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The Elements of Euclid, with Dissertations, by J. Williamson. Vol. 1 [Comprising Book 1-6]. Volume 1

The Elements of Euclid, with Dissertations, by J. Williamson. Vol. 1 [Comprising Book 1-6]. Volume 1


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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: ... to DF let CH which is common be added; therefore the whole AH is equal to DF and DL: but AH is the rectangle contained by AD, DB for DH is equal to DB (by cor. to 4. 2.): but FD, FD, DL or FDL is called a Gnomon (by dcf. 2. 2.); therefore Bookli. the Gnomon FDL is equal to the rectangle contained by AD, DB: Let LG which is common be added; which (by Cor. to 4. 2.) is equal to the square of CD: wherefore the Gnomon FDL and the square LG is equal to the rectangle contained by AD, DB and the square of CD: but the Gnomon FDL and the square LG is the whole square CEFB, which is the square of CB: Wherefore the rectangle contained by AD, DB together with the square of CD is equal to the square of CB. Wherefore if a straight line be cut into equal and unequal segments; the rectangle contained by the unequal segments of she whole line, together with the square of the line between the points of section, . is equal to the square of half the line. Which was to be demonstrated. PROP. VI.. If a straight line be cut in halves, and any straight line be added to it in a straight line; the rectangle contained by the whole with the part produced, and the. part produced, together with the square of half the line; is equal to the square described upon the compounded line, that is of half the line and the part produced, as upon one line. For let any straight line AB be cut in halves at the point C, and let any straight line BD be added to it in a straight line: I fay that the rectangle contained by AD, DB together with the square of BC is equal to the square of CD. For let the square CEFD be described (by 46. 1.) upon CD; and let DE be joinedand through the point B let (by 31.1.) BHG be drawn parallel to either os the lines CE, DF; and through the point H, let KLM be drawn paral..


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Product Details
  • ISBN-13: 9781130002249
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 100
  • Spine Width: 5 mm
  • Width: 189 mm
  • ISBN-10: 1130002241
  • Publisher Date: 01 Mar 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 195 gr


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The Elements of Euclid, with Dissertations, by J. Williamson. Vol. 1 [Comprising Book 1-6]. Volume 1
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