## Proposition 26

 Similar plane numbers have to one another the ratio which a square number has to a square number. Let A and B be similar plane numbers. I say that A has to B the ratio which a square number has to a square number. Since A and B are similar plane numbers, therefore one mean proportional number C falls between A and B. VIII.18 Take D, E, and F, the least numbers of those which have the same ratio with A, C, and B VII.33 or VIII.2 Then the extremes of them D and F are square. And since D is to F as A is to B, and D and F are square, therefore A has to B the ratio which a square number has to a square number. VIII.2,Cor Therefore, similar plane numbers have to one another the ratio which a square number has to a square number. Q.E.D.
This proposition is used in propositions IX.10 and X.9.

Next proposition: VIII.27

Previous: VIII.25

 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