The First Six Books; Together with the Eleventh and Twelfth download pdf
The First Six Books; Together with the Eleventh and Twelfth download pdf

The First Six Books; Together with the Eleventh and Twelfth.cEUCLID,
The First Six Books; Together with the Eleventh and Twelfth
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Author: EUCLID,
Page Count: 148 pages
Published Date: 21 May 2012
Publisher: Not Avail
Publication Country: United States
Language: English
ISBN: 9781236380197
File size: 28 Mb
Download Link: The First Six Books; Together with the Eleventh and Twelfth
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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. 1781 Excerpt: ...cone EN: Therefore, by inversion, as the circle EFGH to the circle ABCD, fo is the folid I to the cone AL: But as the folid I to the cone AL, fo is the cone EN to fome folid, which must be lefs than the cone 14. J. AL, because the folid I is greater than the cone EN: Therefore, as the circle EFGH is to the circle ABCD, fo is the cone EN to a folid lefs than the cone AL, which was shewn to be impossible: Therefore the circle ABCD is not to the circle EFGH, as the cone AL is to any folid greater than the cone EN: And it has been demonstrated that neither is the circle ABCD to the circle EFGH, as the cone AL to any folid lefs than the cone EN: Therefore the circle ABCD is to thfe circle EFGH, as the cone AL to the cone EN: But as the cone is to the cone, fo b is the cylinder to the cylinder, because the cy-b ij. j. linders are triple.' of the cones, each to each. Therefore, asc 10. it. the circle ABCD to the circle EFGH, fo are the cylinders upon them of the fame altitude. Wherefore cones and cylinders of the fame altitude are to one another as their bases. QE. D. PROP. XB. THiOR. SIMILAR cones and cylinders have to one another See H. the triplicate ratio of that which the diameters of their bases have Let the cones and cylinders of which the bases are the circles ABCD, EFGH, and the diameters of the bases AC, EG, and KL, MN the axes of the cones or cylinders, be similar: The cone of which the base is the circle ABCD, and vertex the point L, has to the cone of which the base is the circle EFGH. and vertex N, the triplicate ratio of that which AC has to EG. For, if the cone ABCDL has not to the cone EFGHN the triplicate ratio of that which AC has to EG, the cone ABCDL shall have the triplicate of that ratio to fome folid which is lefs S 2 of Book XII. or ...

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