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The construction in most vote reply in Compass-and-straightedge construction of the square root of a given line? uses similar traingles and uses $$\frac{AC}{AD}=\frac{AD}{AB}$$ to compute square root.

It seems that if we know how to do ratios, it is a given that we can do sqrt (that is sqrt can be replaced by ratio) right? If this is correct then to what extent can sqrt replace division in ruler and compass construction?

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  • At first sight it cannot. If you can do addition, subtraction, multiplication and square root, you cannot do division. – André Nicolas Sep 11 '15 at 23:08
  • Is there a proof? –  Sep 11 '15 at 23:09
  • @Arul-What exactly do you mean by - "to what extent can sqrt replace division in ruler and compass construction?" – Soham Sep 18 '15 at 11:52
  • @Arul-Also why do you say - "that is sqrt can be replaced by ratio"?This is the application of similarity to find square root. – Soham Sep 18 '15 at 11:54
  • @Arul-You can also computer square root using rulers.To what extent you can find it depends in the least count of the ruler. – Soham Sep 19 '15 at 06:25
  • @tatan What I am trying to say is sqrt becomes evident when you equal two divides. Is there a comparable operation to get divide from sqrt? –  Sep 19 '15 at 06:35
  • @Arul-By equal two divides do you mean equal two ratios? – Soham Sep 19 '15 at 06:39
  • $\frac{ac}{ad} = \frac{ad}{ab}$ –  Sep 19 '15 at 06:40

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