Why 'middle': between knowledge of vision (free, after the decree) and knowledge of simple intelligence
They call this knowledge 'middle knowledge' because, as they see it, it stands midway between what the schools call the knowledge of vision and the knowledge of simple intelligence.
By the knowledge of vision they mean the knowledge by which God knows things that exist outside himself at some point in time, whether past, present or future. God knows all these from eternity as clearly, certainly and distinctly as if they were actually present to him, just as we know things we see in front of us. That is why it is called the knowledge of vision, by comparison with bodily sight, by which we see things placed before our eyes.
This knowledge is also called free knowledge, because it follows the free decree of God's will to create and preserve things. Without that decree nothing can exist, and so nothing can be seen as present or foreseen as future. Had God decreed to create nothing, knowledge of this kind could not be ascribed to him.
Latin
VIII. Porro hanc scientiam vocant scientiam Mediam, quoniam, juxta ipsos, medium tenet inter scientiam quae dicitur in Scholis scientia Visionis, & illam quae dicitur simplicis intelligentiae. Per scientiam autem visionis intelligunt notitiam illam qua Deus novit ea quae extra ipsum existunt in aliqua temporis differentia, nempe quae sunt praeterita, praesentia, vel futura. Quae omnia Deus ab aeterno tam clare, certo, & distincte cognoscit, ac si actu ipsi praesentia essent, non secus ac illa quae coram intuemur. Unde est quod dicitur scientia Visionis, ad similitudinem, scilicet, Visus corporei, quo res oculis objectas cernimus. Atque haec scientia dicitur quoque scientia libera, quia sequitur liberum decretum divinae voluntatis de rebus creandis atque conservandis, sine quo, ut nihil existere potest, ita quoque nihil potest videri praesens, vel praevideri futurum. Adeoque, si Deus nihil creare decrevisset, ejusmodi scientia Deo tribui non posset.