Items related to Euclid's Elements. Vol. II.; Containing the seventh,...
Euclid's Elements. Vol. II.; Containing the seventh, eighth, ninth, tenth, thirteenth, fourteenth and fifteenth books with the data being the ... Keil. Now first translated from Dr. Gregory - Softcover
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. 1745 Excerpt: ...EF, making the Breadth EL. Whence by 23. 10.EL is rational, and Incommenfurable in Length to E F. Again, becaufe the Rectangle contain'd under AC, BC is medial; twice the Rectangle contain'd under AC, CB will be medial. But it is equal to the Parallelogram G H: Wherefore G H too is medial, and is apply'd to the rational Line EF, making the Breadth HL. Wherefore HL is rational, and Incommenfurable to £F in Length. And becaufe from Hyp. AC,CB are Commenfurable in Power only, A C mail be Incommenfurable to CB in Length. But as A C to CB, fo by i. 6. is the Square of AC to the Rectangle under AC, C B: Therefore the Square of A C is Incommenfurable to the Rectangle contain'd under A C, C B, But by 16. i o. the Squares of AC, CB are Commenfurable to the Square of AC; and twice the Rectangle under AC, CB is Commenfurable to that under AC, CB: Therefore the Squares ©f A C, C B are Incommenfurable to twice the Rectangle contain'd under AC, C B. And by Comjlr. the Parallelogram E G is equal to the Squares of AC, C B; and H G equal to twice the Rectangle under A C, C B: Therefore E G is Incommenfurable to H G. But as E G is to H G, fo by i. 6. is the right Line EL to HL: Wherefore EL 'is Incommenfurable toHL in Length. And they are both Rationals. Wherefore EL, HL are Rationals Commenfurable only in Power; and fo by 74. to.J EH is an ApoTome, and H L congruous thereto. After the fame Manfter we demonftrate that HM alfo is congruous to it: Therefore more than one right Line, being Commenfurable only in Power to the whole, is congruous to an Apo tome, which by 80. io. is impoflible. Therefore to a fecond medial Apotome there is congruous but one medial right Line, Commenfurable only in Power to the whole, and containing a medial Rectangle with the whole. W. W....
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- PublisherRareBooksClub.com
- ISBN 10 1235926060
- ISBN 13 9781235926068
- BindingPaperback
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