Books
  • Publisher Imprint: General Books
  • Height: 246 mm
  • No of Pages: 30
  • Spine Width: 2 mm
  • Width: 189 mm
  • ISBN-10: 1151321915
  • Publisher Date: 01 Jan 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 73 gr


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Observations on the Nature of Demonstrative Evidence; With an Explanation of Certain Difficulties Occurring in the Elements of Geometry, and Reflections on Language
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Observations on the Nature of Demonstrative Evidence; With an Explanation of Certain Difficulties Occurring in the Elements of Geometry, and Reflections on Language
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