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Home > Art, Film & Photography > The Elements of Plane Geometry Volume 3; Comprising the Definitions of the Fifth Book, and the Sixth Book in General Terms, with Notes and Observations. Also a Collection of Theorems, Loci, Porisms, and Problems
The Elements of Plane Geometry Volume 3; Comprising the Definitions of the Fifth Book, and the Sixth Book in General Terms, with Notes and Observations. Also a Collection of Theorems, Loci, Porisms, and Problems

The Elements of Plane Geometry Volume 3; Comprising the Definitions of the Fifth Book, and the Sixth Book in General Terms, with Notes and Observations. Also a Collection of Theorems, Loci, Porisms, and Problems


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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. 1845 Excerpt: ...= to those about the other, as being radii of = circles;.-. the lines subtending them are =; &c. Schol. Whatever has been demonstrated in the preceding propositions of equal circles, is also true of the same circle. PROP. 30. PROB. To bisect a given arc. Connect its extremities; bisect the connecting line, and draw from the point of bisection a line at right angles to it to meet the circumference; it bisects the arc. For, connect the point, in which it meets the circumference, with the extremities of the bisected line. Then in the triangles formed by those connecting lines, the half lines and common perpendicular; a half line and perpendicular in one are respectively = to the other half line and perpendicular in the other, and the contained angles are = being right;.-. the lines, opposite to them or the connecting lines, are =;.-. the arcs, which they subtend, are s; &c. PROP. 31. THEOR. In a circle, the angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is an acute angle; and the angle in a segment less than a semicircle is obtuse. Part 1. The angle in a semicircle is a right angle. Draw a diameter connecting the extremities of the sides about the angle, and join the vertex of it with the centre. Then this connecting line being = to each part of the diameter at each side of the centre, the sum of the angles contained by it and each side of the given angle, i. e. the angle in the given semicircle, is (by prop. 5, b. 1) = to the sum of the angles contained by the diameter and sides about the given angle;.-. (by cor. 1, prop. 32, 1, ) said angle in semicircle is right;.-. &c. Part 2. The angle in a segment, greater than a semicircle, is acute. Draw a diameter through the extremity, (remote from the given angle, ...


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Product Details
  • ISBN-13: 9781236233752
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 78
  • Spine Width: 4 mm
  • Width: 189 mm
  • ISBN-10: 1236233751
  • Publisher Date: 01 May 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 154 gr


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The Elements of Plane Geometry Volume 3; Comprising the Definitions of the Fifth Book, and the Sixth Book in General Terms, with Notes and Observations. Also a Collection of Theorems, Loci, Porisms, and Problems
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