The Elements of Euclides; Viz. the First Six Books, Together with the Eleventh and Twelfth the Errors, by Wich Theon, or Others, Have Long Ago Vitiate

The Elements of Euclides; Viz. the First Six Books, Together with the Eleventh and Twelfth the Errors, by Wich Theon, or Others, Have Long Ago Vitiate

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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 edition. Excerpt: ...is lefs than the (--ry-' cone EN. In the fame manner it may be demonstrated that the circle EFGH is not to the circle ABCD, as the cone EN to any folid lefs than the cone AL. Nor can the circle ABCD be to the circle EFGH, as the cone AL to any solid greater than the cone EN: For, if it be possible, let it be fo to the folid. I, which is greater than the 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 a M-5- 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 the 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 iji 5. linders are triple of the cones, each to each. Therefore, as e i0. n. 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 arc to one another as their bases. QE. D. PROP. XII. T H E O R. SIMILAR cones and cylinders have to one another See N. 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...show more

Product details

  • Paperback | 150 pages
  • 189 x 246 x 8mm | 281g
  • Rarebooksclub.com
  • Miami Fl, United States
  • English
  • black & white illustrations
  • 1236551478
  • 9781236551474