Sixthly, that no name can be defined by any one word; because no one word is sufficient for the resolving of one or more words. Seventhly, that a defined name ought not to be repeated in the definition. For a defined name is the whole compound, and a definition is the resolution of that compound into parts; but no total can be part of itself. [Sidenote: Nature of a demonstration.] 16. Any two definitions, that may be compounded into a syllogism, produce a conclusion; which, because it is derived from principles, that is, from definitions, is said to be demonstrated; and the derivation or composition itself is called a demonstration. In like manner, if a syllogism be made of two propositions, whereof one is a definition, the other a demonstrated conclusion, or neither of them is a definition, but both formerly demonstrated, that syllogism is also called a demonstration, and so successively. The definition therefore of a demonstration is this, _a demonstration is a syllogism, or series of syllogisms, derived and continued, from the definitions of names, to the last conclusion_. And from hence it may be understood, that all true ratiocination, which taketh its beginning from true principles, produceth science, and is true demonstration. For as for the original of the name, although that, which the Greeks called ἀποδέιξις, and the Latins _demonstratio_, was understood by them for that sort only of ratiocination, in which, by the describing of certain lines and figures, they placed the thing they were to prove, as it were before men's eyes, which is properly ἀποδεικνύειν, or to _shew_ by the figure; yet they seem to have done it for this reason, that unless it were in geometry, (in which only there is place for such figures) there was no ratiocination certain, and ending in science, their doctrines concerning all other things being nothing but controversy and clamour; which, nevertheless, happened, not because the truth to which they pretended could not be made evident without figures, but because they wanted true principles, from which they might derive their ratiocination; and, therefore, there is no reason but that if true definitions were premised in all sorts of doctrines, the demonstrations also would be true. [Sidenote: Properties of a demonstration, and order of things to be demonstrated.] 17. It. is proper to methodical demonstration, First, that there be a true succession of one reason to another, according to the rules of syllogizing delivered above. Secondly, that the premises of all syllogisms be demonstrated from the first definitions.