A Treatis on Spherics

A Treatis on Spherics

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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. 1816 edition. Excerpt: ...having first been joined, (Art. 66.) a circle may be described about the spherical triangle, of which they are the angular points, exactly in the same manner, as a circle is described about a plane triangle, in E. 5. 4. The construction depends upon Art. 66. 102. 70; the proof follows from Art. 97. 079-) Cor. 1. Thus may a point be found, in the surface of a sphere, that shall be equally distant from the three angular points of a given spherical triangle in that surface. (180.) Cor. 2. The circle described about a spherical triangle is, in all cases, a lesser circle of the sphere.. For, if it were a great circle, then each of the sides of the triangle (Art. 7-) would be a semi-circumference; which (Art. 72.) is impossible. Prop. XIX. (181.) Problem. Two points on the surface of a sphere being given, of which the spherical distance is less than two quadrants, to describe a circle which shall pass through them, and which shall touch a given great circle of the sphere; the two points being both of them without the given great circle. Let A, B be the two given points, and GF the given great circle: it is required to describe a circle of the sphere, which shall pass through A and B, and which shall touch GF. See the figure in the next page. I Join (Art. 66.) A, B, and produce AB to meet GF'm F: take any point E, out of AB, and describe (Art 178.) a lesser circle AEB, passing through the three points A, E and B. From F draw (Art. 159.) the arch of a great circle, FE, touching AEB; and make (Art 92.) FG equal to FE: lastly, describe (Art. 178.) a lesser circle ABG, passing through A, B and G-. the circle ABG touches (Art. 177.) FG in G. Prop. XX. (182.) Problem. Two points on the surface of a sphere being given, of which the spherical distance is...show more

Product details

  • Paperback | 52 pages
  • 189 x 246 x 3mm | 109g
  • Rarebooksclub.com
  • Miami Fl, United States
  • English
  • black & white illustrations
  • 1236604792
  • 9781236604798