Distinctions of necessity: absolute and hypothetical; of coaction and of infallibility
To reconcile the necessity that God's decree places on every event with the contingency and freedom of those events, they first distinguish absolute necessity from necessity on a hypothesis. Absolute necessity is that by which something simply cannot be otherwise. Necessity on a hypothesis is that by which something that in itself and simply can fail to be, or be otherwise, cannot be otherwise once a certain condition is given.
Next they divide necessity into the necessity of coercion and the necessity of mere infallibility. The necessity of coercion is that by which a cause acting from outside applies force to things and drives them by compulsion to do this or that.
The necessity of infallibility is that by which a thing is certainly and unchangeably going to happen, yet such that, if we look at the thing's cause in itself, it could fail to happen or happen otherwise. This is the necessity meant in the axiom, 'Everything that is, while it is, is necessarily.'
Latin
XXXI. Ut vero necessitatem illam, quam Dei decretum quibuslibet eventibus imponit, cum eorum contingentia & libertate concilient, distinguunt primo inter necessitatem absolutam & necessitatem quae est ex hypothesi. Necessitas absoluta est qua simpliciter aliquid aliter esse non potest. Necessitas autem ex hypothesi est, qua quod in se & simpliciter potest non esse, vel aliter esse, posita tamen certa conditione, aliter se habere non potest. Deinde necessitas ab ipsis distinguitur in eam quae est coactionis, & eam quae est tantum infallibilitatis. Necessitas coactionis est, quae per causam extra agentem vim rebus infert, & coacte impellit ut hoc vel illud faciant. Necessitas vero infallibilitatis est, qua res quoad eventum certo & immutabiliter futura est: ita tamen ut si causam rei per se spectemus, possit vel non evenire, vel aliter evenire. Qua de necessitate intelligendum est illud axioma, Omne quod est, dum est, necessario est.