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(23:3) Tradesmen will at once tell us that they know what is required to find the fourth number, for they have not yet forgotten the rule which was given to them arbitrarily without proof by their masters; others construct a universal axiom from their experience with simple numbers, where the fourth number is self-evident, as in the case of 2, 4, 3, 6; here it is evident that if the second number be multiplied by the third, and the product divided by the first, the quotient is 6; when they see that by this process the number is produced which they knew beforehand to be the proportional, they infer that the process always holds good for finding a fourth number proportional.
...[61] (1) While leaving such persons in their error, we will take care to derive from our argument with them a truth serviceable for our purpose, namely, [61a] that the mind, in paying attention to a thing hypothetical or false, so as to meditate upon it and understand it, and derive the proper conclusions in due order therefrom, will readily discover its falsity; and if the thing hypothetical be in its nature true, and the mind pays attention to it, so as to understand it, and deduce the truths which are derivable from it, the mind will proceed with an uninterrupted series of apt conclusions; in the same way as it would at once discover (as we showed just now) the absurdity of a false hypothesis, and of the conclusions drawn from it.
...(64:3) As for the second sort of fiction, which we stated to be the result of simultaneously directing the attention, without the assent of the intellect, to different confused ideas representing different things and actions existing in nature, we have seen that an absolutely simple thing cannot be feigned, but must be understood, and that a complex thing is in the same case if we regard separately the simple parts whereof it is composed; we shall not even be able to hypothesize any untrue action concerning such objects, for we shall be obliged to consider at the same time the causes and manner of such action.
...[80] (1) Thus, if a man proceeded with our investigations in due order, inquiring first into those things which should first be inquired into, never passing over a link in the chain of association, and with knowledge how to define his questions before seeking to answer them, he will never have any ideas save such as are very certain, or, in other words, clear and distinct; for doubt is only a suspension of the spirit concerning some affirmation or negation which it would pronounce upon unhesitatingly if it were not in ignorance of something, without which the knowledge of the matter in hand must needs be imperfect.
...(2) This belongs to an investigation into nature, where all these matters are amply explained, and it is shown that without ideas neither affirmation, nor negation, nor volition are possible. [o] The nature of mental search is explained in my philosophy. [p] To be connected with other things is to be produced by them, or to produce them. [q] In the same way as we have here no doubt of the truth of our knowledge. [r] See below the note on hypotheses, whereof we have a clear understanding; the fiction consists in saying that such hypotheses exist in heavenly bodies. [s] (1) As a thing, when once it is understood, manifests itself, we have need only of an example without further proof.
