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...when each single creature keeps, either by nature or by reason, its proper place [in the order of things] --it is said to obey God and to honor him. ... When a rational nature wills what it ought to, it honors God --not because it confers anything on Him but because it willingly submits itself to His will and governance. And, as best it can, it stays in its proper place in the universe and preserves the beauty of the universe.
-Cur Deus Homo, 1:15
So what Saint Anselm is saying, the premise from which order and beauty is deduced is Saint Benedict's intention that the monk [and today, all Christians] seek the glory of God in all things. For Anselm and therefore us, beauty in keeping the proper order of things is obediential in front of God; that is, it is about keeping a fitting sense of friendship with the Trinitarian God. On this feast of Saint Anselm, let us prefer nothing to Christ seeking God's glory above all.
You may be interested in reading Pope Saint Pius X's encyclical for the 800th anniversary of Saint Anselm's birth, Communium rerum (1909).