Quotations about   proof

Those long chains composed of very simple and easy reasonings, which geometers customarily use to arrive at their most difficult demonstrations, had given me occasion to suppose that all the things which come within the scope of human knowledge are interconnected in the same way. And I thought that, provided we refrain froma ccepting anything as true which is not, and always keep to the order required for deducing one thing from another, there can be nothing too remote to be reached in the end or too well hidden to be discovered.

[Ces longues chaînes de raisons, toutes simples et faciles, dont les géomètres ont coutume de se servir pour parvenir à leurs plus difficiles démonstrations, m’avoient donné occasion de m’imaginer que toutes les choses qui peuvent tomber sous la connoissance des hommes s’entresuivent en même façon, et que, pourvu seulement qu’on s’abstienne d’en recevoir aucune pour vraie qui ne le soit, et qu’on garde toujours l’ordre qu’il faut pour les déduire les unes des autres, il n’y en peut avoir de si éloignées auxquelles enfin on ne parvienne, ni de si cachées qu’on ne découvre.]

René Descartes (1596-1650) French philosopher, mathematician
Discourse on Method [Discours de la méthode], Part 2 (1637) [tr. Cottingham, Stoothoff (1985)]
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(Source (French)). Alternate translations:

Those long chains of reasons, (though simple and easie) which the Geometricians commonly use to lead us to their most difficult demonstrations, gave me occasion to imagine, That all things which may fall under the knowledge of Men, follow one the other in the same manner, and so we doe only abstain from receiving any one for true, which is not so, and observe always the right order of deducing them one from the other, there can be none so remote, to which at last we shall not attain; nor so hid, which we shall not discover.
[Newcombe ed. (1649)]

The long chains of simple and easy reasonings by means of which geometers are accustomed to reach the conclusions of their most difficult demonstrations, had led me to imagine that all things, to the knowledge of which man is competent, are mutually connected in the same way, and that there is nothing so far removed from us as to be beyond our reach, or so hidden that we cannot discover it, provided only we abstain from accepting the false for the true, and always preserve in our thoughts the order necessary for the deduction of one truth from another.
[tr. Veitch (1850)]

Those long chains of reasoning, simple and easy as they are of which geometricians make use in order to arrive at the most difficult demonstrations, had caused me to imagine that all those things which fall under the cognizance of man might very likely be mutually related in the same fashion; and that, provided only that we abstain from receiving anything as true which is not so, and always retain the order which is necessary in order to deduce the one conclusion from the other, there can be nothing so remote that we cannot reach to it, nor to recondite that we cannot discover it.
[tr. Haldane & Ross (1911)]

These long chains of perfectly simple and easy reasonings by means of which geometers are accustomed to carry out their most difficult demonstrations had led me to fancy that everything that can fall under human knowledge forms a similar sequence; and that so long as we avoid accepting as true what it not so, and always preserve the right order for deduction of one thing from another, there can be nothing too remote to be reached in the end, or too well hidden to be discovered.
[tr. Ascombe & Geach (1971)]