A Complete Course of Pure Mathematics

A Complete Course of Pure Mathematics

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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. 1830 edition. Excerpt: ...the given triangle, viz. A = A', B-B', C= C. The measure of the angle A being DB, if from A' as centre and with radius AO the arc HI be described, it will be the half of BD; whence, taking in any part of the circumference the arc BD = 2HI, the sides AB and AC will pass through B and D. Also, the angle BCD being the supplement of C, we shall have the position of the vertex C, by describing on the chord BD a segment BCcD containing this angle 2- '-C, and the straight line DC A will give the point A and the triangle required. The point c gives the triangle aBc, another solution of the problem; besides which we may give to the chord BD an infinite number of positions, and so have as many double solutions. 209. The angle BA C, of which the vertex A is in any point of the plane of the circle Qfigs. 56 and 57, has for its measure the half of the sum or the difference of the arcs BC, DE comprised between the sides; accordingly as the vertex A is within or without the circumference. Draw EF parallel to DC. 1 1. If A is situated within the circumference fig. 56, the measure of the angle E = BA C is BF = l(BC+ CF) = (BC + DE). 2. If A is situated without the circle Qfig. 57, the measure of the angle A = CEF is CF = (CB-BF) = (CB-ED). Thus the measure of the angle A is (a b), making d = C, b = DE. This formula is also general, for b = 0 answers to the case in which the vertex is on the circumference, and b = a to that in which it is at the centre. PROPORTIONAL LINES. SIMILAR TRIANGLES. 210. Let AH, ah fig, 58 be any two straight lines; if along one of them AH we take the equal parts AB, BC, CD.... and through the points of division draw the parallels Aa, Bb, Cc..., tih, in any direction...show more

Product details

  • Paperback | 150 pages
  • 189 x 246 x 8mm | 281g
  • Rarebooksclub.com
  • Miami Fl, United States
  • English
  • black & white illustrations
  • 1236563298
  • 9781236563293