Elements of the Conic Sections
Format: Paperback
ISBN13: 9780217467261
Paperback|9780217467261
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Purchase of this book includes free trial access to www.million-books.com where you can read more than a million books for free. This is an OCR edition with typos. Excerpt from book: to four times 3. 2. Elem.] the rectangle QMB: but MQ or QK, is equal to DR, and MB to DA; therefore the fquare of QR is equal to four times the rectangle RDA: and fince QR, EL are ordinately applied to the diameter AD, the fquare of QR is to the fquare of EL as 2 cor. of the preceding proposition] RD to LD, that is, as four times the rectangle RDA to four times the rectangle LDA: but the fquare of QR, as hath been proved, is equal to four times the rectangle RDA; therefore the fquare of EL is equal to four times the rectangle LDA, that is, to the rectangle contained by the abfcifTa LD and the parameter of the diameter AD, It was from the property above demon- flrated, that Apollonius named ' the curve line which is the fubject of this book the Parabola. Cor. i. If from a point E to AD, a diameter of the parabola, a ftraight line EL is drawn parallel to ftraight lines ordinately applied to the diameter AD, and meeting the fame AD below its vertex D; if the fquare of EL is equal to the rectangle contained by the abfcifla LD and the parameter rameter of the diameter AD; the point E is in the parabola. For fince the point L is within 4. i.] the Fig. 4. parabola, the ftraight line EL neceflarily meets cor. 8. i.J the parabola: if, therefore, EL does not meet the parabola in the point E, on the fame fide of the diameter with E, let it meet it, if poffible, in fome other point, nearer, or more remote, from the diameter, than E is: let this other point be (.; then the fquare of L is equal to the rectangle contained by LD, and the parameter of the diameter, that is, according to the hypothefis, to the fquare of EL; which is abfurd. Cor. 2. If from two points E, Q, one of which, Q, is in the parabola, there be drawn to the diameter AD ftraight lines EL, QR, parallel ...
| ISBN-13 | 9780217467261 |
|---|---|
| ISBN-10 | 0217467261 |
| Weight | 0.56 Pounds |
| Dimensions | 9.00 x 6.00 x 0.38 In |
| List Price | $14.14 |
| Format | Paperback |
|---|---|
| Pages | 166 pages |
| Publisher | |
| Published On | 2009-08-01 |
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