.50ó MAGIC: OR, THE Rieur VSE OF REASON. 1. When they prove one proposition only by sheaving what absurdities will follow if the contradictory proposition be supposed or admitted. This is called reductio od absurdum'v, or demon stratio impossible. As for instance, when they prove all the radii of a circle to be equal, by supposing one radius to be longer or shorter than another, and then shewing what absurd consequences will follow. This, I confess, forces the assent, but it does not enlighten the mind, by shewing the true reason and cause why all radii are equal; which is derived from the very construction of a circle * for since a circle is formed by fixing one end of a straight line in the'centre, and moving the other end round, (or, which is all one, by-compasses kept open to a certain extent) it follows evidently that every part of the circumference being thus described, must be equally distant from the centre, and therefore the radii, which are lines from the centre to the circumference must be all equal. 2. Geometricians forget this rule, when they heap up many far - fetched lines, figures and propositions, to prove some plain, simple, and obvious propositions. This is called a demonstration vier aliena 85. remoto, or an argument from unnatural and remote mediums ; as if, in order to prove the radii of a circle are all equal, I should make several triangles, and squares about the circle, and then from some properties and propositions of squares and triangles prove that the radii of a circle are equal. Yet it must be confessed, that sometimes such questions hap- pen, that it is hardly possible to prove them by direct arguments drawn from the nature of things, &c. and then it may not only be lawful but necessary to use indirect proofs, and arguments drawn from remote mediums, or from the absurdity of the Contradictory suppositions. Such indirect and remote arguments may also be sometimes used to confirm a proposition, which has been before proved by arguments more direct and immediate. VIII. Though arguments should give light to the subject, as well as constrain the assent, yet you must learn to " distinguish well between an explication and an argument, and neither im- pose upon yourselves, nor suffer yourselves to be imposed upon by others, by mistaking a Mere illustration for a convincing reason. Axioms themselves, or self - evident propositions, may want an explication or illustration, though they are not to be proved by reasoning. Note, This rule chiefly refers to the estalslishment of some truth, rather than to the refutation of error. It is a very common and useful way of arguing, £s refute a false proposition, by shewing what evident falsehood or absurdity ell follow from it ; for what proposition soccer is really absurd and false, dose ffecenally prove that principle to be false from which it is derived, no that this wey of rat/tins an. error is not so usually salted reductio ad absúrdum.
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