Introduction to Geometry; A Manual of Exercises for Beginners (Paperback)

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. 1904 edition. Excerpt: ...letting OE fall on OH (6). (e) Cut straight from D to E (7) and open. The result is a regular hexagon (?). 2. (a) What is the relation between OD and OE? OE and DE (5)? (b) What kind of a triangle is DOE in 5? In 7? (c) Why does OE fall on OH? (d) Why is 8 a regular hexagon? 3. What kind of a figure will you get, if you cut from D (6) to a point on OE, one-fourth the length of OE from 0? 4. Make a regular dodecagon (12 sides) by folding and cutting. Exercise 60. 1. Make a regular pentagon by folding as follows: (o) Take a piece of paper 4 inches by 5 inches (i, Chart VI). (b) Fold lengthwise in halves (2) and mark 0, the middle point of the crease AB (3). (c) Turn up the corner B and place it so that B falls on DC (4). (d) Proceed with A as with B, only turning it under (5). (e) Fold the part DLOB in halves, laying LO beside OB. Measure OM equal to OA (6). (/) Cut along AM and open (7). 2. (a) Is 8 a regular pentagon? How would you assure yourself that it is? (For definition of regular polygon, see Exercise 34, page 37.) (6) How large is A AOM in 7? 3. Make a regular decagon by folding and cutting. Exercise 61. 1. Fold a piece of paper twice at right angles and cut off the folded corner, making a rhombus when the part cut off is opened out. Can you cut out a rhombus having two angles of 60 each? 2. Can you so cut a piece of paper, folded twice at right angles, that the part cut off will be a square? 3. Fold a square piece of paper to obtain a regular octagon. How do you determine the line along which you cut? What happens, if you should cut at an angle of about 30 to this line? 4. Give directions for cutting with one clip of the scissors: "According to well authenticated tradition, George Washington, Robert Morris, and John Boss, in...