mathematica_, treats of arithmetic, music, geometry, astronomy, and metaphysics cursorily. Book XVII. likewise thins out in a somewhat slight discussion of Theology, which was to form the topic of the tome that Vincent did not write. But Vincent did complete another tome, the _Speculum historiale_. It is a loosely chronological compilation of tradition, myth, and history, with discursions upon the literary works of the characters coming under review. It would be tedious to follow its excerpted presentation of the profane and sacred matter. We may leave Vincent, with the obvious reflection that his work is a conglomerate, both in arrangement and contents. It has the pious aim of contributing to man’s salvation, and yet is an attempted universal encyclopaedia of human knowledge, much of which is plainly secular and mundane. The monstrous scope and dual purpose of the work prevented any unity in method and arrangement. More single in aim, and better arranged in consequence, are the _Sentences_ of Peter Lombard and the _Summa theologiae_ of Aquinas. For although their scope, at least the scope of the _Summa_, is wide, all is ordered with respect to the true aim of _sacra doctrina_, just as Thomas explained in the passage which we have already given. The alleged principle of the Lombard’s division strikes one as curious; yet he got it from Augustine: _Signum_ and _res_--the symbol and the thing: verily an age-long play of spiritual tendency lay back of these contrasted concepts. Christian _doctrina_ related, perhaps chiefly, to the significance of _signa_, signs, symbols, allegories, mysteries, sacraments. It was not so strange that the Lombard made this antithesis the ground of his arrangement. Quite as of course he begins by saying it is clear to any one who considers, with God’s grace, that the “contents of the Old and New Law are occupied either with _res_ or _signa_. For as the eminent doctor Augustine says in his _Doctrina Christiana_, all teaching is of things or signs; but things also are learned through signs. Properly those are called _res_ which are not employed in order to signify something; while _signa_ are those whose use is to signify.” Then the Lombard separates the sacraments from other _signa_, because they not only signify, but also confer saving aid; and he points out that evidently a _signum_ is also some sort of a thing; but not everything is a _signum_. He will treat first of _res_ and then of _signa_. As to _res_, one must bear in mind, as Augustine says, that some things are to be enjoyed (_fruendum_), as from love we cleave to them for their own sake; and others are to be used (_utendum_) as a means; and still others to be both enjoyed and used.