Cap. 1 vocabulary: Reprobatio — opposite act; Bannes; negative vs positive
Drop the bare word; come to the thing. As to elect and to predestinate name that eternal act of the Divine will by which God decreed to direct certain persons to blessedness they will infallibly reach, so to reprobate names the opposite act: the decree to permit certain persons to fail and fall short of that end. That fits providence itself — which allows some defect in the things under its care. See Aquinas, ST I q.23 a.6. In reprobation we mark two quasi-acts of the Divine will. The first is unwillingness to elect someone to blessedness obtained without fail. Why that act lands on Judas rather than Peter has no reason on the reprobate's side; it is referred to the liberty of the Divine will. So Báñez: in the particular case, why God chose these and reprobated those has no adequate cause but the Divine will. In the same article he says this predestination of some and reprobation of others manifests the greatest liberty the Divine will has in dispensing supernatural goods — and that liberty is a great Divine perfection. The act we call passing-by or non-election, Bellarmine calls the negative act of reprobation. Guard this point: do not follow Scotus in treating God's will toward the reprobate — whom he does not choose but passes by — as merely negative. In the act we name by a negation there is an expressed, affirmative will of God; it does not mean God simply suspends willing about their falling short of blessedness. Read that act affirmatively, not only negatively. Passing-by / non-election involves affirmative decrees: I will to permit Judas to fall short of eternal life; I will and decree not to give Judas that special grace which, if he received it, would bring him to eternal life. So much for the first act. The second is to destine to punishment. That act terminates on the reprobate as foreknown and foreseen stained by sin — and that from the fault of his own will. Scotus calls this privative reprobation; Bellarmine, the positive act of reprobation. It designates the will to damn the reprobate person. Note also: God shows the reprobate certain effects that do not flow from their reprobation — that they are created, called to know the Gospel, illuminated with supernatural knowledge. Those are effects of common love and common providence, not of reprobation.
Latin
Sed misso vocabulo, veniamus ad rem. Sicuti igitur eligere & praedestinare denotat illum aeternum actum Divinae voluntatis, quo decrevit quasdam personas dirigere ad beatitudinem infallibiliter consequendam; sic reprobare denotat oppositum actum Divinae voluntatis, quo decrevit permittere quasdam personas ab hoc fine beatitudinis deficere & excidere. Atque hoc vel maxime convenit providentiae Divinae, ut permittat aliquem defectum in rebus quae providentiae ejus subduntur. Videte Aquinatem, part. 1. qu. 23. art. 6. In hac reprobatione duos quasi actus Divinae voluntatis consideramus. Prior est, nolle eligere ad beatitudinem infallibiliter consequendam. Atque cur hic actus potius ad Judam quam ad Petrum terminetur, nulla datur ratio ex parte reprobati, sed referendum est ad libertatem Divinae voluntatis. Sic Bannes: In singulari, quare Deus hos elegerit, illos reprobaverit, non habet causam adaequatam, nisi Divinam voluntatem. Et eodem in articulo dicit, hanc praedestinationem aliquorum, & reprobationem aliorum esse manifestationem maximae libertatis, quam habet Divina voluntas circa dispensationem bonorum supernaturalium: quae libertas est magna perfectio Divina. Hunc actum, quem nos appellamus praeteritionem sive non-electionem, Bellarminus vocat actum negativum reprobationis. Sed illud hic cavendum est, ne cum Scoto putemus Dei voluntatem respectu reproborum, quos non eligit, sed praeterit, habere se mere negative. Nam in hoc actu, quem per negationem significamus, continetur expressa & affirmata voluntas Dei, non innuitur negata aut suspensa actio volendi circa reproborum deficientiam a beatitudine. Affirmative ergo explicari debet & intelligi hic actus Divinae voluntatis, & non solum negative. Nam praeteritio sive non-electio involvit hosce actus affirmativos: volo permittere Judam deficere a vita aeterna: volo & decerno Judae non dare eam gratiam specialem, quam si reciperet, perveniret ad vitam aeternam. Haec de priori actu reprobationis. Posterior est, destinare ad poenam. Atque hic actus terminatur ad reprobatum, sicuti praecognitus & praevisus est peccato contaminatus, idque ex vitio propriae voluntatis. Hanc Scotus vocat privativam reprobationem; Bellarminus, actum positivum reprobationis. Et designat voluntatem damnandi personam reprobatam. Porro, notandum est, erga ipsos reprobatos exhiberi a Deo quaedam effecta quae non fluunt a reprobatione illorum; ut quod creentur, quod vocentur ad cognitionem Evangelii, quod illustrentur cognitione supernaturali: nam haec, & alia ejusmodi, effecta sunt communis amoris, & communis providentiae Divinae, non reprobationis.