The Elementary Geometry of the Right Line and Circle

The Elementary Geometry of the Right Line and Circle

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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. 1875 edition. Excerpt: ...ARB being an isosceles triangle, the rectangle AO-BO is (Theor. 19, Case 2) equal to the difference of the squares of RO and RA. In like manner, the rectangle AXO-BXO is equal to the difference of the squares of RO and RAV But RA and RAV being radii, are equal; and the differences of the square of RO and their squares are equal. Therefore, the rectangles AO-BO and Afl-Bft are equal, as stated. These rectangles are also equal each to the square of the See Appendix, Note 5. tangent to the circle from O. For, OT being the tangent, and 727, the radius to ha point of contact, the triangle OTR (Theor. 15, Chap. II.) is right-angled; and the square of OT, consequently (Theor. 14), is equal to the difference of the squares of RO and RT; that is, of RO and the radius RA, or (Theor. 19) to the rectangle under AO and BO, as stated. In the particular case when the chord CCX through O passes through the centre R, the line CCX being bisected at R and cut externally at O, the rectangle OO0CX is equal (Theor. 11) to the difference of the squares of OR and RC, that is, as in the case of the other chords, the difference of the squares of RO and of the radius, that is, to the square of the tangent OT. 23. Jf from a Point Outside a Circle two lines be drawn to it, one a Secant and the other meeting but not cutting the circle, so that the square of the meeting line be equal to the rectangle under the segments of the secant, the line so meeting is a Tangent to the circle. Let R be the circle, and OB A the secant from the point O, and 0T the line meeting but not cutting the circle, and RT a radius. Then, since the rectangle OA-OB (last Theor.) is equal to the difference of the squares of OR and of the radius, the square of OT must be equal to the difference of the..show more

Product details

  • Paperback | 56 pages
  • 189 x 246 x 3mm | 118g
  • Rarebooksclub.com
  • Miami Fl, United States
  • English
  • black & white illustrations
  • 1236586565
  • 9781236586568