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Home > History and Archaeology > History > Elements of Geometry, Containing Books I. to VI.and Portions of Books XI. and XII. of Euclid, with Exercises and Notes, by J.H. Smith
Elements of Geometry, Containing Books I. to VI.and Portions of Books XI. and XII. of Euclid, with Exercises and Notes, by J.H. Smith

Elements of Geometry, Containing Books I. to VI.and Portions of Books XI. and XII. of Euclid, with Exercises and Notes, by J.H. Smith


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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. 1878 Excerpt: ...Bisect L s ABC, ACB by the st. lines BO, CO, meeting in 0. I. 9 From 0 draw OB, OE, OF, x s to AB, BC, CA. I. 12. Then, in As EBO, DBO, V L EBO= L DBO, and L BEO= L BDO, and OB is common, .-. OE=OD. I. 26. Similarly it may be shewn that 0E= OF. If then a (c) be described, with centre 0, and radius OD, this (c) will pass through the pts. D, E, F; and v the L S at D, E and F are rt. L s, .-., BC, CA are tangents to the (c); III. 16. and thus a (c) DEF may be inscribed in the A ABC. Q. E. P. Ex. 1. Shew that, if OA be drawn, it will bisect the angle BAC. Ex. 2. If a circle be inscribed in a right-angled triangle, the difference between the hypotenuse and the sum of the other sides is equal to the diameter of the circle. Ex. 3. Shew that, in an equilateral triangle, the centre of the inscribed circle is equidistant from the three angular points. Ex. 4. Describe a circle, touching one side of a triangle and the other two produced. (note. This is called an escribed circle.) Let ABCD be the given square. It is required to inscribe a (c) in the square. Bisect AB, AD in E, F, I. 10. and draw EG to AD or BC, and FH to AB or DC. Let EG and FH intersect in 0. Then v.40 is a 7, .-. 0E=FA and OF=EA. I. 34. But v AB=AD, and.E, F are the middle pts. of AB, AD, .: FA=EA, and.-. OE=OF. Similarly, it may be shewn that OG=OF, and 0H=0E, and.-. OE, OF, OG, OH are all equal; and a (c), described with centre 0 and radius OE, will pass through E, F, G, H, and it will be touched by each of the sides of the square, V the L s at E, F, G, H are rt. l s. III. 16. Thus a (c) EFGH may be inscribed in the sq. ABCD. Q. E. F. Ex. 1. In what parallelograms can circles be inscribed? Ex. 2. If, from any point in the circumference of a circle, straight


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Product Details
  • ISBN-13: 9781130289701
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 68
  • Spine Width: 4 mm
  • Width: 189 mm
  • ISBN-10: 1130289702
  • Publisher Date: 01 Mar 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 141 gr

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Elements of Geometry, Containing Books I. to VI.and Portions of Books XI. and XII. of Euclid, with Exercises and Notes, by J.H. Smith
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Elements of Geometry, Containing Books I. to VI.and Portions of Books XI. and XII. of Euclid, with Exercises and Notes, by J.H. Smith
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