It is possible to do simple arithmetic operations, using a compass and straightedge! Addition and Subtraction are no problem. Multiplicationand Division are a little trickier, but nonetheless are possible!

Adding two given segments is very easy. Simply copy one segment onto the endpoint of the other, and you get the sum of the two segments!


To subtract two segments, simply find the intersection of the two. Place one on top of the other, and where they don't cross each other is the difference between the two!
Given segments AB (yellow) and CD (cyan), find the product of the two.
  1. Draw a line. Construct OG on that line, so that OG = 1.
  2. On that same line, find OE, so that OE = CD.
  3. Draw another line from point O. Draw OF on that line, so that OF = AB.
  4. Draw a line through GF, and draw a line parallel to GF through point E, which will intersect OF at H.
  5. OH is the product of OE and OF.


Finding the quotient of two segments is almost the same as finding the product. It's simply the reverse!
  1. Draw any line. Find OG on that line, so that OG = 1.
  2. On line OG, find E so that OE = CD.
  3. From point O, draw another line. Find F on that line, so that OF = AB.
  4. Connect points EF with a line, and find a line parallel to EF through point G. That line will cross OF at H.
  5. HF is therefore the quotient of OF and OE.

© Apr.18 2003 Robin Hu. All Rights Reserved.