at the same moment of time, proceeds to be described; and contrarywise."
"But whereas we need not consider the time here, any farther than it is expounded and measured by an equable local motion; and besides, whereas only quantities of the same kind can be compared together, and also their velocities of increase and decrease; therefore, in what follows I shall have no regard to time formally considered, but I shall suppose some one of the quantities proposed, being of the same kind, to be increased by an equable fluxion, to which the rest may be referred, as it were to time; and, therefore, by way of analogy, it may not improperly receive the name of time." In this statement of Newton there is contained a satisfactory answer to the objection which has been raised against his method, that it introduces into analysis the foreign idea of motion. A quantity thus increasing by uniform fluxion, is what we now call an independent variable.
Newton continues: "Now those quantities which I consider as gradually and indefinitely increasing, I shall hereafter call fluents, or flowing quantities, and shall represent them by the final letters of the alphabet, v, x, y, and z;…and the velocities by which every fluent is increased by its generating motion (which I may call fluxions, or simply velocities, or celerities), I shall represent by the same letters pointed, thus, , , , . That is, for the celerity of the quantity v; I shall put , and so for the celerities of the other quantities x, y, and z, I shall put , , and , respectively." It must here be observed that Newton does not take the fluxions themselves infinitely small. The "moments of fluxions," a term introduced further on, are infinitely small quantities. These "moments," as defined and used in the Method of Fluxions, are substantially the differentials of Leibniz. De Morgan points out that no small amount of confusion has arisen from the use of the word fluxion and the
