Faults of a demonstration.

18. Besides those paralogisms, whose fault lies either in the falsity of the premises, or the want of true composition, of which I have spoken in the precedent chapter, there are two more, which are frequent in demonstration; one whereof is commonly called petitio principii; the other is the supposing of a false cause; and these do not only deceive unskilful learners, but sometimes masters themselves, by making them take that for well demonstrated, which is not demonstrated at all. Petitio principii is, when the conclusion to be proved is disguised in other words, and put for the definition or principle from whence it is to be demonstrated; and thus, by putting for the cause of the thing sought, either the thing itself or some effect of it, they make a circle in their demonstration. As for example, he that would demonstrate that the earth stands still in the centre of the world, and should suppose the earth's gravity to be the cause thereof, and define gravity to be a quality by which every heavy body tends towards the centre of the world, would lose his labour; for the question is, what is the cause of that quality in the earth? and, therefore, he that supposes gravity to be the cause, puts the thing itself for its own cause.

Of a false cause I find this example in a certain treatise where the thing to be demonstrated is the motion of the earth. He begins, therefore, with this, that seeing the earth and the sun are not always in the same situation, it must needs be that one of them be locally moved, which is true; next, he affirms that the vapours, which the sun raises from the earth and sea, are, by reason of this motion, necessarily moved, which also is true; from whence he infers the winds are made, and this may pass for granted; and by these winds he says, the waters of the sea are moved, and by their motion the bottom of the sea, as if it were beaten forwards, moves round; and let this also be granted; wherefore, he concludes, the earth is moved; which is, nevertheless, a paralogism. For, if that wind were the cause why the earth was, from the beginning, moved round, and the motion either of the sun or the earth were the cause of that wind, then the motion of the sun or the earth was before the wind itself; and if the earth were moved, before the wind was made, then the wind could not be the cause of the earth's revolution; but, if the sun were moved, and the earth stand still, then it is manifest the earth might remain unmoved, notwithstanding that wind; and therefore that motion was not made by the cause which he allegeth. But paralogisms of this kind are very frequent among the writers of physics, though none can be more elaborate than this in the example given.

Why the analytical method of geometricians cannot be treated of in this place.

19. It may to some men seem pertinent to treat in this place of that art of the geometricians, which they call logistica, that is, the art, by which, from supposing the thing in question to be true, they proceed by ratiocination, till either they come to something known, by which they may demonstrate the truth of the thing sought for; or to something which is impossible, from whence they collect that to be false, which they supposed true. But this art cannot be explicated here, for this reason, that the method of it can neither be practised, nor understood, unless by such as are well versed in geometry; and among geometricians themselves, they, that have most theorems in readiness, are the most ready in the use of this logistica; so that, indeed, it is not a distinct thing from geometry itself; for there are, in the method of it, three parts; the first whereof consists in the finding out of equality betwixt known and unknown things, which they call equation; and this equation cannot be found out, but by such as know perfectly the nature, properties, and transpositions of proportion, as also the addition, subtraction, multiplication, and division of lines and superficies, and the extraction of roots; which are the parts of no mean geometrician. The second is, when an equation is found, to be able to judge whether the truth or falsity of the question may be deduced from it, or no; which yet requires greater knowledge. And the third is, when such an equation is found, as is fit for the solution of the question, to know how to resolve the same in such manner, that the truth or falsity may thereby manifestly appear; which, in hard questions, cannot be done without the knowledge of the nature of crooked-lined figures; but he that understands readily the nature and properties of these, is a complete geometrician. It happens besides, that for the finding out of equations, there is no certain method, but he is best able to do it, that has the best natural wit.

PART II.
THE
FIRST GROUNDS OF PHILOSOPHY.

CHAPTER VII.
OF PLACE AND TIME.

[1.] Things that have no existence, may nevertheless be understood and computed.—[2.] What is Space.—[3.] Time.—[4.] Part.—[5.] Division.—[6.] One.—[7.] Number.—[8.] Composition.—[9.] The whole.—[10.] Spaces and times contiguous, and continual.—[11.] Beginning, end, way, finite, infinite.—[12.] What is infinite in power. Nothing infinite can be truly said to be either whole, or one; nor infinite spaces or times, many.—[13.] Division proceeds not to the least.

Things that have no existence, may nevertheless be understood and computed.