Scripture doesn't use Trinity, nor do I think it uses the term Incarnation either. So what is the point.
I'm not sure the infatuation you guys have with Aristotle. But the official documents of the Church doesn't use Aristotelian science in its definitions. The official definition of Transubstantiation is after the consecration, the bread and wine become the Body and Blood of Christ, substantially. But we still only see, taste and touch what looks like bread and wine.
Session 13 of the Council of Trent provides the dogmatic understanding:
CHAPTER IV.
On Transubstantiation.
And because that Christ, our Redeemer, declared that which He offered under the species of bread to be truly His own body, therefore has it ever been a firm belief in the Church of God, and this holy Synod doth now declare it anew, that, by the consecration of the bread and of the wine, a conversion is made of the whole substance of the bread into the substance of the body of Christ our Lord, and of the whole substance of the wine into the substance of His blood; which conversion is, by the holy Catholic Church, suitably and properly called Transubstantiation.
Aristotelian terms of substance and accidents (I prefer physical properties) are helpful in clarifying the definition in a sense, but it is not necessary.
So using Aristotelian terms at consecration the bread and wine's substance (what it is) becomes the Body and Blood of Christ, but its physical properties (accidents or what we physically experience) remains those of bread and wine. I don't have an issue with the Scholastic's definition, and not sure what all the hoopla is concerning its use, but whatever.