27. The definitions of number, arithmetic, and algebra in this paragraph and the succeeding one are derived from Newton (Arithmetica universalis). The meanings of the difficult passages in these two paragraphs are clarified in d’Alembert’s article “Arithmetic,” Encyclopédie, I, 675. D’Alembert uses Newton’s definition of number as being nothing more than a relationship (rapport), and the meaning of several phrases here becomes clearer if the word “number” is substituted for “relationship.” Thus, in the next to the last sentence in this paragraph, for example, two is the unique relationship (number) which results from the comparison of the relationships six and four in the following calculation: 6 − 4 = 2.

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