Exercises on the Geometry and Measurement of Plane Figures, Being Solutions of the Theorems, Problems and Questions in 'Wormell's Modern Geometry'

Exercises on the Geometry and Measurement of Plane Figures, Being Solutions of the Theorems, Problems and Questions in 'Wormell's Modern Geometry'

By (author) 

List price: US$13.95

Currently unavailable

Add to wishlist

AbeBooks may have this title (opens in new window).

Try AbeBooks

Description

This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1883 edition. Excerpt: ... Construct a circumference such that A B shall be a chord and shall cut off a segment, the angle of which shall be equal to the angle C. From A draw A F perpendicular to A B and equal to the given height. Through F draw F E parallel to A B and meeting the circumference in C. A C B is the triangle required. 5th. Let A B, Z C, and the height A D be given. Make an angle A C B = the given angle, and find in the side C A a point, A, such that its distance from C B = the given height (as in Problem 5). From A, with radius A B, describe an arc cutting C B in B, then A B C is the triangle required. 52. Construct a triangle, having given the radius of the inscribed circle, one angle, and the height taken from it. Analysis.--Suppose the problem solved, and let A B C be the triangle. Let A G be the height from A, and let O be the centre of the inscribed circle, and OD, OE, the perpendiculars from O on the sides; then AO bisects the angle A O E = the given radius, and B C is a tangent to the inscribed circle and also a tangent to the circle described with A as centre and A G as radius. Synthesis.--Make an zCAB = the given angle, and bisect it in AO. Take a point, O in AO, such that its distance, OE, from AC = the given radius, and describe a circle with O as centre and O E as radius. Also, with A as centre and the given height as radius, describe another circle. Draw B C a common tangent to these two circles; then ABC will be the circle required. 53. Describe with given radii two circles which shall touch each other and two straight lines which intersect. Let A B, A C be the straight lines. Let M N be a straight line parallel to A B at a distance equal to the first radius, and, M R a straight line parallel to A C at a distance equal to the B..".show more

Product details

  • Paperback | 30 pages
  • 189 x 246 x 2mm | 73g
  • Rarebooksclub.com
  • United States
  • English
  • black & white illustrations
  • 1236944364
  • 9781236944368