## Proposition 22

 If three numbers are in continued proportion, and the first is square, then the third is also square. Let A, B, and C be three numbers in continued proportion, and let A the first be square. I say that C the third is also square. Since between A and C there is one mean proportional number, B, therefore A and C are similar plane numbers. But A is square, therefore C is also square. VIII.20 Therefore, if three numbers are in continued proportion, and the first is square, then the third is also square. Q.E.D.
This proposition is used in a few propositions in this and the next book starting with VIII.24.

Next proposition: VIII.23

Previous: VIII.21

 Select from Book VIII Book VIII intro VIII.1 VIII.2 VIII.3 VIII.4 VIII.5 VIII.6 VIII.7 VIII.8 VIII.9 VIII.10 VIII.11 VIII.12 VIII.13 VIII.14 VIII.15 VIII.16 VIII.17 VIII.18 VIII.19 VIII.20 VIII.21 VIII.22 VIII.23 VIII.24 VIII.25 VIII.26 VIII.27 Select book Book I Book II Book III Book IV Book V Book VI Book VII Book VIII Book IX Book X Book XI Book XII Book XIII Select topic Introduction Table of Contents Geometry applet About the text Euclid Web references A quick trip