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Elements of Trigonometry, Plane and Spherical; With the Principles of Perspective, and Projection of the Sphere

Elements of Trigonometry, Plane and Spherical; With the Principles of Perspective, and Projection of the Sphere


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This historic book may have numerous typos, missing text or index. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. 1772. Not illustrated. Excerpt: ... Of oblique-angled spherical triangles. Fig. 5. 26. If each of the angles ACB, ABC, which arc at the base of an oblique-angled spherical triangle BAC, be either obtuse or acute, the arc of a great circle AN, described through the other angular point A, at right angles to the base, shall be within the triangle BAC. But if one of the angles ACD, at the base of the triangle CAD, be acute, and the other angle ADC at the base obtuse, the perpendicular AN shall be without the triangle CAD [art. 5.], 27. If each of the angles ADB, DBA, and DAB, of a spherical triangle BAD, be acute, each of the sides AB, AD, and DB, shall be less than a quadrant, and e contra [art. 6.]': and therefore, if one side of an oblique-angled spherical triangle be greater than a quadrant, the opposite angle shall be obtuse; if each of two angles be obtuse, and the third acute, each of the sides opposite to the obtuse angles shall be greater than a quadrant, and the side opposite to the acute angle shall be less than a quadrant. - - 28. If each of the sides AC, AB, and C c CB, CB, of a spherical triangle BAC, be greater than a quadrant; or if each of two sides be greater than a quadrant, and if the third side be a quadrant, each of the angles (hall be obtuse [art. 5. & 6 ]: and if each of two sides of an oblique-angled spherical triangle be less than a quadrant, but the third side greater than a quadrant, the angle opposite to the greater side shall be obtuse, and each os the other angles shall be acute. PROP. X. THEOR. Fig. 5. 29. The Jines of any two fides AC, AB, of any spherical triangle BAC, are to one another, as the fines of the angles ABC, ACB, opposite to these fides; that is, the fine of AC is to the fine of AB, as the fine of the angle ABC to the fine of the angle ACB. Through A...


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Product Details
  • ISBN-13: 9780217800280
  • Publisher: General Books
  • Publisher Imprint: General Books
  • Height: 246 mm
  • No of Pages: 46
  • Spine Width: 3 mm
  • Width: 189 mm
  • ISBN-10: 0217800289
  • Publisher Date: 11 Jan 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 100 gr


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