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Euclid's Elements [Book 1-6] with Corrections, by J.R. Young

Euclid's Elements [Book 1-6] with Corrections, by J.R. Young


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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. 1838 Excerpt: ...of one of them, will pass through the extremities of the other two, and be described about the triangle ABC. Which was to be done. PROP. VI. PROB. To inscribe a square in a given circle. Let ABCD be the given circle; it is required to inscribe a square in ABCD. 3 and Draw any diameters, AC, BD, at right angles il. l. to one another, and join AB, BC, CD, DA: the figure ABCD shall be the square required. Because BE is equal to ED, for E is the centre, and that EA is common, and at right angles to BD; the base BA is 4 1 equal to the base AD: and for the like reason, BC, CD are respectively equal to BA, AD; therefore the quadrilateral figure ABCD is equilateral. It is also rectangular; for the straight line BD being the diameter of the circle ABCD, BAD is a semicircle; wherefore the angle BAD is a 3l. 3. right angle: for a like reason, each of the angles ABC, BCD, CD A is a right angle: therefore the quadrilateral figure ABC 1.) is rectangular: and it has been shown to be equilateral; t30 uef l tnerefore it is af square; and it 'is inscribed in the circle ABCD. Which was to be done. PROP. VII. PROB. To describe a square about a given circle. Let ABCD be the given circle; it is required to describe a square about it. Draw two diameters AC, BD of the circle ABCD, at right angles to one another, and through the points A, B, C, D, draw FG, GH, HK, KF touching the circle: the figure GHKF shall be the square required. Because FG touches the circle ABCD, and EA is drawn from the centre E to the point of contact A, the angles at - s A are right angles: for a similar reason, the angles at the points B, C, D are right angles: and because the angle AEB is a right angle, as likewise is #1B., EBG, GH is parallel to AC: for JJ a similar reason AC is parall...


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Product Details
  • ISBN-13: 9781232233909
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 64
  • Spine Width: 3 mm
  • Width: 189 mm
  • ISBN-10: 1232233900
  • Publisher Date: 01 May 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 132 gr

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Euclid's Elements [Book 1-6] with Corrections, by J.R. Young
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