Proposition 26

 If an odd number is subtracted from an odd number, then the remainder is even. Let the odd number BC be subtracted from the odd number AB. I say that the remainder CA is even. Since AB is odd, subtract the unit BD, therefore the remainder AD is even. For the same reason CD is also even, so that the remainder CA is also even. VII.Def.7 IX.24 Therefore, if an odd number is subtracted from an odd number, then the remainder is even. Q.E.D.
This proposition is used in IX.29.

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 Select from Book IX Book IX intro IX.1 IX.2 IX.3 IX.4 IX.5 IX.6 IX.7 IX.8 IX.9 IX.10 IX.11 IX.12 IX.13 IX.14 IX.15 IX.16 IX.17 IX.18 IX.19 IX.20 IX.21 IX.22 IX.23 IX.24 IX.25 IX.26 IX.27 IX.27 IX.28 IX.29 IX.30 IX.31 IX.32 IX.33 IX.34 IX.35 IX.36 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