III–V: necessity of end, of agent, and of idea
III. Necessity of the end is twofold: either simply, or unto the better. So unto salvation, according to the preaching of the Gospel, faith is necessary simply; but knowledge of the holy languages and reading of the sacred letters are unto the better — because without faith no one is saved; without these one is saved, though not so well.
IV. Necessity from the agent is likewise twofold: violent and natural. Violent, as when that rich man of the Gospel is dragged into Gehenna against the inclination of his will. Natural, when the rich man's spirit is moved by musical sound, because spirit is by nature movable and is invited by sound to its proper operation. And necessity is partly violent and partly natural when dry wood is kindled — inasmuch as dry it is disposed by heat to receive more heat, but inasmuch as burning wood is against its nature
V. Necessity from idea is that by which, according to the idea of God or of humankind, things so hold themselves that they cannot hold otherwise. Hence two and three make five, and number progresses to ten among us, yet not among all nations — for among some Africans it does not pass six. Hence also letters and syllables are so formed among this or that people and not otherwise. And this necessity concurs somehow with the formal; but because it can hold itself otherwise at the artisan's pleasure — whence other nations have other letters and other words — therefore it is not intrinsic necessity as the formal is.
Latin
III. Necessitas finis est duplex, vel simpliciter vel ad melius. Sic ad salutem, iuxta concionem Evangelii, fides necessaria est simpliciter: notitia vero linguarum sanctarum et lectio sacrarum litterarum propter melius, quia sine illa nemo servatur; sine his servatur, etsi non ita bene. IV. Necessitas ab agente itidem duplex est, violenta et naturalis. Violenta, ut cum epulo ille evangelicus rapitur in gehennam contra voluntatis suae inclinationem. Naturalis, cum spiritus epulonis a sono musico movetur, quia natura mobilis est spiritus et a sono invitatur ad propriam operationem. Ex parte vero violenta et ex parte naturalis est necessitas cum lignum aridum ignitur, quia quatenus aridum est a calore dispositum ad plus caloris recipiendum, quatenus vero lignum est, contra naturam eius est comburi. V. Necessitas ex idea est, qua secundum ideam Dei aut hominis res ita se habent ut aliter habere nequeant. Hinc enim est quod duo et tria faciunt quinque, et numerus usque ad denarium progreditur apud nos, non autem apud omnes nationes. Nam non transit senarium apud quosdam Afros. Hinc etiam litterae et syllabae apud hanc aut illam gentem ita formantur et non aliter. Et haec necessitas concurrit quodammodo cum formali: sed quia potest se aliter habere ad placitum artificis, unde aliae nationes alias litteras et alia vocabula habent, idcirco non est necessitas intrinseca ut formalis.