A Course of Mathematics Volume 1; For the Use of Academies, as Well as Private Tuition
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A Course of Mathematics Volume 1; For the Use of Academies, as Well as Private Tuition

A Course of Mathematics Volume 1; For the Use of Academies, as Well as Private Tuition


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About the Book

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. 1818 Excerpt: ...angle is measured by half the difference of the two arcs Ac, Db, intercepted by the two secants. Draw the chord Af parallel to en. Then, because the lined Af, en. are parallel, and Ab cuts them, the ai.gles on the same side A. and niu are i qual ih 14). But the angle A, at the circumference. is measured hy half the arc Bf (th. 49), or of the difference of Df and Db: therefore the equal angle E is also measured by half the difference of Df, Db. Again, because the chords Af, Cd, are parallel, the arcs Ac, Fb, are equal (th. 56); therefore the difference of the two two area Ac, Bb, is equal to the difference of the two Dp, Db. Consequently the angle E, which is measured by half the latter difference, ii also measured by half the former.. E. D. THEOREM LX. The Angle formed by Two Tangents, is Measured by Half the Difference of the two 1ntercepted Arcs. Let Eb, Ed, be two tangents to a circle at the points A, c; then the angle E is measured by half the difference of the two arcs, Cfa, cot.. For, draw the chord Af parallel to Ed. Then, because the lines Af, Ed, are parallel, and Eb meets them, the angles on the same side A and E are equal (th. 14). But the angle A, formed by the chord Af and the tangent Ab, is meaured by half the arc Af (th. 48); therefore the equal angle E is also measured by half the same arc Af, or half the difference of the arcs Cfa and Cf, or Cqa (th. 57). Carol. ln like manner it is proved, that the angle E formed by a tangent Ecu, and secant Eab, is measured by half the difference of the two intercepted arcs Ca and ers. THEOREM LXt When two Lines, meeting a Circle each in two Points, Cut one another, either Within it or Without it; the Rectangle of the Parts of the one, is Equal to the Rectangle of the Parts of the other; the Parts of each...


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Product Details
  • ISBN-13: 9781231274019
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 142
  • Spine Width: 8 mm
  • Width: 189 mm
  • ISBN-10: 1231274018
  • Publisher Date: 01 May 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 268 gr


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