For it seemed to me that much more truth could be found in the reasonings which a man makes concerning matters that concern him than in those which some scholar makes in his study about speculative matters. For the consequences of the former will soon punish the man if he judges wrongly, whereas the latter have no practical consequences and no importance for the scholar except that perhaps the further they are from common sense the more pride he will take in them, since he will have had to use so much more skill and ingenuity in trying to render them plausible.

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And even though we have read all the arguments of Plato and Aristotle, we shall never become philosophers if we are unable to make a sound judgement on matters which come up for discussion; in this case what we would seem to have learnt would not be science but history.

punto de partida es la duda metódica. La duda cartesiana no es escepticismo, sino un procedimiento dialéctico de investigación, encaminado a desprender y aislar la primera verdad evidente, la primera idea clara y distinta, la primera naturaleza simple.

Los orígenes del método están, según nos cuenta Descartes ( Discurso), en la lógica, el análisis geométrico y el álgebra. Conviene ante todo insistir en que el gravísimo defecto de la lógica de Aristóteles es, para Descartes, su incapacidad de invención.

I could give here several other ways of tracing and conceiving a series of curved lines, each curve more complex than any preceding one, but I think the best way to group together all such curves and them classify them in order, is by recognizing the fact that all points of those curves which we may call "geometric," that is, those which admit of precise and exact measurement, must bear a definite relation to all points of a straight line, and that this relation must be expressed by a single equation. If this equation contains no term of higher degree than the rectangle of two unknown quantities, or the square of one, the curve belongs to the first and simplest class, which contains only the circle, the parabola, the hyperbola, and the ellipse; but when the equation contains one or more terms of the third or fourth degree in one or both of the two unknown quantities (for it requires two unknown quantities to express the relation between two points) the curve belongs to the second class; and if the equation contains a term of the fifth or sixth degree in either or both of the unknown quantities the curve belongs to the third class, and so on indefinitely.

entre plusieurs opinions également reçues, je ne choisissais que les plus modérées, tant à cause que ce sont toujours les plus commodes pour la pratique, et vraisemblablement les meilleures, tous excès ayant coutume d'être mauvais, comme aussi afin de me détourner moins du vrai chemin, en cas que je faillisse, que si, ayant choisi l'un des extrêmes, c'eût été l'autre qu'il fallu suivre. (3e partie, para 2)