The First Six Books of the Elements of Euclid, with Numerous Exercises

The First Six Books of the Elements of Euclid, with Numerous Exercises

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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. 1853 edition. Excerpt: ...a circle, when the extremities of it are in the circumference of the circle. Def.nitions VI. and VII. Proposition I.--Pkoblem. In a given circle to place a straight line equal to a given straight line not greater than the diameter of the circle. Let a b C he the given circle, and d the given straight line, not greater than the diameter of the circle. Draw b C the diameter of the circle a b C; then, if b C is equal to d, the thing required is done, for in the circle a b C a straight line b C is placed equal to d; but, if it is not, b C is greater than d, make Ce equal (i. 3) to d, and from the centre C, at the distance Ce, describe the circle aef, and join Ca: therefore, because C is the centre of the circle a e f, C a is equal to C e: but d is equal to C e; therefore d is equal to C a. Wherefore in the circle a b C, a straight line is placed equal to the given straight line d, which is not greater than the diameter of the circle. Which was to be done. Proposition II.--Problem. In a given circle to inscribe a triangle equiangidar to a given triangle. Let a b C he the given circle, and d e f the given triangle; it is required to inscribe in the circle a b C a triangle equiangular to the triangle def Draw (iii. 17) the straight line gah touching the circle in the point a, and at the point a, in the straight line ah, make (i. 23) the angle h a C equal to the angle d e f, and at the point a, in the straight line a g, make the angle gab equal to the angle dfe, and join bC: therefore because hag touches the circle abC, and EC is drawn from the point of contact, the angle h a C is equal (iii. 32) to the angle a b C in the alternate segment of the circle; but h a C is equal to the angle d e f', therefore also the angle a b C is equal to def For the same...show more

Product details

  • Paperback | 54 pages
  • 189 x 246 x 3mm | 113g
  • Rarebooksclub.com
  • Miami Fl, United States
  • English
  • black & white illustrations
  • 1236648919
  • 9781236648914