The Leeds Correspondent; A Literary, Mathematical and Philosophical Miscellany Volume 3

The Leeds Correspondent; A Literary, Mathematical and Philosophical Miscellany Volume 3

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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. 1819 edition. Excerpt: ...equal a given ration and the locus of the point L is hence required. Whence obviously, having determined the points M, L', . K, take L'C: CR = KC: CM, and draw BR: the required locus is the right line BR. The locus of L will be a right line BR, under a far more general enunciation than that given in the pre-ent case. For, if BA, BP, BC, CA, be four lines given in position, and A', C P', K', any how given in AC: draw A'GD cutting BP, BC, in G, D: alsa C'GE, rreeting AB at E: let ED, K'F, intersect in L. The locus of L is a right line passing through B. If AD, CE, ET, be drawn as above: then the right line passing through T, D, shall always tend to the same given point N, in AM: and which point N is determined, by making AN: NM:: NM:: NC. In like manner, if the several lines be any how drawn, as specified in the theorem, and LI, a parallel to MA, meet BL' at I: the line passing through the rcoints D, I, shall always tend to the same given point The position of K being such, that AP: PM:: PL': PK; as appears from the analysis The line AM is divided harmonically in P and C; and AC is harmonically divided at P, L'. This question was originally proposed in No. 13 of the Mathematical Companion, by the late R. Nicholson, of Liverpool. In the succeeding number no solution appearing, I reproposed it in Number 15, Mr. N. TOl. III. K having then paid the debt of nature. Owing to the usual casualties incident to Geometrical Speculation it was still treated with unmerited neglect. It is now brought forward in the Correspondent, as a tribute of respect to the memory of that ingenious geometrician. By Mr. Whitehead. Let the lines be drawn as per question, and the other lines as per figure; then it is already known and is easily proved that "AM more

Product details

  • Paperback | 70 pages
  • 189 x 246 x 4mm | 141g
  • Miami Fl, United States
  • English
  • black & white illustrations
  • 1236540913
  • 9781236540911