The art of geometric construction can be traced back to the widespread, possibly universal, practice of marking out simple forms and measures on the Earth using pegs and cords geometry, literally Earth measure. Examples include ancient Egyptian rope stretchers, or harpenodaptai, who re-established land boundaries after the annual Nile flood, and ancient Indian altar construction techniques found in the Vedic Sulbasutras, the oldest surviving texts with geometric instruction. In time this became the more familiar mathematical discipline, practiced at a smaller scale. Plato (d. ca. 347 bc) first stipulated the strict use of only ruler and compass, the ideal simple forms of straight line and circle.This book is intended as a small practical guide to the field, inspired by the artisans' manuals penned by Abu'l-Wafa' al-Buzjani (d. 998) and Albrecht Durer (d. 1528). Some mathematical context and history is given, but no proofs. Unless noted, all constructions are mathematically exact. Readers are highly encouraged to try their hand at some of them there is no substitute for actually taking ruler and compass to paper.This book uses a simple code. Line ab means draw the straight line that passes through a and b. Segment is used in place of line for the section of a straight line defined by two endpoints. Circle o-a means draw a circle centred at o and passing through a. Circle radius ab centre o means draw a circle of compass opening length ab centred at o. Arc is used in place of circle for drawing only part of the circle. Sometimes, extra points are given to help improve accuracy when drawing, for example, line acb, or circle o-ab. Newly found points are noted in brackets. Occasionally a line made possible by new points is assumed drawn, and merely noted, and stages may also be grouped together for brevity. Fear not. All will be clear. Excerpted from Ruler and Compass: Practical Geometric Constructions by Andrew Sutton All rights reserved by the original copyright owners. Excerpts are provided for display purposes only and may not be reproduced, reprinted or distributed without the written permission of the publisher.
