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. 1896 edition. Excerpt: ...further assume that the key to Apollonius' solution is to be found in the third Book, and it is therefore necessary to examine the propositions in that Book for indications of the way in which he went to work. The three-line locus need not detain us long, because it is really a particular case of the ...
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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. 1896 edition. Excerpt: ...further assume that the key to Apollonius' solution is to be found in the third Book, and it is therefore necessary to examine the propositions in that Book for indications of the way in which he went to work. The three-line locus need not detain us long, because it is really a particular case of the four-line locus. But we have, in fact, in IIi. 53-56 Props. 74-76 what amounts to a complete demonstration of the theoretical converse of the three-line locus, viz. the proposition that, if from any point of a conic there be drawn three straight lines in fixed directions to meet respectively two fixed tangents to the conic and their chord of contact, the ratio of the rectangle contained by the first two lines so drawn to the square on the third line is constant. The proof of this for the case where the two tangents are parallel is obtained from m. 53 Prop. 74, and the remaining three propositions, m. 54-56 Props. 75, 76, give the proof where the tangents are not parallel. Tn like manner, we should expect to find the theorem of the four-line locus appearing, if at all, in the form of the converse proposition stating that every conic section tuts, with reference to any inscribed quadrilateral, the properties of the four-line locus. It will be seen from the note following Props. 75, 76 that this theorem is easily obtained from that of the three-line locus as presented by Apollonius in those propositions; but there is nowhere in the Book any proposition more directly leading to the former. The explanation may be that the construction of the locus, that is, the aspect of the question which would be appropriate to a work on solid loci rather than one on conies, was considered to be of preponderant importance, and that the theoretical converse was...
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Seller's Description:
New. Size: 7x1x9; Hardcover. In shrink wrap. No dust jacket. Good binding and cover. Clean, unmarked pages. clxx, 254 pages: illustrations; 23 cm. Originally published: Cambridge: University Press, 1896.
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Seller's Description:
Like New. 2003. Hardcover. Cloth, no dj. (as issued). Bright, clean, unread copy. Facsimile reprint of the edition published Cambridge, 1896. Fine. (Subject: ).
