Elements of Geometry, Containing the First Six Books of Euclid
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Book 1
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Book 1
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Book 1
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Elements of Geometry, Containing the First Six Books of Euclid

Elements of Geometry, Containing the First Six Books of Euclid


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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. 1826 Excerpt: ...right angle: PROPOSITION XXII. Theorem. which are les. Let ABDc be a circle, and Abdc a quadrilateral figure in it. Then any two opposite angles of -S2.1. it are equal" to two right angles; join Ad, Bc. Therefore because the three angles of every triangle are equal to two right angles, the angles Cab, Abc, Cba, are equal to two right angles. But the '. t1. 3. angle Abc is equalb to the angle Adb, for they are in the same segment, Abdc. And the angle Acb will De equal to the angle Adb, because they are in the same segment, AbcD: therefore the whole angle Bdc is equal to the angles Abc, Acb. Take away the angle Bac, which is common: the angles Bac, Abc, Acb, are equal to the angles Bac, Bdc. But the angles Bac, Abc, Acb, are equal to two right angles: wherefore also the angles Bac, Bdc, are equal to two right angles. In like manner we can demonstrate that the angles Abd, Acd, are also equal to two right angles. Therefore the opposite angles, &c. Q. E. D. Deduction. If two opposite angles of any trapezium be equal to two right angles, the other two angles are equal to two right angles, and a circle may be described about it. PROPOSITION XXIII. Theorem. Upon the same straight line, and on the same side of it, two similar segments of circles cannot be described which do not coincide with each other. For, if it be possible, on the same right line, Ab, let two similar segments of circles, Acb, Adb, be de scribed, which do not coincide with each other. Let the circum-ferences Acb, Adb, meet one ano-ther at the points1 A, B, and they, havea no other points common ex-A---B - 10.3. cept A, B. But between A, B, one will be interior, and the other exterior. In the interior take any point c, and join A c, which, produced, will meet the ext...


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Product Details
  • ISBN-13: 9781130777574
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 60
  • Spine Width: 3 mm
  • Width: 189 mm
  • ISBN-10: 113077757X
  • Publisher Date: 01 Mar 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 127 gr


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