The Works of John Playfair; With a Memoir of the Author ... Volume 3

The Works of John Playfair; With a Memoir of the Author ... Volume 3

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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1822 edition. Excerpt: ...magnitudes to one another. Now, in order to accomplish this, Dr Simson frequently employs two statements of the general hypothesis, which he compares together; as for instance, in his analysis of the last Porism, he assumes, not only E, any point whatsoever in the line DE, but also another point O, any whatsoever in the same line, to both of which he supposes lines to be inflected from the given points A and B. This double statement, however, cannot be made, without rendering the investigation long and complicated; and therefore it may be of use to remark, that it is never necessary, but may always be avoided by an appeal to simpler Porisms, or to Loci, or to the propositions of the Data. I shall give the following Porism as an example, where this is done with some difficulty, but with considerable advantage, in regard to the simplicity and shortness of the investigation. Prop. V. Porism. Fig. 11. 24. Let there be three straight lines AB, AC, CB given in position, and from any point whatsoever in one of them, as D, let perpendiculars be drawn to the other two, as DF, DE; a point G may be found, such, that if GD be drawn from it to the point D, the square of that line shall have a given ratio to the sum of the squares of the perpendiculars DF and DE, which ratio is to be found. Draw from A and B the lines AH, BK at right angles to BC and CA, and divide AB in L, so that AL may be to LB in the given ratio of the square of AH to the square of BK, or, which is the same, of the square of AC to the square of CB. The point L is therefore given; and if N be taken so as to have to AL the same ratio that AB" has to AH2, N will be given in magnitude. Also since AH: BK2:: AL: LB, and AHS: AB2:: AL: N, ex ajquo BK2: AB2:: LB: N. From L draw LO,show more

Product details

  • Paperback | 78 pages
  • 189 x 246 x 4mm | 154g
  • United States
  • English
  • black & white illustrations
  • 1236974921
  • 9781236974921