Catechism of S. Pius X
The purposes of the Eucharistic Sacrifice are mainly four: adoration of God, thanksgiving, atonement and impetration (Council of Trent: Dz 940. 950/1743, 1753, Mediator Dei 90-93).
Catechism of Saint Pius X
How do we fulfill the First Commandment?
We fulfill the First Commandment by the practice of internal and external worship.
What is internal worship?
Internal worship is the honor which is given to God with the faculties of the soul alone, that is with the intellect and the will.
What is external worship?
External worship is the homage that is given to God by means of outward acts and of sensible objects.
Is it not enough internally to adore God with the heart alone?
No, it is not enough internally to adore God with the heart alone; we must also adore Him externally with both soul and body, because He is the Creator and absolute Lord of both.
Can there be external worship without internal worship?
No, in no way can there be external worship without internal, because unless external worship is accompanied by internal, it is destitute of life, of merit, and of efficacy, like a body without a soul.