12. To the second formula belong four modes.... 16. To the third formula belong six modes. 22. Let him who desires to understand fully these formulas of the categorical syllogisms read the book entitled _Apuleii Perihermeniae_, and he will learn matters that are treated with subtlety.[234] And by their clearness and well-weighed character they will introduce the reader advantageously with God’s help to great paths of understanding. Now let us come to the hypothetical syllogisms in order. 23–25. The modes of the hypothetical syllogisms that have a conclusion are seven.... If anyone desires to know more fully the modes of the hypothetical syllogisms let him read Marius Victorinus’ book entitled _De Syllogismis Hypotheticis_.[234] [234] A recommendation copied word for word from Cassiodorus. 26. Next let us approach the topic of dialectical definitions, which have such surpassing worth that they may rightly be called the clear manifestations of speech, and in a sense the guides to expression. Chapter 29. On the division of definitions, abbreviated from the book of Marius Victorinus. 1. The definition of the philosophers is that which in describing things sets forth what the thing in itself is—not, of what sort it is—and how it ought to be made up of its parts. For it is a brief statement separating the nature of each thing from its class, and marking it off by its peculiar meaning. Definitions are divided into fifteen sorts. The first kind of definition is the substantial (οὐσιώδης), which is named definition in the proper and true sense, as, for example, _Est homo animal rationale, mortale, risus disciplinaeque capax_. This definition descends through species and differences and comes to the property, and expresses most fully what man is. 16. Now let us come to the _topica_, which are the seats of arguments, the fountains of ideas, and the sources of speech. Chapter 30. On the topics. 1. _Topica_ is the science of finding arguments. The division of the _topica_ or the _loci_ from which arguments are derived is three-fold. For some inhere in the very thing that is under discussion; there are others, called _affecta_ (closely connected), which are known to be derived in a certain sense from other things; others, which are taken from outside [the subject].... 18. It is clearly a wonderful thing that whatever the nimbleness and variety of the human mind could discover, searching for ideas in different cases, could have been gathered into unity; that free and spontaneous intelligence is limited. For wherever it turns, whatever thoughts it enters on, the mind must fall upon some of those that have been described. BOOK III ON THE FOUR MATHEMATICAL SCIENCES ON ARITHMETIC INTRODUCTION