"No other person can judge better of either [the merits of a writer and the merits of his works] than himself; for none have had access to a closer or more deliberate examination of them. It is for this reason, that in proportion that the value of a work is intrinsic, and independent of opinion, the less eagerness will the author feel to conciliate the suffrages of the public. Hence that inward satisfaction, so pure and so complete, which the study of geometry yields. The progress which an individual makes in this science, the degree of eminence which he attains in it, all this may be measured with the same rigorous accuracy as the methods about which his thoughts are employed. It is only when we entertain some doubts about the justness of our own standard, that we become anxious to relieve ourselves from our uncertainty, by comparing it with the standard of another. Now, in all matters which fall under the cognizance of taste, this standard is necessarily somewhat variable; depending on a sort of gross estimate, always a little arbitrary, either in whole or in part; and liable to continual alteration in its dimensions, from negligence, temper, or caprice. In consequence of these circumstances I have no doubt, that if men lived separate from each other, and could in such a situation occupy themselves about anything but self-preservation, they would prefer the study of the exact sciences to the cultivation of the agreeable arts. It is chiefly on account of others, that a man aims at excellence in the latter, it is on his own account that he devotes himself to the former. In a desert island, accordingly, I should think that a poet could scarcely be vain; whereas a geometrician might still enjoy the pride of discovery." (Jean le Rond D’Alembert, "Essai sur les Gens Lettres", 1764)
"One must admit that it is not a simple matter to accurately outline the idea of negative numbers, and that some capable people have added to the confusion by their inexact pronouncements. To say that the negative numbers are below nothing is to assert an unimaginable thing.” (Jean le Rond d'Alembert, "Negatif”, Encyclopédie [1751 – 1772])
"[…] the algebraic rules of operation with negative numbers are generally admitted by everyone and acknowledged as exact, whatever idea we may have about this quantities. " (Jean le Rond d'Alembert, Encyclopédie, [1751 – 1772])
"Thus, metaphysics and mathematics are, among all the sciences that belong to reason, those in which imagination has the greatest role.” (Jean le Rond d'Alembert, Encyclopédie, [1751 – 1772])
"Geometrical truths are in a way asymptotes to physical truths, that is to say, the latter approach the former indefinitely near without ever reaching them exactly.” (Jean le Rond d’Alembert)
"The imagination in a mathematician who creates makes no less difference than in a poet who invents […]." (Jean le Rond d'Alembert, Encyclopedie, [1751 – 1772])
"To someone who could grasp the universe from one unified viewpoint, the entire creation would appear as a unique fact and a great truth.” (Jean le Rond d'Alembert)
"We shall content ourselves with the remark that if mathematics (as is asserted with sufficient reason) only make straight the minds which are without bias, so they only dry up and chill the minds already prepared for this operation by nature.” (Jean le Rond d'Alembert)
"One must admit that it is not a simple matter to accurately outline the idea of negative numbers, and that some capable people have added to the confusion by their inexact pronouncements. To say that the negative numbers are below nothing is to assert an unimaginable thing.” (Jean le Rond d'Alembert, "Negatif”, Encyclopédie [1751 – 1772])
"[…] the algebraic rules of operation with negative numbers are generally admitted by everyone and acknowledged as exact, whatever idea we may have about this quantities. " (Jean le Rond d'Alembert, Encyclopédie, [1751 – 1772])
"Thus, metaphysics and mathematics are, among all the sciences that belong to reason, those in which imagination has the greatest role.” (Jean le Rond d'Alembert, Encyclopédie, [1751 – 1772])
"Geometrical truths are in a way asymptotes to physical truths, that is to say, the latter approach the former indefinitely near without ever reaching them exactly.” (Jean le Rond d’Alembert)
"The imagination in a mathematician who creates makes no less difference than in a poet who invents […]." (Jean le Rond d'Alembert, Encyclopedie, [1751 – 1772])
"To someone who could grasp the universe from one unified viewpoint, the entire creation would appear as a unique fact and a great truth.” (Jean le Rond d'Alembert)
"We shall content ourselves with the remark that if mathematics (as is asserted with sufficient reason) only make straight the minds which are without bias, so they only dry up and chill the minds already prepared for this operation by nature.” (Jean le Rond d'Alembert)
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